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TOPICAL EDITORS

INTERNATIONAL ADVISORY BOARD

OLEG V. ANGELSKY, Chernivtsy University, UkraineYASUHIKO ARAKAWA, The University of Tokyo, JapanIVAN GLESK, University of Strathclyde, UKCHRISTOPHE GORECKI, FEMTO-ST, Besançon, FranceEUGENIUSZ JAGOSZEWSKI (Chairman), Wrocław University of Technology, PolandROMUALD JÓŹWICKI, Warsaw University of Technology, Poland FRANCISZEK KACZMAREK, Adam Mickiewicz University, Poznań, Poland BOLESŁAW KĘDZIA, Poznań University of Medical Sciences, Poland MAŁGORZATA KUJAWIŃSKA, Warsaw University of Technology, Poland NORBERT LINDLEIN, University of Erlangen–Nürnberg, GermanyMIROSLAV MILER, Institute of Photonics and Electronics of the ASCR, v.v.i., Prague, Czech Republic JAN MISIEWICZ, Wrocław University of Technology, PolandWŁODZIMIERZ NAKWASKI, Technical University of Łódź, Poland WOLFGANG OSTEN, Universität Stuttgart, GermanyJAN PEŘINA, Palacký University, Olomouc, Czech Republic BARBARA PIERŚCIONEK, University of Ulster, UKCOLIN SHEPPARD, National University of Singapore CONCITA SIBILIA, Università di Roma “La Sapienza”, ItalyTADEUSZ STACEWICZ, University of Warsaw, Poland TOMASZ WOLIŃSKI, Warsaw University of Technology, Poland JAN WÓJCIK, Maria Curie-Skłodowska University in Lublin, Poland PAVEL ZEMANEK, Institute of Scientific Instruments of the ASCR, v.v.i., Brno, Czech Republic

HONORARY EDITOR IN CHIEF – MIRON GAJEDITOR IN CHIEF – WACŁAW URBAŃCZYK

VICE-EDITOR – AGNIESZKA POPIOŁEK-MASAJADA

KRZYSZTOF ABRAMSKI, Wrocław University of Technology, Poland

Fiber optics and optical communication,spectroscopy, lasers and their applications

TADEUSZ PUSTELNY,Silesian University of Technology, Gliwice, Poland

Integrated optics, acoustooptics, microoptics,optical instrumentation, optical measurements,optical sensing

TOMASZ SZOPLIK,Warsaw University, Poland

Nanooptics, plasmonics, optical imaging, opticalcomputing, optical data storage and processing

HENRYK KASPRZAK,Wrocław University of Technology, Poland

Holography, diffraction and gratings, biooptics,medical optics, optometry, optical imaging,Fourier optics

EWA WEINERT-RĄCZKA,Szczecin University of Technology, Poland

Nonlinear optics, optical waveguides, photoniccrystals

OPTICAAPPLICATA

The quarterly of the Institute of PhysicsWrocław University of Technology, Poland

PL ISSN 0078-5466Index 367729

OPTICAAPPLICATA

Contents

Biomedical optics

Fiber optics

Nonlinear optics

Optical communication

Optical instrumentation

Optical measurements

The influence of displacement compounds on the binding of ochratoxin A to human serum albuminexamined with fluorescence anisotropy methods T. WYBRANOWSKI, B. ZIOMKOWSKA, A. CWYNAR, S. KRUSZEWSKI . . . . . . . . . . . . . . . . . . . . . 357

Fluctuations in settling velocity of red blood cell aggregates A. KEMPCZYŃSKI, M. BOSEK, B. GRZEGORZEWSKI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

A new design of a photonic crystal fiber with a beam shaping effect and flexible management ofdispersion and confinement loss YUCHUN HUANG, PING JIANG, HUAJUN YANG, MINGYIN YU . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

Nonlinear-optical refraction of silver nanoparticle composites R. GAMERNYK, M. PERIV, S. MALYNYCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

Optical solitons in birefringent fibers with parabolic law nonlinearity QIN ZHOU, QIUPING ZHU, ANJAN BISWAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

Optical generation of ultra-wideband signals with a reconfigurable spectral notch-band PENG XIANG, YINFANG CHEN, DALEI CHEN, JIYONG ZHAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

Theoretical analysis of a hollow laser beam transmitting in an off-axis Cassegrain optical antennasystem CONGWEI MI, PING JIANG, HUAJUN YANG, SHASHA KE, BO LI, JIANHUA LIU . . . . . . . . . . . . . . 421

Monitoring and identification of marine oil spills using advanced synthetic aperture radar images Z. MIHOUB, A. HASSINI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

Deflectometry for phase retrieval using a composite fringe TONGCHUAN LIU, CANLIN ZHOU, YEPENG LIU, SHUCHUN SI, ZHENKUN LEI . . . . . . . . . . . . . . . 451

Vol. XLIV (2014) No. 3

356

Optical properties of nanocrystals

Light sources

Luminescence of hydrothermally fabricated PbF2:Er3+ particles and their application in bifacialsilicon solar cells FANG YANG, CHENYANG WU, XIULI HAO, YONGSHENG CHEN, JINGXIAO LU, SHI-E YANG . . . . . 463

Miniaturized ultraviolet sources driven by dielectric barrier discharge and runaway electronpreionized diffuse discharge M. EROFEEV, E. BAKSHT, V. TARASENKO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475

Optica Applicata, Vol. XLIV, No. 3, 2014DOI: 10.5277/oa140301

The influence of displacement compounds on the binding of ochratoxin A to human serum albumin examined with fluorescence anisotropy methods

TOMASZ WYBRANOWSKI1*, BLANKA ZIOMKOWSKA1, ANNA CWYNAR2, STEFAN KRUSZEWSKI1

1Medical Physics Division, Biophysics Department, Collegium Medicum of Nicolaus Copernicus University, Jagiellońska 13, 85-067 Bydgoszcz, Poland

2Laboratory of Cell Biology and Genetics, Collegium Medicum of Nicolaus Copernicus University, Jagiellońska 13, 85-067 Bydgoszcz, Poland

*Corresponding author: [email protected]

The subject of the research is the application of the methods of fluorescence anisotropy measurementsto study the interaction between human serum albumin (HSA) and toxins and selected medicines(ibuprofen, warfarin, flurbiprofen). Optical spectroscopic methods are useful tools for the studyof biologically active compounds. Determining binding intensity of ochratoxin A (OTA) to albu-min may be helpful in explaining the effects of toxic influence of OTA. The main factor influencingthe distribution of OTA is its affinity for plasma proteins. It was shown that ochratoxin bindsstrongly to albumin. By the use of the method of fluorescence anisotropy it was proved thatthe unbound fraction of OTA is higher due to competing interactions with drugs. As a result of sep-arating ochratoxin from protein by competitive compounds, a decrease in the fluorescence anisot-ropy of the HSA-OTA complex was observed. The largest increase in free fraction of OTA is causedby flurbiprofen, then ibuprofen and warfarin. It will accelerate OTA transport to target organs andshortening its half-life period, leading consequently to a decrease in chronic toxic effects.

Keywords: ochratoxin A, binding of drug to albumin, flurbiprofen, ibuprofen, warfarin.

1. Introduction

The biophysical properties of compounds of therapeutic value, determined by fluores-cence spectroscopy methods, help to predict the behaviour of such compounds underphysiological conditions [1, 2]. Fluorescence methods of determining the affinity ofligands for plasma proteins may be in many cases competitive in comparison with pre-

358 T. WYBRANOWSKI et al.

viously used methods. They eliminate the need for dissolution of the tested solutionsamples in mobile phase solvents, what enables the measurement under physiologicalconditions. Their main advantage is non-invasiveness, because the tested systems in-teract only with low intensity UV-VIS radiation. Compared to other methods, theseprovide a more accurate measurement of the protein-ligand affinity constant [3, 4]. Itis relatively easy to analyse even a large group of samples. The most important advan-tage of fluorescence methods is their high sensitivity which enables to test compoundsof low concentration. The disadvantage is the fact that only those compounds, the mol-ecules of which have delocalized electrons, are subject to fluorescence.

Serum albumin is the basic protein of blood plasma. This protein serves a signifi-cant function in pharmacotherapy – it binds drugs and transports them to the tissue [5].Albumin molecule has at least two important sites called Sudlow site I and Sudlowsite II [6]. Drugs and toxins bind usually to one of this site with high affinity. The in-teraction between drugs and serum protein has an effect on biological half-life, metab-olism and excretion of drugs. If the unbound fraction of drug diffuses across the wallof small arterioles, the equilibrium is disturbed and the bound fraction starts to separatefrom albumin. Drugs strongly bound to plasma proteins to a lesser extent penetrate intothe organs. Drugs and toxins compete for a binding position in albumin [7]. If bothligands pretend to take the same position in albumin, there may be an increase in theirfree fractions. Drug–toxin interaction is pharmacologically important, because it cancause more or less toxicity of the toxin.

Ochratoxin A is a toxic chemical substance produced by certain species of mouldsgrowing on some food products, particularly cereals. After penetrating into the circu-lation of blood, OTA is distributed in the whole volume of blood plasma in the courseof several minutes and then it binds reversibly with albumins [8]. Determination ofaffinity of OTA to plasma proteins may be crucial for choosing the method of treatingacute poisonings or dialysis application.

Flurbiprofen is used in the symptomatic treatment in rheumatoid arthritis, arthroses,in other chronic pains, as well as in the symptomatic treatment of respiratory tract in-fections with sore throat. Warfarin is an anticoagulant which belongs to the group ofcoumarins. It is a vitamin K antagonist. Ibuprofen is used as an anti-inflammatory andanalgesic drug in diseases of locomotion system and connective tissue such as: rheu-matoid arthritis, chronic polyarthritis and in other osteoarticular diseases of a degen-erative origin [9].

2. Materials and methods

Flurbiprofen, warfarin, ibuprofen, ochratoxin A (OTA) and human serum albumin (HSA)were received from Sigma-Aldrich. Stock solutions of drugs were prepared in ethanol.For fluorescence anisotropy measurements, concentration of OTA in final samples wasequal to 1 μM. The albumin was diluted in phosphate-buffered saline (PBS) at pH 7.4.A PTI (Photon Technology International, Birmingham, NJ, USA) spectrofluorometer

The influence of displacement compounds... 359

was used for the measurement of steady-state fluorescence anisotropy. Measurementsof fluorescence anisotropy of OTA in HSA solution containing competing drugs wereperformed with the instrument in the “L-format” using excitation at 370 and 420 nmlong-pass filters on the emission channel. Using of long-pass filters on the emissionchannel ensures the separation of fluorescence from scattering light. The single fluo-rescence anisotropy measurements for each albumin concentration were recorded.The temperature of the sample was kept constant (37°C) using the ultrathermostatTW2.03 (ELMI). Coefficients of determination and standard errors of slopes and in-tercepts were calculated with the use of ORIGIN 7.0 software application. Then,the standard error of the binding constant K was estimated.

Fluorescence anisotropy of the mixture of bound and unbound drug molecules isgiven by [10]

(1)

where rF and rB are the anisotropies of the free and bound drugs, respectively,fF and fB are the fractions of fluorescence intensity of the free and bound drugs,respectively. By rearranging Eq. (1) and assuming that the quantum yield of the drugis not changed by binding to HSA, one can obtain

(2)

where FB is the fraction of drug bound to human serum albumin. Equation (2) permitson the basis of measurements of fluorescence anisotropy to calculate the fraction ofbound drug. For determining the binding constant of quercetin to HSA, the followingformula was used [11]:

(3)

where HSAB is the concentration of bound protein, while CF and HSAF are concentra-tions of free drug and free protein, respectively. By substituting HSAF = HSAT – HSABinto Eq. (3), the following formula can be obtained:

(4)

where HSAT is the total concentration of HSA. Because CF = FF CT and CB = FB CT,Eq. (4) can be rearranged yielding the modified Scatchard equation

(5)

r rF fF rB fB+=

FB fBr rF–rB rF–

-----------------------= =

KHSAB

CF HSAF

----------------------------------------=

HSAB

HSAT-----------------------

KCF

1 KCF+----------------------------=

FB

HSAT 1 FB–( )-------------------------------------------

FBCT

HSAT---------------------- K– K+=


where CT is total concentration of ochratoxin. The affinity constant can be calculatedby determining a slope or intercept of a line fitted to the points (FBCT / HSAT ,FB / [HSAT (1 – FB)]). By rearranging Eq. (4) to the quadratic equation, one can obtain

(6)

On the basis of Eq. (6) one can estimate free and bound fractions of drugs in blood.

3. Results and discussionThe measurement of fluorescence anisotropy provides useful information aboutthe behaviour of molecules in the presence of albumin. As a result of combiningthe fluorescent molecules and albumin, the possibility of rotational motion of mole-cules significantly decreases and the value of anisotropy will increase greatly in a func-tion of albumin concentration. After the introduction of a ligand, there are 2 types offluorophores in the albumin solution – bound and free. Fluorescence anisotropy ofbound fluorophores is high (close to 0.3) and of free (not bound) fluorophores – low(close to 0) [10]. Figure 1 shows the changes in fluorescence anisotropy of ochratoxindepending on the concentration of albumin in the presence of ibuprofen at differentconcentrations. To measure the fluorescence anisotropy, ochratoxin at a concentrationof 1 μM and albumin – at 0–3 μM, were used.

For OTA alone, the value of anisotropy increased significantly with the rise in al-bumin concentration. At the albumin concentration of 3 μM, the value of fluorescenceanisotropy is about 0.28. The increase in anisotropy proves the attachment of the toxinto the protein as the albumin concentration increases. As a result of being attached tothe protein, the toxin becomes a less mobile molecule and its anisotropy increases.Adding a competing compound, ibuprofen, to the OTA-HSA complex causes a smalleranisotropy increase in the function of albumin concentration. This increase becomes

KCF2 CF K HSAT KCT– 1+( ) CT–+ 0=

Ibuprofen

0100200300

0.30

0.25

0.20

0.15

0.10

0.05

0.000.5 1.0 1.5 2.0 2.5 3.0

HSA concentration [μM]

Fluo

resc

ence

ani

sotro

py

concentration [μM]

Fig. 1. Fluorescence anisotropy of OTA depending on HSA concentration in presence of ibuprofen.


smaller with the increase in the amount of ibuprofen. At the albumin concentration of3 μM, fluorescence anisotropy values equal 0.24, 0.22, 0.2, respectively, for ibuprofenconcentrations of 100, 200 and 300 μM. It proves that ibuprofen detaches ochratoxinfrom the protein. OTA free molecules move faster, thus the solution anisotropy de-creases. By plotting the values FB / [HSAT (1 – FB)] versus FB CT / HSAT , a straight linewas obtained (see Fig. 2).

Its intersection with the axis of ordinates is, according to Eq. (5), the value ofan affinity constant. Thus determined affinity constant of OTA to albumin equals5271 mM–1. On the basis of the obtained values it can be concluded that ochratoxinpresents very high affinity for albumin. Assuming 640 μM as the average HSA con-centration in the human blood, it can be calculated that about 99.97% of OTA is boundwith HSA. In the view of the fact that the half-life of albumin in plasma is approxi-mately 19 days and over 99% of the toxin binds with albumins, a long-term exposureto the toxin after its consumption is to be expected. OTA is still present even 2 monthsafter the exposure [12]. Moreover, it is released from bindings with proteins mainlyas a result of catabolism. Ones of the main organs involved in this process are the kid-neys. This process strongly exposes kidneys to the toxin, which causes kidney failure.The toxic potential of ochratoxin A has been extensively documented in experimentalstudies which have revealed that a high content of the toxin in fodder resulted innephropathy of pigs and rats [12–14]. The protein-bound part of the toxin is releasedwith a decrease in free fraction of OTA in the body. It can be concluded that as longas OTA is albumin-bound, it does not cause any toxic effects. Only after disconnectiondue to protein catabolism or decreasing the free fraction, it goes into tissue and causesharmful effects.

In HSA-containing solutions to which ibuprofen was added, a significant reductionin the affinity constant of OTA to HSA can be seen. At ibuprofen concentration of 100,

Ibuprofen

0100200300

concentration [μM]

×106

3.5

3.0

2.5

2.0

1.5

1.0

0.50.2 0.3 0.4 0.5 0.6 0.7 0.8

R2 = 0.99

F BH

SA

T(1

– F

B)

FBCTHSAT

R2 = 0.91

R2 = 0.68

R2 = 0.46

Fig. 2. The Scatchard plot obtained according to Eq. (5).


200 and 300 μM, affinity constants of OTA to HSA are, respectively, 1830, 1000 and705 mM–1. It is interesting to note a larger spread of values with the increase in ibu-profen concentration. The adjustment of trendline to all test points, not as good as inthe case of OTA itself, shows the changes in the binding positions in albumin underthe influence of ibuprofen. The coefficient of determination drops with the increase inibuprofen concentration. This may be due to the fact that in the presence of ibuprofensome OTA molecules bind non-specifically to HSA. Some authors claim that displaceddrug rebounds to its low affinity binding site on albumin especially with large concen-tration of competing drug [7].

In the same manner, the affinity of OTA to albumin was determined in the presenceof flurbiprofen and warfarin. The calculated values are presented in Table 1. The larg-est decrease in affinity constant of OTA to HSA is caused by flurbiprofen, andthe smallest – warfarin. This is connected with the fact that flurbiprofen has larger af-finity for albumin. It is notable that despite about seven times lower warfarin affinityto albumin as compared with ibuprofen [2], warfarin displaces ochratoxin only about2–2.5 times weaker.

This is connected with the fact that ochratoxin binds mainly at site I, where alsowarfarin is built in. However, based on the measured values of affinity constants of OTAto HSA in the presence of competing compounds, it can be concluded that they can beused to displace OTA from protein binding. It will result in an increase in the free frac-tion of ochratoxin in blood and cause its faster removal from the body.

Knowing the affinity constant and albumin concentration in the blood, one cansolve Eq. (6), and estimate the percentage of drug bound and not bound with HSA(Fig. 3). For the concentration of ibuprofen equal to 300 μM, about a 7-fold increasein concentration of OTA free fraction will occur. Such a big increase in free fractionconcentration results in serious pharmacological consequences. Since only the freefraction is pharmacologically active, it may be stated that at the concentration of flur-biprofen equal to 300 μM, OTA will induce an 11 times higher toxic effect (Fig. 3).However it will be also much faster expelled from the organism.

It seems that the influence of displacement compounds is important in the case ofkidney diseases. Ochratoxin in a human body probably has a weak mutagenic effect,

T a b l e 1. HSA affinity constants of OTA [mM–1] in presence of different concentrations of flurbipro-fen, ibuprofen and warfarin.

DrugCompeting drug concentration [μM]100 200 300

Ibuprofen 1830 ± 190 1000 ± 130 710 ± 100Flurbiprofen 1160 ± 130 640 ± 100 500 ± 80Warfarin 3220 ± 270 2600 ± 190 1750 ± 170


which is caused by the induction of oxidative damage in the DNA structure [15].The use of displacement compounds may contribute to increased short-term oxidation,but this process can be reduced by using antioxidants [16]. However, these analysesshould be considered along with personal observation of the particular patient. Takinginto account numerous, often very complex interactions in a body, only clinical trialscan answer the question of whether the tested displacement compounds can help toreduce the side effects caused by ochratoxin.

4. ConclusionThe obtained results indicate the usefulness of a fluorescence anisotropy measurementmethod under in vitro conditions in determining the affinity constant of ochratoxin Ato albumin. The compatibility of the our results with literature values can provethe correctness of the methods developed and applied in this work. It can be concludedthat OTA shows a very high affinity for albumin. The data obtained from the mea-surements of fluorescence anisotropy of OTA-HSA complexes in the presence of com-peting compounds show that these compounds largely contribute to the weakening ofOTA binding to albumin. It was shown that adding of drugs to the solution of OTAand HSA reduces the rate of an increase in OTA fluorescence anisotropy in dependenceon HSA concentration. The degree of displacement of drugs depends on bindingthe affinity constant of competitive drugs to albumin and their concentration. How-ever, the decrease in binding constant of OTA to albumin is much lower than expected.Probably OTA being displaced from a high affinity site rebinds to another site.The matter of using the competing compounds examined in this work to reduce toxicityof OTA needs further research. Displacement compounds and their possibly protectiveeffect against the toxic effect of OTA require clinical trials of their application asan antidote. Moreover, the research shows that in pathological states with the patient

IbuprofenFlurbiprofenWarfarin

12

10

8

6

4

2

00 50 100 150 200 250 300

Competing drug concentration [μM]

Incr

ease

in fr

ee fr

actio

n of

OTA

Fig. 3. Increase in free fraction of OTA in dependence on competing drug concentration.


taking several drugs at the same time, parallel to the exposure to the effect of ochra-toxin, a rapid release of the toxin may take place, which may lead to developing strongsymptoms of poisoning.

References

[1] KRUSZEWSKI S., SIUDA R., ZIOMKOWSKA B., CYRANKIEWICZ M., Application of principal componentand factor analysis of fluorescence spectra in camptothecin studies, Optica Applicata 33(2–3), 2003,pp. 369–380.

[2] WYBRANOWSKI T., CYRANKIEWICZ M., ZIOMKOWSKA B., KRUSZEWSKI S., The HSA affinity of warfarinand flurbiprofen determined by fluorescence anisotropy measurements of camptothecin, Biosystems94(3), 2008, pp. 258–262.

[3] DASGUPTA A., Handbook of Drug Monitoring Methods: Therapeutics and Drugs of Abuse, HumanPress INC, Totowa, New Jersey, 2008.

[4] COHEN L.H., Plasma protein-binding methods in drug discovery, [In] Optimization in DrugDiscovery, Methods in Pharmacology and Toxicology, Zhengyin Yan, Caldwell G.W. [Eds.],Humana Press, 2004, pp. 111–122.

[5] SJÖHOLM I., EKMAN B., KOBER A., LJUNGSTEDT-PÅHLMAN I., SEIVING B., SJÖDIN T., Binding of drugsto human serum albumin: XI. The specificity of three binding sites as studied with albuminimmobilized in microparticles, Molecular Pharmacology 16(3), 1979, pp. 767–777.

[6] SUDLOW G., BIRKETT D.J., WADE D.N., The characterization of two specific drug binding sites onhuman serum albumin, Molecular Pharmacology 11(6), 1975, pp. 824–832.

[7] RAHMAN M.M., RAHMAN M.H., RAHMAN N.N., Competitive binding of ibuprofen and naproxen tobovine serum albumin: modified form of drug–drug displacement interaction at the binding site,Pakistan Journal of Pharmaceutical Sciences 18(1), 2005, pp. 43–47.

[8] IL’ICHEV YU.V., PERRY. J.L., SIMON J.D., Interaction of ochratoxin A with human serum albumin.A common binding site of ochratoxin A and warfarin in subdomain IIA, The Journal of PhysicalChemistry B 106(2), 2002, pp. 460–465.

[9] PODLEWSKI J.K., CHWALIBOGOWSKA-PODLEWSKA A., Leki Współczesnej Terapii – Encyklopedia dlaFarmaceuty, Split Trading, 2007, (in Polish).

[10] LAKOWICZ J.R., Principles of Fluorescence Spectroscopy, Kluwer Academic, New York, 1999.[11] MISHRA B., BARIK A., PRIYADARSINI K.I., MOHAN H., Fluorescence spectroscopic studies on binding

of a flavonoid antioxidant quercetin to serum albumins, Journal of Chemical Sciences 117(6), 2005,pp. 641–647.

[12] RUTQVIST L., BJÖRKLUND N.E., HULT K., HÖKBY E., CARLSSON B., Ochratoxin A as the cause ofspontaneous nephropathy in fattening pigs, Applied and Environmental Microbiology 36(6), 1978,pp. 920–925.

[13] KROGH P., Ochratoxin A residues in tissues of slaughter pigs with nephropathy, Nordisk Veterinaer--Medicin 29(9), 1977, pp. 402–405.

[14] ELLING F., MØLLER T., Mycotoxic nephropathy in pigs, Bulletin of the World Health Organization49(4), 1973, pp. 411-418.

[15] PETZINGER E., ZIEGLER K., Ochratoxin A from a toxicological perspective, Journal of VeterinaryPharmacology and Therapeutics 23(2), 2000, pp. 91–98.

[16] WYBRANOWSKI T., ZIOMKOWSKA B., KRUSZEWSKI S., Antioxidant properties of flavonoids and honeysstudied by optical spectroscopy methods, Medical and Biological Sciences 27(4), 2013, pp. 53–58.

Received April 16, 2014in revised form June 9, 2014


Fluctuations in settling velocity of red blood cell aggregates

ADAM KEMPCZYŃSKI, MACIEJ BOSEK, BRONISŁAW GRZEGORZEWSKI*

Biophysics Department, Collegium Medicum in Bydgoszcz, Nicolaus Copernicus University, ul. Jagiellońska 13, 85-067 Bydgoszcz, Poland


Sedimentation of red blood cell aggregates was experimentally investigated by optical imaging.Suspensions of red blood cell at low hematocrit were obtained from blood of healthy donors.The velocity of three-dimensional red blood cell aggregates was measured using particle image ve-locimetry. The magnitude and spatial correlation functions of the velocity fluctuations of the set-tling aggregates were determined. It is shown that the fluctuations in the settling velocity exhibitcharacteristic correlations in the form of swirls. The formation of 3-D red blood cell aggregatesleads to a large initial swirl. The growth of the aggregates and their sedimentation diminishesthe swirls size.

Keywords: particle image velocimetry, red blood cell aggregation, sedimentation, velocity fluctuations.

1. Introduction

Sedimentation of a suspension of particles is an important issue in many areas of science,technology and medicine. Ever since the pioneering work of BATCHELOR [1] in the early1970s, many efforts were made to understand the sedimentation of non-Brownianmonodisperse spherical particles. The mean settling velocity gives some insight intohow sedimentation takes place, while fluctuations of velocity, caused by long-rangehydrodynamic interactions, considerably provide more information about the process.Theoretical considerations predict a divergence of the magnitude of the fluctuationswith system size [2] while most experiments do not confirm this divergence [3, 4].The velocity fluctuations reveal long-range correlations, in the form of swirls, and scal-ing of the swirl size has been found [4]. The numerical simulations of sedimentationof non-isotropic and deformable particles exhibit similarities to the sedimentation pro-cess of spherical particles, however, they are much more non-stationary [5]. Moreoverthe description of the processes observed for sedimenting spherical particles for highervolume fraction rather cannot be simple extrapolation of that for lower volumefraction [6, 7]. Although recent numerous studies have brought a wealth of information

366 A. KEMPCZYŃSKI et al.

on the settling dynamics of particles, the authors agree that an understanding ofthe sedimentation process is far from complete.

An investigation of the red blood cell (RBC) sedimentation process is significantfrom a medical point of view. RBCs are flexible, biconcave discs that tend to formaggregates in the presence of proteins or polymers [8]. Suspended RBCs form linear orbranched aggregates called rouleaux, which later coalesce into three-dimensional (3-D)RBC aggregates [9]. These large aggregates sediment and form a deposit at the bottomof a container [9, 10]. RBC sedimentation has been studied theoretically since the turnof the 1980s [11] but the proposed models were insufficient in explaining the process.In investigations of RBC aggregation and sedimentation, difficulties still arise in iden-tifying how the objects form and sediment [12, 13]. The formation of rouleaux has beenstudied both experimentally [14–17] and theoretically [18]. To investigate the size ofthe particles, the light scattering study of RBC suspensions has been performed [19–21].Recently, new theoretical techniques are developed for the analysis of optical fieldsscattered by particles with possible application in biomedicine [22–24]. Formation andsedimentation of 3-D RBC aggregates are much less recognized. However, the velocityof 3-D aggregates was frequently studied with the use of the image analysis, whereFourier method [25], Hough method [25, 26] as well as particle image velocimetry [27]were applied. The differences between the suspension of monodisperse rigid spheresand blood suggest that the sedimentation process in these systems may be significantlydifferent. Thus, 3-D RBC aggregate dynamics remains one of the most important prob-lems to be resolved in order to provide more insight into RBC sedimentation.

In this paper, the sedimentation of 3-D RBC aggregates was investigated. The ve-locity of the settling 3-D RBC aggregates was measured using particle image veloci-metry. The aim of the paper is to describe the long-range correlations in the fluctuationsof the aggregates velocity.

2. Material and method

The blood of healthy donors was examined in this study. The RBCs were extracted fromthe blood, washed in phosphate saline buffer and resuspended in autologous plasmaat hematocrit 0.03, 0.05 and 0.07. A rectangular glass-walled container 30 mm wide,1 mm deep and 30 mm high was used to perform the sedimentation experiment.The container was filled by injection of RBCs suspended in plasma. Measurementswere performed at room temperature 22±1°C. A sequence of images of the suspensionwas obtained using an optical system shown in Fig. 1. The light from an illuminationsystem passed through the container with the blood sample and next was registered byan imaging system. The imaging system with a CCD camera (1280×960 pixels) wasfocused on a plane near the wall of the container. It sampled a cross-section of the con-tainer sized 9×12 mm2, located 8 mm above the bottom of the container. Images weretaken every second. This period is approximately equal to the minimal ratio of the ra-dius of the observed objects, estimated using the correlation function of the intensityin the image plane to their sedimentation velocity.

Fluctuations in settling velocity of red blood cell aggregates 367

The Reynolds number Re = 2aVsedρ /η and the Péclet number Pe = πa2Vsedη /kTof the sedimenting particles were estimated, where sedimentation velocity Vsed and ag-gregate radius a are taken from the experiment, ρ = 1030 kg/m3 is the density ofthe plasma, η = 1.6×10–3 Pa·s is the viscosity of the plasma, T is the temperature andk is the Boltzmann constant. These numbers for RBC aggregates change in time duringthe process. The Reynolds number was very low, Re < 4.1×10–3. The Péclet numberafter the initial 300 s was attaining very high values, Pe > 1.2×104. Thus, the motionof the RBC aggregates was practically unaffected by thermal fluctuations and inertialeffects.

RBC aggregate velocities V were obtained using particle image velocimetry (PIV).LabView software was applied to process the data. Two-dimensional RBC aggregate ve-locity-vector fields were received. Each velocity vector was determined by a cross-cor-relation of the interrogation regions from successive pairs of images with the accuracyof 2 μm/s. The interrogation region, in the first step, was 64×64 pixels (0.64×0.64 mm2)and next, to increase accuracy, it was decreased to 32×32 pixels (0.32×0.32 mm2).The velocity fluctuation fields were determined from the velocity fields using the for-mula

3. Results and discussionThe RBC aggregates occurring at characteristic times during the process at hematocrit0.05 are displayed in Fig. 2. The experimental technique does not enable the preciseidentification of individual objects that appear up to about 300 s. During this initial

IlluminationBlood Imaging system

CCD PC

samplesystem

Fig. 1. Experimental setup.

δV V V⟨ ⟩ .–=

6

5

45 6 7

x [mm]

z [m

m]

a b c d

x [mm] x [mm]5 6 7 5 6 7 5 6 7

x [mm]

Fig. 2. Images of the suspension of RBC aggregates obtained at 300 s (a), 600 s (b), 1700 s (c) and2000 s (d).


phase, the RBC rouleaux formation mainly occurred. At 300 s just formed 3-D RBCaggregates appeared in the suspension. At 600 s the formation of the aggregates is com-pleted and the largest aggregates can be observed. Later due to a stratification, the frac-tion of small 3-D RBC aggregates dominates in the area of observation. The velocityfluctuations of these aggregates were estimated and the velocity fluctuation fields ap-pearing at these times are shown in Fig. 3. The velocity fluctuation fields reveal regionsof correlated movement of the aggregates in the form of swirls. Figure 3 shows thatthe formation of 3-D RBC aggregates is associated with creation of a large initial swirl.The growth of the aggregates causes creation of smaller swirls. To quantify the sizeof the swirls, the autocorrelation functions of the velocity fluctuations [4] were ana-lyzed. This function was determined in a vertical direction for the horizontal velocityfluctuations, and in a horizontal direction for the verticalvelocity fluctuations It should be noted that in the aboveformulas the angled brackets represent an average from the data given by a single ve-locity field as the data are available only from the RBC sedimentation experiment.Figure 4 shows the velocity correlations in both directions. The position of the first

7

5

34 6 8

x [mm]

z [m

m]

a b c d

x [mm] x [mm]4 6 8 4 6 8 4 6 8

x [mm]

Fig. 3. Velocity fluctuation fields obtained for the suspension of RBC aggregates at 300 s (a), 600 s (b),1700 s (c) and 2000 s (d). The respective vectors of the velocity fluctuations δV are at a fixed magnifi-cation of the vector scale.

300 s600 s

1700 s2000 s

1.0

0.5

0.0

–0.5

0 2 4 6

Cz/

Cz(

0)

x [mm]

a

300 s600 s

1700 s2000 s

1.0

0.5

0.0

–0.5

0 2 4 6

Cx/

Cx(

0)

z [mm]

b

Fig. 4. Normalized autocorrelation functions determined in the vertical direction for the horizontalvelocity fluctuations Cz(x)/Cz(0) (a), and in the horizontal direction for the vertical velocity fluctuationsCx(z)/Cx(0) (b) obtained at 300 s, 600 s, 1700 s and 2000 s.

Cx z( ) δVx 0( )δVx z( )⟨ ⟩ ,=Cz x( ) δVz 0( )δVz x( )⟨ ⟩ .=


minimum of these functions in a vertical and horizontal direction defines the correla-tion length, and representing, respectively, the vertical and horizontal size ofthe swirls.

Figure 5 summarizes the results obtained for the RBC sedimentation process.These results reveal the non-stationary behavior of this process. The sedimentation ve-locity as well as the vertical and horizontal velocity fluctuations,

and respectively, first increased, at about 600 sreached a maximum value and finally decreased (Fig. 5a). As it is shown in Fig. 5b atthe maximum of the aggregate velocity, the ratio between vertical and horizontal ve-locity fluctuations was close to 2 and next it began to decrease. Figure 5c shows thatat 300 s formed aggregates initially created a large swirl. The growth of the aggregatesat time interval from 300 to 600 s caused decay of the initial transient swirl. After 600 s,in the investigated region, smaller aggregates appeared. Figure 5c shows that the small-er 3-D RBC aggregates created smaller swirls, which after stabilizing become verti-cally elongated. After about 1700 s the swirls again increased. In this final phase ofthe process, the investigated region was depleted of large aggregates and it was occu-

ξ| |x ξ⊥

z ,

50

40

30

20

10

0

4

2

0

8

6

4

2

0300 600 900 1200 1500 1800

Vsed

ΔV||

ΔV⊥

Vse

d, Δ

V [μ

m/s

]ΔV

||/Δ

V⊥

ξ [m

m]

t [s]

a

b

cξ| |

ξ⊥

Fig. 5. Time evolution of the parameters of the RBC sedimentation process at hematocrit 0.05:sedimentation velocity Vsed, vertical ΔV| | and horizontal ΔV⊥ velocity fluctuations (a), the ratio betweenvertical and horizontal velocity fluctuations ΔV| | /ΔV⊥ (b) and the vertical and horizontal correlationlength of, respectively, horizontal and vertical velocity fluctuations (c).

ξ| |x ξ⊥

z

Vsed Vz⟨ ⟩ ,=ΔV | | δV z

2⟨ ⟩1/2= ΔV⊥ δV x2⟨ ⟩1/2,=


pied by small slowly sedimenting aggregates, which can be observed in Fig. 2d. InFigure 6 the same evolutions at hematocrit 0.03 and 0.07 were shown. It is seen thatin spite of the complexity of the process, the main features of these evolutions can beobserved for the investigated samples.

The sedimentation of the 3-D RBC aggregates has some common features withthe sedimentation of monodisperse rigid spheres. For the monodisperse spheres scal-ing laws for the size of the swirls ξ = 15aϕ–1/3 and for the velocity fluctuationsΔV| | /Vsed = 2ϕ1/3 and ΔV⊥/Vsed = ϕ1/3 have been found [4]. Furthermore, in the suspen-sion of rigid spheres cessation of mixing causes creation of a large initial swirl whichrelatively quickly decays to reach the size predicted by the scaling laws [28]. In thispaper, it was shown that the formation of the 3-D RBC aggregates gives a comparableeffect, i.e., in both cases an initial large swirl was observed. Next, when smaller swirlsappear, the ratio between vertical and horizontal velocity fluctuations of the largestRBC aggregates were about 2, as was found by SEGRÈ for monodisperse spheres beforethe front arrives [4]. The most important common feature of the processes was the long--range correlations of the velocity fluctuations in the form of swirls. However, in gen-

40

20

0

4

2

0

8

4

0300 600 900 1200 1500 1800

VsedΔV||ΔV⊥

V sed

, ΔV

[μm

/s]

ΔV||

/ΔV⊥

ξ [m

m]

t [s]

a

b

cξ| |ξ⊥

60

40

20

0

VsedΔV||ΔV⊥

4

2

0

8

4

0300 600 900 1200 1500 1800

t [s]

ξ| |ξ⊥

Fig. 6. Time evolution of the parameters of the RBC sedimentation process at hematocrit 0.03 (leftcolumn) and 0.07 (right column): sedimentation velocity Vsed, vertical ΔV| | and horizontal ΔV⊥ velocityfluctuations (a), the ratio between vertical and horizontal velocity fluctuations ΔV| | /ΔV⊥ (b) andthe vertical and horizontal correlation length of, respectively, horizontal and vertical velocityfluctuations (c).

ξ| |x ξ⊥

z


eral, the results presented in this paper show that the settling dynamics of 3-D RBC ag-gregates exhibits much higher complexity than that of spherical monodisperseparticles. A departure from the results for monodisperse spheres, similar to the caseof the RBC aggregates, was observed by SAINTILLAN et al. [5] in the study of the sed-imentation of spheroids and deformable particles. Both for RBC aggregates as well asspheroids and deformable particles, the sedimentation velocity and the velocity fluc-tuations exhibited non-stationary behavior. The growth of 3-D RBC aggregates stim-ulates an increase in sedimentation velocity and velocity fluctuations. For non-isotropicprolate particles as well as for deformable particles, these parameters increased withtime as a result of the forming of clusters. This increase was also due to the verticalorienting of non-isotropic particles and deforming of deformable particles. After at-taining the maximum, the sedimentation velocity and velocity fluctuations for theseparticles decreased with time, which was caused by considerable stratification inthe suspension. A decrease of the RBC aggregate size exhibits high polydispersity ofthe aggregates and the stratification in their suspension. So, similarly as to the case ofspheroids and deformable particles, stratification in the suspension of RBC aggregatesdecreased the sedimentation velocity and velocity fluctuations. The mean size ofthe swirls created by the spheres and spheroids was stable up to the arrival of the sed-imentation front. For RBC aggregates, this stabilization appeared despite a lack ofa clear sedimentation front. In the RBC suspension, the stabilization of the swirls sizewas observed as long as there were enough sedimenting RBC aggregates. Finally, forspheroids as well as for RBC aggregates, the swirls, at the final stage of their evolution,again increased, whereas for the spheres they vanished.

4. ConclusionIn this study, a new approach to the problem of RBC aggregate sedimentation wasproposed. It allowed the revealing of long-range correlations of 3-D RBC aggregatevelocity fluctuations in the form of swirls. Although we have found common featuresof the 3-D RBC aggregate sedimentation and sedimentation of monodisperse spheres,differences between the processes are significant. The growth of 3-D RBC aggregatesstimulates similar behavior of the systems as the clustering effect. The results shownew mechanisms of the RBC sedimentation process. In this way, these effects shouldbe taken into account in the formulation of RBC sedimentation theory.

Acknowledgements – This work was supported by the UMK grant.

References

[1] BATCHELOR G.K., Sedimentation in a dilute dispersion of spheres, Journal of Fluid Mechanics 52(2),1972, pp. 245–268.

[2] CAFLISCH R.E., LUKE J.H.C., Variance in the sedimentation speed of a suspension, Physics of Fluids28(3), 1985, pp. 759–760.


[3] NICOLAI H., GUAZZELLI E., Effect of the vessel size on the hydrodynamic diffusion of sedimentingspheres, Physics of Fluids 7(1), 1995, pp. 3–5.

[4] SEGRÈ P.N., HERBOLZHEIMER E., CHAIKIN P.M., Long-range correlations in sedimentation, PhysicalReview Letters 79(13), 1997, pp. 2574–2577.

[5] SAINTILLAN D., SHAQFEH E.S.G., DARVE E., The growth of concentration fluctuations in dilute dis-persions of orientable and deformable particles under sedimentation, Journal of Fluid Mechanics553, 2006, pp. 347–388.

[6] SEGRÈ P.N., LIU F., UMBANHOWAR P., WEITZ D.A., An effective gravitational temperature forsedimentation, Nature 409(6820), 2001, pp. 594–597.

[7] SNABRE P., POULIGNY B., METAYER C., NADAL F., Size segregation and particle velocity fluctuationsin settling concentrated suspensions, Rheologica Acta 48(8), 2009, pp. 855–870.

[8] ARMSTRONG J.K., WENBY R.B., MEISELMAN H.J., FISHER T.C., The hydrodynamic radii of macromole-cules and their effect on red blood cell aggregation, Biophysical Journal 87(6), 2004, pp. 4259–4270.

[9] FABRY T.L., Mechanism of erythrocyte aggregation and sedimentation, Blood 70(5), 1987,pp. 1572–1576.

[10] MUTRYNOWSKA J., GRZEGORZEWSKI B., Optical analysis of red blood cell sediment formation,Biorheology 44(4), 2007, pp. 285–297.

[11] REUBEN A.J., SHANNON A.G., Some problems in the mathematical modelling of erythrocytesedimentation, Mathematical Medicine and Biology 7(3), 1990, pp. 145–156.

[12] PRIBUSH A., MEYERSTEIN N., Methodological aspects of erythrocyte aggregation, Recent Patents onAnti-Cancer Drug Discovery 2(3), 2007, pp. 240–245.

[13] PRIBUSH A., MEYERSTEIN D., MEYERSTEIN N., The mechanism of erythrocyte sedimentation. Part 2:The global collapse of settling erythrocyte network, Colloids and Surfaces B: Biointerfaces 75(1),2010, pp. 224–229.

[14] PONDER E., On sedimentation and rouleaux formation–II, Experimental Physiology 16(2), 1926,pp. 173–194.

[15] KERNICK D., JAY A.W.L., ROWLANDS S., SKIBO L., Experiments on rouleau formation, CanadianJournal of Physiology and Pharmacology 51(9), 1973, pp. 690–699.

[16] SHIGA T., IMAIZUMI K., HARADA N., SEKIYA M., Kinetics of rouleaux formation using TV image an-alyzer. I. Human erythrocytes, American Journal of Physiology – Heart and Circulatory Physiology245(2), 1983 pp. H252–H258.

[17] BARSHTEIN G., WAJNBLUM D., YEDGAR S., Kinetics of linear rouleaux formation studied by visualmonitoring of red cell dynamic organization, Biophysical Journal 78(5), 2000, pp. 2470–2474.

[18] SAMSEL R.W., PERELSON A.S., Kinetics of rouleau formation. I. A mass action approach withgeometric features, Biophysical Journal 37(2), 1982, pp. 493–514.

[19] POP C.V.L., NEAMTU S., Aggregation of red blood cells in suspension: study by light-scatteringtechnique at small angle, Journal of Biomedical Optics 13(4), 2008, article 041308.

[20] TSINOPOULOS S.V., SELLOUNTOS E.J., POLYZOS D., Light scattering by aggregated red blood cells,Applied Optics 41(7), 2002, pp. 1408–1417.

[21] SHVARTSMAN L.D., FINE I., Optical transmission of blood: effect of erythrocyte aggregation,IEEE Transactions on Biomedical Engineering 50(8), 2003, pp. 1026–1033.

[22] BEKSHAEV A.YA., ANGELSKY O.V., HANSON S.G., ZENKOVA C.YU., Scattering of inhomogeneouscircularly polarized optical field and mechanical manifestation of the internal energy flows, PhysicalReview A 86, 2012, article 023847.

[23] SHEPPARD C.J.R., Fractal model of light scattering in biological tissue and cells, Optics Letters 32(2),2007, pp. 142–144.

[24] MIN XU, Electric field Monte Carlo simulation of polarized light propagation in turbid media, OpticsExpress 12(26), 2004, pp. 6530–6539.


[25] KEMPCZYŃSKI A., BOSEK M., GRZEGORZEWSKI B., Comparison of Hough and Fourier transformapproach in the study of kinetics of red blood cell aggregates, Proceedings of SPIE 7141, 2008,article 714118.

[26] KEMPCZYŃSKI A., GRZEGORZEWSKI B., Estimation of red blood cell aggregate velocity duringsedimentation using the Hough transform, Optics Communications 281(21), 2008, pp. 5487–5491.

[27] KALIVIOTIS E., DUSTING J., BALABANI S., Spatial variation of blood viscosity: modelling usingshear fields measured by a μPIV based technique, Medical Engineering and Physics 33(7), 2011,pp. 824–831.

[28] BERGOUGNOUX L., GHICINI S., GUAZZELLI E., HINCH J., Spreading fronts and fluctuations insedimentation, Physics of Fluids 15(7), 2003, pp. 1875–1887.

Received May 21, 2014in revised form July 11, 2014


A new design of a photonic crystal fiber with a beam shaping effect and flexible management of dispersion and confinement loss

YUCHUN HUANG, PING JIANG*, HUAJUN YANG, MINGYIN YU

School of Physical Electronics, University of Electronic, Science and Technology of China, Chengdu 610054, China


A new design of a guiding-index photonic crystal fiber which possesses a beam shaping effect andflexible control of dispersion has been proposed in this paper. It can shape a Gaussian beam intoa circular hollow beam with certain dimension, which can be used in optical communicationsystems with a Cassegrain antenna to improve transmission efficiency by avoiding the loss ofenergy caused by the subreflector center reflection. In addition, its dispersion and confinementloss can be changed in a broad range by slightly adjusting structural parameters under conditionthat the hollow beam dimension remains about the same. Fairly practical properties, zero dispersionor flattened dispersion, can be obtained when structural parameters are set appropriately. A seriesof models with different parameters are analyzed and compared. Results of numerical simulationshow that the ultra-low dispersion of 1.802 ps/km/nm can be obtained when λ = 1.31 μm. Severalmodest design parameters are given as well.

Keywords: photonic crystal fiber, hollow beam, chromatic dispersion.

1. IntroductionPhotonic crystal fiber (PCF) [1] is a novel kind of an optical fiber whose clad iscomposed of air holes running along its length. Since its first fabrication in 1996 [1],PCF has attracted considerable attention because of excellent propagation properties. Ithas exhibited extraordinary features such as a wide range of single-mode operations [2],easily controllable dispersion [3, 4], birefringence [5, 6], and tailorable effective modearea [7, 8]. Strong potential has been shown in nonlinear fiber optics such as the gen-eration of a super-continuum [9] and in many other novel fiber devices [10]. What ismore, a flexible and precise management of chromatic dispersion in a broad spectralrange makes it receive wide attention in applying in optical communication, such ascoping with ever-increasing data rate and spectral density of wavelength division mul-tiplexing (WDM) channels [11].

376 YUCHUN HUANG et al.

Many designs have been proposed to engineer chromatic dispersion in PCF. Someresearches transform material to achieve it by doping the core area [12, 13] or fillingthe cladding air holes with liquid [14], other researches vary structures by employingspecial shaped air holes [15, 16] instead of circular air holes. Flattened or near-to-zerodispersion characteristics can be obtained. In some cases, a special ring-shaped beam,usually hexagonal or square, can be generated as a by-product [17]. However, on oneside, these polygonal ring-shaped beams cannot apply to some optical systems per-fectly. For example, in the optical communication systems with a Cassegrain antenna,to avoid the loss of energy caused by the subreflector center reflection [18], a circularhollow beam [19] works more efficiently than those polygonal ring-shaped beams. Onthe other side, a change in structure parameters aiming at a proper beam size may de-teriorate the dispersion characteristics.

In this paper, a novel large-mode-area PCF with a coaxial ring-shaped defect inthe air hole clad is constructed based on the index guiding principle. The design detailsof the PCF are proposed in this paper and numerical analysis has been elaborated.The modes of the proposed fiber are analyzed by the finite element method (FEM).The results of simulation with the analysis and comparison covering electric field dis-tribution, beam dimension, chromatic dispersion and confinement loss have been pre-sented. The proposed fiber can be used in space optical communication systems togreatly enhance the transmission efficiency. And a good management of chromatic dis-persion can be achieved under the premise that the beam size and type remain the same.

2. Design method and numerical analysis

As a new kind of optical fiber, PCF consists of a core and clad, obeying the propagationlaw of total internal reflection, which is similar to a traditional optical fiber. PCF ismade up of unitary material, whose clad is a microstructure built by punching sub-mi-crometer air holes tightly and periodically. It can be sorted to two types according todistinct structures: index-guiding PCF [20] and band-gap PCF. The core of index-guid-ing PCF is composed of host material, hence the refractive index of the core is higherthan that of the clad. The new designed structure proposed in this paper exactly belongsto this type.

The optical beam with zero central intensity is called a hollow beam (HB). Con-ventional geometry [17, 21, 22] of PCF was always built based on a hexagonal or tri-angular lattice, thus the cross-section of the core is a hexagon or hexagonal ringactually. On the contrast, the air holes are arranged in a series of concentric circularrings regularly in the proposed PCF, whose cross-section is shown in Fig. 1a. To pro-duce HB, a new structure is designed, which is shown in Fig. 1b. The host material isfused silica. Several layers of the air holes are removed to form an annular core, andthe light can propagate in this area whose refractive index is higher than in the restregion of the fiber. The air hole pitch Λ, the distance between any two adjacent layersis 1.2 μm and the radius of the air hole r is 0.4 μm. Obviously, an annular core ofthe new design is a circular ring. While, a hexagonal ring-shaped core can be obtained

A new design of a photonic crystal fiber with a beam shaping effect... 377

when a similar removing method is applied to conventional geometry. The differencebetween them may cause distinct field distribution of a propagating beam, which willbe particularly discussed in the simulation section.

Chromatic dispersion is an essential indicator when estimating a nonlinear fiber,because it has direct effects on pulse broadening, walk-off and phase-matching con-ditions [23], thus determining the bandwidth and energy requirement of the device towhich the fiber is applied. The total chromatic dispersion is separated into two parts:material dispersion and waveguide dispersion. The former only relies on wavelengthin vacuum for certain material, while the latter has relation with both the wavelengthin vacuum and the effective refractive index which is gained by simulation.

The total dispersion Dt is approximately a combination of material dispersion Dmand waveguide dispersion Dw, therefore we obtain [24]

Dt ≅ Dw + Dm (1)

Waveguide dispersion Dw is given by [25]

(2)

where c denotes the speed of light in vacuum and λ denotes the wavelength of light invacuum and neff means the effective refractive index.

Due to the finite number of layers of air holes, leaking of the light of the ring toexterior matrix material is occurring through bridges between air holes, resulting inthe confinement loss α, which can be obtained by [26]

(3)

Here, λ denotes the wavelength of light in vacuum and neff means the effectiverefractive index as well.

2r

Λ

a b

Fig. 1. Cross-section of new proposed PCF (see text for explanation).

Dwλc

-------d2Re neff λ( )[ ]

dλ2-----------------------------------------–=

α40π Im neff( )λ 10( )ln

-------------------------------------=


3. Simulation and discussion3.1. Proposed structure

A model is built based on the structure shown in Fig. 1b. The refractive index n2 ofthe host material (fused silica) is 1.45, while that of air, n1 is 1. The finite element meth-od (FEM) was employed to analyze the mode properties of the PCF. The advantageof this way is that it can handle PCF with any structure parameters and any arrangementof the air holes. Using the FEM, the electric field distribution in a cross-section canbe obtained when the incident beam is a Gaussian beam. Figure 2a shows the electricfield distributions of an incident beam. Figures 2b and 2c show the electric field dis-tribution of a beam propagating in proposed PCF by 3D and 2D separately.

Comparing Fig. 2a with Fig. 2b, it turns out that the incident Gaussian beam isshaped into a circular HB, whose main electric field region is a circular ring, rather

×107

3.5

3.0

2.5

2.0

1.5

1.0

0.5 xyz

15

10

5

0

50–5

3.1133×107

6420.3

86420–2–4–6–8

a

b

c

5

0

–5

8

6

4

2

0

–2

–4

–6

–8

3.0

2.5

2.0

1.5

1.0

0.5

3.0

2.5

2.0

1.5

1.0

0.5

×107

×1073.1133×107

6420.3

Fig. 2. Electric field distribution of proposed structure (see text for explanation).


than a disc. From Fig. 2c, it can be easily observed that the electric field of a beampropagating in proposed PCF is almost wholly confined to the ring-shaped core.Compared with the simulation result in [17, 22], whose HB shape is hexagonal, a cir-cular HB is more suitable for space optical communication systems to avoid the lossof energy caused by the subreflector center reflection in the optical antenna. The trans-mission efficiency in the optical communication system will be greatly enhanced.

To study the influence of a ring-shaped core size on circular HB dimension, threestructures are considered and discussed. The three structures are the same in the pa-rameter setting of Λ = 1.2 μm and r = 0.4 μm, so as materials. The only differenceamong them is size and position of the defect. One is formed by removing the thirdand the fourth rings of air holes, as is shown in Fig. 1b. Similarly, the other two areformed by removing the second and the third rings, the second to the fourth rings re-spectively. In order to state conveniently, they were named r34, r23 and r234 in order.

In [19], DSS is defined as the full-width half-maximum (FWHM) of the radial in-tensity distribution of HB. Parameter WDHB is the full-width of the maximum intensitytimes e–2. And r0 is half of the distance between two peak values. Then the width ofthe hollow beam Wr can be obtained by the following equation: Wr = WDHB – 2r0.The normalized intensity distribution of the fundamental mode in above three struc-tures is illustrated in Fig. 3. Images of the corresponding PCF profile are placed in each

wDHB2r0

DSS

–8 –6 –4 –2 0 2 4 6 8

1.0

0.8

0.6

0.4

0.2

0.0

x [μm]

1.0

0.8

0.6

0.4

0.2

0.0

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

inte

nsity

[W/m

2 ]

Fig. 3. Normalized intensity of HB generated by corresponding structure.


subgraph, they are r23, r234 and r34 from top to the bottom. In the first subgraph, indi-cators WDHB, 2r0 and DSS have been marked using arrows.

Dimension parameter of HB generated by the three structures was obtained by dataprocessing, which is shown in Table 1. It can be seen from the Table that r234 reachesmaximum in Wr, meanwhile, r23 and r34 achieve minimum and maximum as to DSS.Obviously, there is a positive correlation between the annular core width and HB width,as with the annular core internal diameter and HB internal diameter. Though not a di-rect proportion, this rule can still be a guideline when PCFs are designed to generatea circular HB with certain dimension.

Then the core size influence on chromatic dispersion was also studied by discussingabove three structures. Figure 4 shows the effective refractive index neff of three struc-tures obtained by simulation. It is obvious that neff is approximate to the refractiveindex of fused silica n2. Moreover, neff of all structures decreases with the increase inwavelength.

According to Eqs. (1) and (2), the total dispersion is obtained, shown in Fig. 5.Apparently, for λ = 1.31–1.55 μm, the wave band of optical communication, the totaldispersion is almost within the range of 30–60 ps/km/nm for each structure, which isfar from ideal on account of being large and not flat.

However, it has also been found that the total dispersion Dt remains about the samein above three structures. That is to say, when the annular core dimension is changedaiming to obtain a circular HB with required dimension, the effect of resizing on dis-persion characteristics could be ignored. Thus more attentions will be focused on dimen-

T a b l e 1. Dimension parameter of HB.

DSS [μm] 2r0 [μm] WDHB [μm] Wr [μm]r23 2.9646 5.5908 8.4903 2.8996r234 3.2185 6.5978 10.3275 3.7298r34 5.6000 8.0582 10.9278 2.8696

r34

r234

r23

1.45

1.44

1.43

1.420.8 1.0 1.2 1.4 1.6 1.8 2.0

neff

Wavelength [μm]

Fig. 4. Effective refractive index vs. wavelength.


sional requirement of the generated HB in its early design phases. As to the managementof dispersion, an optimized structure will be studied in the following section.

3.2. Optimized structure and analysis

For the sake of a more flexible and precise management of chromatic dispersion,the proposed structure above was optimized by punching a circle of air holes in the mid-dle of the ring-shaped core, whose radius R is adjustable and much smaller thanthe radius of other air holes, as is shown in Fig. 5. Other parameters are the same asabove, namely, λ = 1.2 μm, r = 0.4 μm, n1 = 1 and n2 = 1.45. Absolutely, the structurein Fig. 1b can be regarded as a special case of the structure in Fig. 6, namely, R = 0.Based on recent researches [27, 28], electron beam lithography (EBL) can be used torun a super-fine process of 0.1–0.25 μm, with an error of tens of nanometers. Thismethod can satisfy basically the requirements of our design.

Figures 7a and 7b show the electric field distribution of optimized structure basedon Fig. 3 in 2D and 3D, respectively. It can be seen that the optimized structure hasan equally good performance in beam shaping, only with difference in electric fielddistribution of the annular core region.

r34

r234

r23

0.8 1.0 1.2 1.4 1.6 1.8 2.0Wavelength [μm]

100

50

0

–50

Tota

l dis

pers

ion

[ps/

km/n

m]

Fig. 5. Total dispersion curve in a broad wavelength range.

2R

2r

Λ

Fig. 6. Cross-section of optimized structure.


The normalized intensity distribution of the fundamental mode in optimized PCFis illustrated in Fig. 8. Dimension parameters WDHB and DSS are marked in the figureas well. Compared to above three structures in Fig. 3, it can be found that HB generatedby the optimized structure has four peaks. This phenomenon may be explained bythe added air holes in an annular core, which tends to divide the annular core into twocoaxial rings. Therefore, the incident beam tends to converge in the two ring-shapedparts simultaneously. The change is obvious, however, it has little effect on the dimen-sion of the generated HB. Owing to the change of HB shape, above computingmethod is not applicable. Instead, HB width can be calculated by the equationWr = (WDHB – DSS)/2. Here, the values of Wr and DSS are 2.9426 μm and 5.4205 μmseparately, being nearly identical with those of r34 in Table 1. In conclusion, addingair holes in the annular core impacts on the HB dimension slightly.

To study the chromatic dispersion change rule vs. wavelength with different struc-tural parameters, the parameter R in model B was set a series value of 0.05, 0.07, 0.09,0.10, 0.12, 0.14, 0.16, 0.18 and 0.20 μm, respectively.

86420–2–4–6–8

×107

5

4

3

2

1

5.1811×107

9355.1

xyz

15

10

5

0

–5

0

8

6

4

2

0

–2

–4

–6

–8

ab

×107

5

4

3

2

1

5.1811×107

9355.1

Fig. 7. Electric field distribution of optimized structure (see text for explanation).

wDHB

DSS

–8 –6 –4 –2 0 2 4 6 8x [μm]

1.2

0.8

0.4

0.0Nor

mal

ized

inte

nsity

[W/m

2 ]

Fig. 8. Normalized intensity of HB generated by optimized structure.


Figure 9 shows the effective refractive index neff vs. wavelength of the designed PCFwith all parameter settings obtained by simulation. The dashed line represents the caseof R = 0. It is obvious that neff decreases with the increase in the wavelength λ inan irregularly varying slope in all cases.

The relation between the waveguide dispersion Dw of the designed PCF and the wave-length λ is described in Fig. 10, according to Eq. (2). Meanwhile, the abstract of ma-terial dispersion –Dm with different wavelength λ is calculated based on the Sellmeierequation, drawn in Fig. 8 as well. Since the total dispersion Dt is regarded as a linearcombination of waveguide dispersion and material dispersion, based on Eq. (1),the points where the waveguide dispersion curve and the abstract of material dispersioncurve intersected indicate the case of zero dispersion. That is to say, the correspondinghorizontal axis values represent zero dispersion wavelength. All the points are markedby red dots. It can be found that the zero dispersion wavelength increases with the pa-

R = 0

R = 0.05 μm

1.46

1.44

1.42

1.40

1.380.8 1.0 1.2 1.4 1.6 1.8 2.0

Wavelength [μm]

Effe

ctiv

e re

fract

ive

inde

x

R = 0.07 μmR = 0.09 μmR = 0.10 μmR = 0.12 μmR = 0.14 μmR = 0.16 μmR = 0.18 μmR = 0.20 μm

Fig. 9. Effective refractive index vs. wavelength.

R = 0

R = 0.05 μm

100

60

20

–20

0.8 1.0 1.2 1.4 1.6 1.8 2.0Wavelength [μm]

Dis

pers

ion

[ps/

km/n

m]


–Dm

–60

–100

Fig. 10. Waveguide dispersion curve in a broad wavelength range.


Fig. 11. Total dispersion curve in a broad wavelength range.

R = 0R = 0.05 μm

100

60

20

–20

0.8 1.0 1.2 1.4 1.6 1.8 2.0Wavelength [μm]

Dis

pers

ion

[ps/

km/n

m]


–40

–60

–100

R = 0.05 μm

40

30

20

10

1.2 1.3 1.4 1.5 1.6Wavelength [μm]

Con

finem

ent l

oss

[dB

/km

]


0

Fig. 12. Confinement loss vs. wavelength for different defect structures.

Y: 3.635Y: 0.69

Y: 32.64

Dis

pers

ion

[ps/

km/n

m]

Wavelength [μm]

–50

–60

–701.2 1.3 1.4 1.5 1.6

R = 0.14 μmR = 0.16 μm

R = 0.18 μm

R = 0.20 μm

Δy = 3.94

15

Dis

pers

ion

[ps/

km/n

m] 10

5

0

–5

–10

–15

Wavelength [μm]1.2 1.3 1.4 1.5 1.6

R = 0.07 μm

R = 0.09 μm R = 0.10 μm

R = 0.12 μm

X: 1.299Y: 0

X: 1.383Y: 0

X: 1.575Y: 0 X: 1.31

Y: 55.98

X: 1.55Y: 52.04


rameter R varying from 0 to 0.20 μm. Therefore, adjusting the parameter R is an ef-fective and precise way to manage zero dispersion wavelength flexibly.

To acquire more intuitive results, a linear combination of material and waveguidedispersion is conducted. Hence, the total dispersion Dt is obtained, shown in Fig. 11.Apparently, for R = 0.09, 0.10 and 0.12 μm, the dispersion wavelength is 1.299, 1.383and 1.575 μm, respectively, approximate to the universe wavelength of optical com-munication, 1.31 μm and 1.55 μm, which is a quite important character for opticalcommunication. Furthermore, Fig. 11 shows that the flatness of the total dispersioncurve varies with different values of the parameter R. Most noticeably, in the case ofR = 0.18 μm, the difference in total dispersion is merely 3.94 ps/km/nm when the wave-length λ is spanning from 1.31 to 1.55 μm, revealing a fairly good quality of opticaltransmission.

For the models built above, the confinement loss was figured out on the basis ofEq. (3). The results shown in Fig. 12 manifest that the confinement loss increases withthe rise of the wavelength λ when the value of the parameter R is determined. The con-finement loss falls from 32.64 to 3.635 dB/km when the parameter R ranges from 0.20to 0.05 μm, reflecting the rule that the confinement loss increases with the rise ofthe parameter R for the same wavelength λ. In the case of R = 0.05 μm, the losses are0.69 and 3.635 dB/km for λ = 1.31 μm and λ = 1.55 μm, respectively, approaching tozero. Hence, the structure can be designed feasible to propagate a light beam.

It can be seen from the above analysis that the optimized design achieves the expectedobjective. In this design, HB dimension and dispersion characteristics are controlledby two different parameters. The size of a ring-shaped core decides about HB dimen-sion in the main, and the radius of air holes in the annular core can manage dispersionflexibly. Considering those designs in [17], a good dispersion characteristic has beenobtained. But the dispersion is controlled by core shape and size, and HB is merelya by-product generated sometimes. So generating a HB with required dimension mayresult in unsatisfied dispersion characteristics. By the above comparison, it is obviousthat the optimized design behaves better and flexibly.

4. Conclusion

A new PCF with an annular core has been proposed, which is effective on shapinga Gaussian beam into a circular HB. The shaping effects are confirmed by analyzingthe electric field distribution of the cross-section. Dimension of the generated HB hasbeen defined and calculated. Moreover, an effective method to manage the dispersioncharacteristics has been proposed which has little effect on the dimension of the gen-erated HB. Using this method assures the primary requirement that the generatedHB dimension remains nearly the same. Moreover, it is of remarkable flexibility ofadjusting chromatic dispersion and confinement loss by slightly altering a certainstructure parameter to meet the demands on practical applications, zero dispersion orflattened dispersion in a specific wavelength range. In particular, the minimum value


and optimum flatness of chromatic obtained by the proposed method are good and ofhigh applicability, such as 1.802 ps/km/nm with λ = 1.31 μm and R = 0.09 μm. Owingto these good properties, the design proposed in this paper is applicable to optical com-munication systems.

Acknowledgements – This work is supported by the National Natural Science Foundation of China underGrant No. 61271167 and No. 61307093, and also supported by the Research Foundation of the GeneralArmament Department of China under Grant No. 9140A07040913DZ02106.

References

[1] KNIGHT J.C., BIRKS T.A., RUSSELL P.S.J., ATKIN D.M., All-silica single-mode optical fiber withphotonic crystal cladding, Optics Letters 21(19), 1996, pp. 1547–1549.

[2] BIRKS T.A., KNIGHT J.C., RUSSELL P.S.J., Endlessly single-mode photonic crystal fiber, Optics Letters22(13), 1997, pp. 961–963.

[3] BIRKS T.A., MOGILEVTSEV D., KNIGHT J.C., RUSSELL P.S.J., Dispersion compensation using single--material fibers, IEEE Photonics Technology Letters 11(6), 1999, pp. 674–676.

[4] FERRANDO A., SILVESTRE E., MIRET J.J., ANDRÉS P., Nearly zero ultraflattened dispersion in photoniccrystal fibers, Optics Letters 25(11), 2000, pp. 790–792.

[5] ORTIGOSA-BLANCH A., KNIGHT J.C., WADSWORTH W.J., ARRIAGA J., MANGAN B.J., BIRKS T.A.,RUSSELL P.S.J., Highly birefringent photonic crystal fibers, Optics Letters 25(18), 2000,pp. 1325–1327.

[6] HANSEN T.P., BROENG J., LIBORI S.E.B., KNUDSEN E., BJARKLEV A., JENSEN J.R., SIMONSEN H., Highlybirefringent index-guiding photonic crystal fibers, IEEE Photonics Technology Letters 13(6), 2001,pp. 588–590.

[7] BRODERICK N.G.R., MONRO T.M., BENNETT P.J., RICHARDSON D.J., Nonlinearity in holey opticalfibers: measurement and future opportunities, Optics Letters 24(20), 1999, pp. 1395–1397.

[8] MORTENSEN N.A., Effective area of photonic crystal fibers, Optics Express 10(7), 2002, pp. 341–348. [9] RANKA J.K., WINDELER R.S., STENTZ A.J., Visible continuum generation in air-silica microstructure

optical fibers with anomalous dispersion at 800 nm, Optics Letters 25(1), 2000, pp. 25–27. [10] EGGLETON B.J., KERBAGE C., WESTBROOK P.S., WINDELER R.S., HALE A., Microstructured optical

fiber devices, Optics Express 9(13), 2001, pp. 698–713.[11] FARIBORZ MOUSAVI MADANI, KAZURO KIKUCHI, Design theory of long-distance WDM dispersion-

managed transmission system, Journal of Lightwave Technology 17(8), 1999, pp. 1326–1335.[12] HANSEN K.P., Dispersion flattened hybrid-core nonlinear photonic crystal fiber, Optics Express 11(13),

2003, pp. 1503–1509.[13] HOO Y.L., JIN W., JU J., HO H.L., WANG D.N., Design of photonic crystal fibers with ultra-low, ultra-

-flattened chromatic dispersion, Optics Communications 242(4–6), 2004, pp. 327–332.[14] KRISHNA MOHAN GUNDU, M. KOLESIK, J.V. MOLONEY, KYUNG SHIK LEE, Ultra-flattened-dispersion

selectively liquid-filled photonic crystal fibers, Optics Express 14(15), 2006, pp. 6870–6878.[15] JINGYUAN WANGA, CHUN JIANGA, WEISHENG HUA, MINGYI GAO, Modified design of photonic crystal

fibers with flattened dispersion, Optics and Laser Technology 38(3), 2006, pp. 169–172.[16] ZHAO-LUN LIUA, XIAO-DONG LIU, SHU-GUANG LI, GUI-YAO ZHOU, WEI WANG, LAN-TIAN HOU, A broad-

band ultra flattened chromatic dispersion microstructured fiber for optical communications, OpticsCommunications 272(1), 2007, pp. 92–96.

[17] RAKHI BHATTACHARYA, SWAPAN KONAR, Dual-core photonic crystal fibers for dispersion compen-sation, Journal of Nanophotonics 6(1), 2012, article 063520.

[18] SCADUTO L.C.N., SASIAN J., STEFANI M.A., JARBAS CAIADO DE CASTRO NETO, Two-mirror telescopedesign with third-order coma insensitive to decenter misalignment, Optics Express 21(6), 2013,pp. 6851–6865.


[19] XIAO-XIA ZHANG, SHU-GUANG LIN, SHUO LIU, YING DU, XING-PING ZHU, Generation of hollow beamfrom photonic crystal fiber with an azimuthally polarized mode, Optics Communications 285(24),2012, pp. 5079–5084.

[20] KNIGHT J.C., Photonic crystal fibers, Nature 424, 2003, pp. 847–851.[21] SAITOH K., FLOROUS N., KOSHIBA M., Ultra-flattened chromatic dispersion controllability using

a defected-core photonic crystal fiber with low confinement losses, Optics Express 13(21), 2005,pp. 8365–8371.

[22] SHUGUANG LI, XIAOXIA ZHANG, AGRAWAL G.P., Characteristics of photonic crystal fibers designedwith an annular core using a single material, Applied Optics 52(13), 2013, pp. 3088–3093.

[23] FEROZA BEGUM, YOSHINORI NAMIHIRA, S.M. ABDUR RAZZAK, SHUBI KAIJAGE, NGUYEN HOANG HAI,TATSUYA KINJO, KAZUYA MIYAGI, NIANYU ZOU, Design and analysis of novel highly nonlinearphotonic crystal fibers with ultra-flattened chromatic dispersion, Optics Communications 282(7),2009, pp. 1416–1421.

[24] DAVIDSON D., Optical-Fiber Transmission, [Ed.] Basch E.E.B., Howard W. Sams & Co, 1987.[25] CHAUDHARI C., SUZUKI T., OHISHI Y., Chalcogenide core photonic crystal fibers for zero chromatic

dispersion in the C-band, Optical Fiber Communication Conference, OSA Technical Digest (CD),2009, paper OTuC4.

[26] KUHLMEY B.T., NGUYEN H.C., STEEL M.J., EGGLETON B.J., Confinement loss in adiabatic photoniccrystal fiber tapers, Journal of the Optical Society of America B 23(9), 2006, pp. 1965–1974.

[27] DEROSE G.A., LIN ZHU, POON J.K.S., YARIV A., SCHERER A., Electron-beam lithography techniquesfor micro- and nano-scale surface structure current injection lasers, CLEO, 2007, CThN7.

[28] SANABIA J.E., BURCHAM K.E., KLINGFUS J., PIASZENSKI G., KAHL M., JEDE R., Fixed beam movingstage electron beam lithography of waveguide coupling device structures, CLEO, 2012, CM4L.3.

Received February 25, 2014in revised form June 4, 2014


Nonlinear-optical refraction of silver nanoparticle composites

ROMAN GAMERNYK1, MYKOLA PERIV1, SERHIY MALYNYCH2*

1Ivan Franko National University of Lviv, Department of Physics, Kyrylo and Methodii St. 8, Lviv 79005, Ukraine

2V.E. Lashkaryov Institute of Semiconductors Physics NAS of Ukraine, Nauky Avenue 41, 03028, Kyiv, Ukraine


In this paper, the experimental data on nonlinear refraction of silver nanoparticle composites usinga standard Z-scan technique are presented. It was found that the colloids of silver nanoparticles ofvarious size possess a defocusing ability. Based on general considerations, one can concludethermal lens nature of the nonlinear refraction of the colloids. Significantly different magnitudesof the nonlinear refractive index of silver nanoparticles suspended in water and in glycerol can beexplained by differences in the specific heat capacity of mentioned fluids. The effective thicknessfor nonlinear-optical interaction of light with a two-dimensional silver nanoparticle array wasestimated.

Keywords: silver nanoparticles, nonlinear optics, Z-scan.

1. IntroductionOne of the most prominent features of metal nanoparticles (NPs) subjected to the elec-tromagnetic irradiation is their ability to support specific electron excitations, termedlocalized surface plasmon resonances (LSPR). Noble metal nanoparticles (Au, Ag, Cu)are of prime interest since the frequency of LSPR for those metals occurs at the visiblespectral range. Moreover, the resonance frequency can be tuned by varying particles’size and shape as well as the dielectric environment [1]. Unique frequency dependenceof the real and imaginary parts of the dielectric function of silver makes the metalmore suitable for various applications using nanoparticles, as compared to gold andcopper. Indeed, the interband transition threshold for silver is about 4 eV, whilethe same for gold and copper occurs at 2.3 and 2.6 eV, respectively [2]. Interband tran-sitions in latter cases substantially damp LSPR in Au and Cu nanoparticles. Resonantcharacter of electron density oscillations in metal nanoparticles along with large cur-vature of the nanoparticle surface results in a giant enhancement of the local electric

390 R. GAMERNYK et al.

field. A number of practical applications of silver NPs is based on that effect such assurface enhanced Raman scattering (SERS) [3] and IR absorption (SEIRA) [4], photo-voltaics [5], biosensors [6], to name a few. Field enhancement and specific interactionsof LSPR with surrounding medium give rise to the nonlinear-optical phenomena thatappear at high intensities of the electromagnetic field. Therefore, studies of nanocom-posite materials, i.e., metal nanoparticles embedded in solids or suspended in liquids,are of great importance. In recent years such nonlinear-optical properties of silver nano-particle colloids as high-order nonlinearities [7], two-photon absorption [8], nonlinearrefraction [9], photochromic effect [10], and optical limiting [11] have been investi-gated. Nanocomposite films Ag/BaTiO3 and Ag/SiO2 were studied in [12, 13]. Report-ed studies were performed employing an experimentally simple but powerful Z-scantechnique [14].

It should be mentioned here that the nature of the nonlinear-optical response ofnoble metal NPs is still disputable. Some authors interpret the results of Z-scan mea-surements by the formation of thermal lens in the medium around metal nanoparticlesdue to the effective heat transfer from the nanoparticles to the medium [9, 15–17] orby the difference in the refractive index of nanoparticles and the matrix [7].BHUSHAN et al. suggest that the third-order nonlinearity has a thermally induced origin,while nonlinear absorption is associated with a quadrupole plasmon mode [8]. The re-sults of nonlinear-optical measurements under resonant and non-resonant excitationare presented in [18]. In the first case, the magnitude of the third-order susceptibilityexceeds that under non-resonant excitation by two orders of magnitude. This fact sup-ports the statement that local electric field enhancement around metal nanoparticlescontributes to the nonlinear optical effects rather than thermal lensing in the surround-ings. Similar conclusions are also presented in [19, 20].

In our paper, we present the results of the third-order refraction Z-scan measure-ments of silver NPs suspended in water and glycerol as well as two-dimensional arraysof nanoparticles self-assembled on glass substrate.

2. Experiment

Silver nanoparticles were synthesized during the chemical reduction of silver oxideby hydrogen gas. A supersaturated aqueous solution of silver oxide was heated up tothe temperature of 70°C under permanent mixing. Hydrogen gas was pressurized at~70 kPa above atmosphere. Initially clear solution turned yellowish immediately afterthe reaction started, indicating the formation of silver particles 10–15 nm in diameter.Growth of the nanoparticles is accompanied by characteristic changes in color ofthe solution. The size of the nanoparticles was determined by the extinction UV–Visspectra measurements and by electron microscopy as well. The particle size can be con-trolled simply by varying the reaction time. A detailed procedure of silver NPs syn-thesis can be found elsewhere [21]. The nanoparticles are mainly polyhedral in shapewith no elongation along any axes; the minor fraction of the suspension includesrod-like particles (Fig. 1). Particle stability is achieved through electrostatic repulsion

Nonlinear-optical refraction of silver nanoparticle composites 391

between the thick electrical double layers that result from the limited dissociation ofsilver oxide [21]. Since hydrogen, water and silver oxide are the only components usedin the reaction, no other chemicals (e.g., surfactants) that may strongly affect the opticalresponse of the NPs are present in the final colloidal suspension. Mass fraction of silvermetal in the suspension was determined by thermogravimetric analysis. Sample char-acterization is presented in Table 1.

Two-dimensional arrays of Ag NPs were prepared by self-assembling of the nano-particles onto glass substrate. Prior to the self-assembling, the surface of the glassslides was modified with poly(vinyl pyridine) (PVP), which is capable of simultaneousinteraction with various substrates via hydrogen bonding and with metal particlesthrough donor–acceptor interactions of the nitrogen atom on the pyridyl group [22].Self-assembly of the nanoparticles on PVP modified surfaces results in the formationof a single layer of randomly distributed nanoparticles with an average interparticledistance comparable to their diameter [23].

Fig. 1. SEM image of silver nanoparticles synthesized by chemical reduction. Left panel corresponds tothe sample Ag-1; right panel – sample Ag-3 (for sample assignment see Table 1).

T a b l e 1. Characterization of the samples.

SampleAg-1 Ag-2 Ag-3 Ag-4

Average NP diameter [nm] 80 100 144 215NP concentration [cm–3] 2.3×1010 1.1×1010 1.7×1010 4.7×1010

Average interparticle distance in colloid [nm] 3500 4540 3900 2800

Surface concentration of NPs in 2D array [cm–2] 4.9×109 3.9×109 1.4×109 7.0×109

Average interparticle distance in 2D array [nm] 143 160 270 380

Nonlinear refraction n2 suspension of NPs [cm2/W] –1.64×10–8 –1.498×10–8 –1.297×10–8 –0.65×10–8


Extinction spectra of the samples were measured using MDR-23 monochromator(LOMO, Saint Petersburg, Russia) equipped with a halogen lamp as a source anda photomultiplier tube as a photon counting mode detector. The signal linearity wasobserved in the range of 102–106 photons·s–1. Integrating sphere was mounted betweenthe monochromator and the detector to measure the absorption spectra. Quartz cuvettewith an optical path of 1 mm was used for the experiments.

Nonlinear refraction was measured employing a standard single beam Z-scantechnique [14]. It relies on the measurement of the intensity of the focused laser beampassed through the sample when the latter moves along the beam. Nearby the focalpoint, where the power density of the laser beam reaches its maximal value, the trans-mittance of the sample increases or decreases relatively to that in the linear regime de-pending on the sign of nonlinearity.

Z-scan measurements were carried out at room temperature using second harmonic532 nm radiation of CW neodymium laser with diode pumping. The output power oflaser radiation was 45 mW. The beam was focused by lens with a focal length of75 mm. Parameters of the focused laser beam used in the experiments are presentedin Fig. 2. Here ω0 is the radius of Gaussian beam at the focal point, 2ω0 = 22.3 μm,β is the Rayleigh length. It is essential that the thickness of the sample is less thanthe Rayleigh length (1 < b = 1.197 mm). Power density of the laser beam at the focalpoint is about I0 = 1.04×104 W/cm2.

3. Results and discussionFigure 3 depicts the extinction, scattering, and absorption spectra of the suspension(sample Ag-1). Absorption band centered at λ = 410 nm is associated with the dipolemode of the LSPR in Ag NPs. Linear absorption spectrum provides a basis for calcu-lating the nonlinear-optical parameters.

Two types of Z-scan arrangement were employed to determine nonlinear refraction(NLR), namely closed aperture and eclipsing Z-scan. In latter case the aperture is re-placed with an opaque disc blocking the central part of the beam [24–26].

Concentration dependence of NLR of the Ag NP suspensions was studied. The con-centration was varied simply by diluting the initial colloid with distilled water or glyc-erol. Assuming a spherical shape of the NPs, one can easily calculate the absolute

b

z

ω0ω(z)2 ω0

Fig. 2. Parameters of the focused laser beam used in Z-scan experiments.


Ag NPs concentration in the suspension using experimentally determined mass frac-tion and an average size of the nanoparticles. Corresponding results are presented inTable 1. Refractive index of the water-glycerol solution was measured using Abbe re-fractometer. As shown in Fig. 4, the amplitude of Z-scan transmittance increases withincreasing the glycerol fraction in the solution. In other words, the nonlinear-opticalresponse of Ag NP suspension becomes stronger with the increase in the refractive in-dex of the medium. Z-scan plots presented in Fig. 4 are typical of the NLR of a negativesign, i.e., the colloid possesses defocusing properties [14].

According to SHEIK-BAHAE et al., the nonlinear refractive index of the third order n2can be extracted from normalized Z-scan dependences and is given as [14]

(1)

1

2

3

1.8

1.2

0.6

0.0300 400 500 600 700 800

α [c

m–1

]

λ [nm]

Fig. 3. Extinction (curve 1), scattering (curve 2), and absorption (curve 3) spectra of silver NPs aqueoussuspension (sample Ag-1).

12

34

5 6 7 8 9

–7 0 7

20

10

0

–10

Nor

mal

ized

tran

smitt

ance

Z [mm]

Fig. 4. Z-scan transmittance of the Ag-4 suspension in water:glycerol solution (curve 1 – 35:65, curve 2– 38:62, curve 3 – 44:56, curve 4 – 47:53, curve 5 – 54:46, curve 6 – 62:38, curve 7 – 70:30, curve 8– 79:21, curve 9 – 89:11). All curves are normalized by the same concentration of the nanoparticles.

n2ΔΦ0

k Leff I0-----------------------=


where ΔΦ0 is the nonlinear phase distortion, k = 2π/λ is the wave vector, I0 is the peakintensity of the laser beam at the focal point, Leff is the effective length of the sample

(2)

where α is the linear absorption coefficient, L is the sample thickness.Nonlinear phase distortion can be empirically determined from normalized trans-

mittance Z-scan curves as

(3)

where S is the aperture transmittance in the linear regime. In our experiments withclosed aperture, the transmittance amounts to 0.07 of the incident beam. In the case ofeclipsing Z-scan, the nonlinear phase distortion is given as

(4)

where S is the fraction blocked by the disk.Figure 5 depicts the concentration dependence of the NLR of the nanoparticles

Ag-3 suspended in water-glycerol solution (curve 1) and in water (curve 2). One cansee a drastic difference between mentioned dependences. Despite the fact that the con-centration of the nanoparticles decreases with diluting of the solutions, the NLR ofAg/water-glycerol suspension rapidly increases. This somewhat unexpected behaviorcan be explained by more favorable thermal lensing conditions in glycerol environmentrather than that in water. Indeed, glycerol possesses substantially lower specific heatcapacity (cp = 2.43 Jg–1K–1) than water (cp = 4.18 Jg–1K–1), which provides fast andeffective heat transfer from Ag nanoparticles to glycerol environment. On the other

Leff1 αL–( )exp–

α-----------------------------------------=

ΔΦ0TpvΔ

0.406 1 S–( )0.27----------------------------------------------≅

ΔΦ0TpvΔ

0.68 1 S–( )–0.44---------------------------------------------≅

1

2–1.0

–2

–3

–4

–5

–6

–70.2 0.6 1.0 1.4 1.8

Nanoparticle concentration [×1010 cm–3]

n 2 [×

10–8

cm

2W

–1]

–0.5

Fig. 5. Nonlinear refraction of Ag-3 NPs suspended in water-glycerol solution (1) and in water (2) forvarious nanoparticle concentrations. Different scale for the curves along y axis is used for clarity.


hand, the refractive index of glycerol (n = 1.47) is higher than that of water (n = 1.33),which also contributes to the increase in the nonlinear refraction. Note also highlynonlinear concentration dependence of n2 for Ag NPs suspended in water-glycerolmixture (curve 1 in Fig. 5). U-like shape of the curve 1 can be explained by the con-tribution of two competitive processes, namely the increase in the glycerol abundancein the mixture and the decreasing in nanoparticles concentration.

Analogous measurements were carried out for two-dimensional arrays of Ag nano-particles self-assembled on glass substrates (samples Ag-1–Ag-3). The sample wasplaced into an empty quartz cuvette. First, Z-scan measurements were done in air en-vironment (n = 1). Later the cuvette was gently poured with water (n = 1.33) usinga syringe. After the measurements the cuvette was evacuated and poured with glycerol(n = 1.47), so the sample did not change its position relatively to the beam. Therefore,all measurements were done at the same spot of the sample. Normalized transmittanceof a two-dimensional array of silver NPs in different environments is shown in Fig. 6.It is worth noting that 2D array placed in liquid (water, glycerol) and in air has an op-posite sign of the nonlinear refraction. Indeed, water and glycerol as well as their mix-ture possess a negative thermo-optic coefficient [27], while air environment possessesa positive one [28].

It was experimentally found that illuminating conditions play a key role in the non-linear-optical response of 2D Ag NPs array, when the latter is placed in air environ-ment. Figure 7 depicts normalized Z-scan transmittance curves for Ag-3 sample underfront (the NPs are exposed directly to the laser beam) and back (laser beam passes glasssubstrate first) illumination. In the former case, the array exhibits lower nonlinear re-fraction (ΔT1pv < ΔT2pv in Eqs. (3) and (4)) in comparison with back illumination con-dition. This phenomenon can be explained by a stronger thermal lensing effect in airrather than that in glass.

Note that the nonlinear refraction n2 is determined, among other parameters, bythe effective thickness Leff of a sample, which in turn is connected with its geometricalthickness (see Equations (1) and (2)). It is not clear however, what geometrical thick-

1 – in air2 – in water3 – in glycerol

1

2

3

2.0

1.5

1.0

0.5

0.0–15 –10 –5 0 5 10 15

Nor

mal

ized

tran

smitt

ance

Z [mm]

Fig. 6. Z-scan transmittance of silver NPs array (sample Ag-3) self-assembled on a glass substrate in air(n = 1), in water (n = 1.33), and in glycerol (n = 1.47).


ness should be taken into account for the calculations of Leff in the case of a single2D layer of nanoparticles. Assuming the thickness to be equal to nanoparticle’s diam-eter (d ≈ 144 nm for Ag-3 sample), the Leff value is unreasonably small. This imme-diately leads to the overestimated value of the nonlinear refraction coefficient n2. Forinstance, the calculations yield n2 = –1.297×10–8 cm2/W for Ag-3 colloid and n2 == –1.47×10–4 cm2/W for 2D array. Apparently, the interaction between the intense la-ser beam and the composite medium (suspension of metal nanoparticles in a liquid)takes place within a finite volume. That means that the nanoparticles surrounding isalso involved in the nonlinear response of such a medium thus increasing the effectivethickness. Let us estimate Leff from following considerations. One can expect an equalnonlinear optical response for the same number of nanoparticles probed by the beameither suspended in water or self-assembled on the surface in water surrounding.According to SEM image analysis, the surface concentration of the nanoparticles forAg-3 array amounts to 1.4×109 cm–2 (see Table 1). Nonlinear refraction for Ag-3 NPsaqueous suspension with the volume concentration of 1.4×109 cm–3 determined fromZ-scan experiments is n2 = –0.73×10–8 cm2/W (curve 2 in Fig. 5). Substituting the de-termined n2 value into Eq. (1), one can find the effective thickness to be Leff ≈ 340 nm,which overlaps nanoparticle’s near-field zone of ~2d [29]. On the other hand, the near--field interaction between the adjacent nanoparticles in a 2D nanoparticle array givesrise to the cooperative surface plasmon mode that manifests itself as an intense narrowabsorption spectral band [23]. Therefore, near-field interactions cannot be neglectedwhen considering nonlinear-optical properties of 2D self-assembled arrays of silvernanoparticles.

4. ConclusionsNonlinear refraction of different composites containing silver nanoparticles was studiedemploying a Z-scan technique. Suspensions of Ag NPs in water and water-glycerol so-lution as well as two-dimensional arrays of the NPs self-assembled on glass substrates

1

2

1.2

1.1

1.0

0.9

0.8

–8 –6 –4 –2 0 4 8

Nor

mal

ized

tran

smitt

ance

Z [mm]2 6

Fig. 7. Normalized Z-scan transmittance of silver NPs array (sample Ag-3) in air environment at differentilluminating conditions: 1 – front illumination, 2 – back illumination.


were investigated. It was found that Ag NP suspensions exhibit negative nonlinear re-fraction, i.e., possess defocusing properties. Concentration of the nanoparticles in thesuspensions was varied by diluting the initial colloids with water or glycerol. The ex-periments reveal a substantial difference in NLR magnitude for the NPs suspended inwater and in glycerol, which is due to more favorable thermal lensing conditions inthe latter case. The estimated effective thickness of a two-dimensional array of self-assembled Ag nanoparticles is twice the nanoparticle’s diameter. Near-fieldinterparticle interactions should be taken into account when considering NLR oftwo-dimensional arrays of Ag NPs.

References

[1] KELLY K.L., CORONADO E., LIN LIN ZHAO, SCHATZ G.C., The optical properties of metal nanoparticles:the influence of size, shape, and dielectric environment, Journal of Physical Chemistry B 107(3), 2003,pp. 668–677.

[2] KREIBIG U., VOLLMER M., Optical Properties of Metal Clusters, Springer-Verlag, Heidelberg, 1995,p. 18.

[3] DOERING W.E., NIE S.M., Single-molecule and single-nanoparticle SERS: examining the roles ofsurface active sites and chemical enhancement, Journal of Physical Chemistry B 106(2), 2002,pp. 311–317.

[4] JENSEN T.R, VAN DUYNE R.P., JOHNSON S.A., MARONI V.A., Surface-enhanced infrared spectroscopy:a comparison of metal island films with discrete and nondiscrete surface plasmons, Applied Spec-troscopy 54(3), 2000, pp. 371–377.

[5] ATWATER H.A., POLMAN A., Plasmonics for improved photovoltaic devices, Nature Materials 9(3),2010, pp. 205–213.

[6] RAY P.C., Size and shape dependent second order nonlinear optical properties of nanomaterials andtheir application in biological and chemical sensing, Chemical Reviews 110(9), 2010, pp. 5332–5365.

[7] FALCÃO-FILHO E.L., DE ARAÚJO C.B., RODRIGUES JR. J.J., High-order nonlinearities of aqueouscolloids containing silver nanoparticles, Journal of the Optical Society of America B 24(12), 2007,pp. 2948–2956.

[8] BHUSHAN B., KUNDU T., SINGH B.P., Two-photon absorption spectrum of silver nanoparticles, OpticsCommunications 285(24), 2012, pp. 5420–5424.

[9] NADJARI H., ABASI AZAD Z., Determining the nonlinear coefficient of gold and silver nano-colloidsusing SPM and CW Z-scan, Optics and Laser Technology 44(5), 2012, pp. 1629–1632.

[10] KARPOV S.V., POPOV A.K., SLABKO V.V., Photochromic reactions in silver nanocomposites witha fractal structure and their comparative characteristics, Technical Physics 48(6), 2003, pp. 749–756.

[11] MIKHEEVA P., SIDOROV A.I., CO2 laser radiation confinement in a composite material containingsilver nanoparticles, Technical Physics Letters 27(9), 2001, pp. 779–780.

[12] GUANG YANG, WEITIAN WANG, YUELIANG ZHOU, HUIBIN LU, GUOZHEN YANG, ZHENGHAO CHEN,Linear and nonlinear optical properties of Ag nanocluster/BaTiO3 composite films, Applied PhysicsLetters 81(21), 2002, pp. 3969–3971.

[13] SCALISI A.A., COMPAGNINI G., D’URSO L., PUGLISI O., Nonlinear optical activity in Ag–SiO2 nano-composite thin films with different silver concentration, Applied Surface Science 226(1–3), 2004,pp. 237–241.

[14] SHEIK-BAHAE M., SAID A.A., VAN STRYLAND E.W., High-sensitivity, single-beam n2 measurements,Optics Letters 14(17), 1989, pp. 955–957.

[15] TINGJIAN JIA, TINGCHAO HE, PENGWEI LI, YUJUN MO, YUTING CUI, A study of the thermal-inducednonlinearity of Au and Ag colloids prepared by the chemical reaction method, Optics and LaserTechnology 40(7), 2008, pp. 936–940.


[16] MEHENDALE S.C., MISHRA S.R., BINDRA K.S., LAGHATE M., DHAMI T.S., RUSTAGI K.C., Nonlinearrefraction in aqueous colloidal gold, Optics Communications 133(1–6), 1997, pp. 273–276.

[17] GANEEV R.A., RYASNYANSKII A.I., KAMALOV SH.R., KODIROV M.K., USMANOV T., Nonlinear opticalparameters of colloidal silver at various stages of aggregation, Technical Physics 72(7), 2002,pp. 889–893.

[18] MOHAN S., LANGE J., GRAENER H., SEIFERT G., Surface plasmon assisted optical nonlinearities ofuniformly oriented metal nano-ellipsoids in glass, Optics Express 20(27), 2012, pp. 28655–28663.

[19] HONG SHEN, BOLIN CHENG, GUOWEI LU, TINGYIN NING, DONGYI GUAN, YUELIANG ZHOU, ZHENGHAO

CHEN, Enhancement of optical nonlinearity in periodic gold nanoparticle arrays, Nanotechnology17(16), 2006, pp. 4274–4277.

[20] OKADA N., HAMANAKA Y., NAKAMURA A., PASTORIZA-SANTOS I., LIZ-MARZÁN L.M., Linear andnonlinear optical response of silver nanoprisms: local electric fields of dipole and quadrupoleplasmon resonances, Journal of Physical Chemistry B 108(26), 2004, pp. 8751–8755.

[21] EVANOFF JR. D.D., CHUMANOV G., Size-controlled synthesis of nanoparticles. 1. “Silver-only”aqueous suspensions via hydrogen reduction, Journal of Physical Chemistry B 108(37), 2004,pp. 13948–13956.

[22] MALYNYCH S., LUZINOV I., CHUMANOV G., Poly(vinyl pyridine) as a universal surface modifier forimmobilization of nanoparticles, Journal of Physical Chemistry B 106(6), 2002, pp.1280–1285.

[23] MALYNYCH S., CHUMANOV G., Light-induced coherent interactions between silver nanoparticles intwo-dimensional arrays, Journal of the American Chemical Society 125(10), 2003, pp. 2896–2898.

[24] CHAPPIE P.B., STAROMLYNSKA J., MCDUFF R.G., Z-scan studies in the thin- and the thick-sample lim-its, Journal of the Optical Society of America B 11(6), 1994, pp. 975–982.

[25] GANEEV R.A., BABA M., RYASNYANSKY A.I., SUZUKI M., KURODA H., Characterization of optical andnonlinear optical properties of silver nanoparticles prepared by laser ablation in various liquids,Optics Communications 240(4–6), 2004, pp. 437–448.

[26] XIA T., HAGAN D.J., SHEIK-BAHAE M., VAN STRYLAND E.W., Eclipsing Z-scan measurement ofλ /104 wave-front distortion, Optics Letters 19(5), 1994, pp. 317–319.

[27] KWANG TAEK KIM, IN SOO KIM, CHERL-HEE LEE, JONGHUN LEE, A temperature-insensitive cladding--etched fiber Bragg grating using a liquid mixture with a negative thermo-optic coefficient, Sensors12(6), 2012, pp. 7886–7892.

[28] CIDDOR P.E., Refractive index of air: new equations for the visible and near infrared, Applied Optics35(9), 1996, pp. 1566–1573.

[29] PINCHUK A.O., SCHATZ G.C., Nanoparticle optical properties: far- and near-field electrodynamiccoupling in a chain of silver spherical nanoparticles, Materials Science and Engineering B 149(3),2008, pp. 251–258.

Received May 6, 2014in revised form May 26, 2014


Optical solitons in birefringent fibers with parabolic law nonlinearity

QIN ZHOU1, 2*, QIUPING ZHU1, ANJAN BISWAS3

1School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, P.R. China

2School of Physics and Technology, Wuhan University, Wuhan, 430072, P.R. China

3Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah-21589, Saudi Arabia


This paper studies the propagation of optical solitons through birefringent fibers with paraboliclaw nonlinearity. The Hamiltonian perturbations that are inter-modal dispersion, self-steepening,third-order dispersion and nonlinear dispersions are taken into account. Both, Riccati equationexpansion method and Jacobian elliptic equation expansion method are used. Finally, analyticalsolutions that are Jacobian elliptic periodic traveling wave solutions, periodic solutions, unboundedsolutions, singular solutions, bright and dark soliton solutions are obtained under several constraintconditions.

Keywords: solitons, parabolic law nonlinearity, birefringent fibers, Jacobian elliptic equation, Riccatiequation.

1. Introduction Optical solitons, the most ideal carriers of information, have important application fea-tures in the optical communications and ultra-fast signal processing systems [1–5].Most of the existing papers mainly focus on the optical solitons in the polarizationpreserving fibers, while there are very few papers that study the optical solitons inthe birefringent fibers [6–14]. So the key idea of this paper is to seek exact soliton so-lutions to the birefringent fibers with Hamiltonian perturbations and parabolic lawnonlinearity.

Birefringence is a natural phenomenon that occurs in optical fibers [6, 8]. The opticalpulse will split into two orthogonally polarized pulses that have different propagationconstants and group velocities, because it is very difficult to have delicate circularlysymmetry for optical fibers [8].

400 QIN ZHOU et al.

In the presence of strong Hamiltonian type perturbations, the governing equationfor the propagation of optical solitons through birefringent fibers with parabolic lawnonlinearity is given by the following Hirota equations:

(1)

(2)

In Equations (1) and (2), the unknown functions q(x, t) and r(x, t) are the opticalwave profiles for the two components in birefringent fibers; x and t represent the spatialand temporal variables, respectively.

For l = 1, 2, the constant parameters al, bl, cl, λ l, sl and γ l are, respectively, the pa-rameters of the group velocity dispersion (GVD), self-phase modulation (SPM), cross--phase modulation (XPM), inter-modal dispersion (IMD), self-steepening and third-or-der dispersion (TOD) for the two polarized pulses. The terms with dl, el, and fl are as-sociated with the quintic terms of the parabolic (cubic-quintic) law nonlinearity [7, 8].Finally, μ l and θ l are the nonlinear dispersions.

The aim of the present work is to construct the Jacobian elliptic periodic travelingwave solutions, periodic solutions, unbounded solutions, singular solutions, singular,bright and dark soliton solutions in the birefringent fibers with Hamiltonian perturba-tions and parabolic law nonlinearity. The strong Hamiltonian type perturbations thatare IMD, self-steepening, TOD and nonlinear dispersions are taken into consideration.The integration methods are the Riccati equation expansion method and Jacobianelliptic equation expansion method. Several constraint conditions for analytical solu-tions to exist are displayed.

In order to obtain exact solutions to Eqs. (1) and (2), making the hypothesis inthe form [6–9]:

(3)

(4)

where η = B(x – vt) and φ l = –κ l x + ω l t +θ l ; Pl(η ) and φ l (x, t) for l = 1, 2 are the am-plitude and phase components of the two solitons, respectively; Al, B and v representthe amplitude, width and velocity of the solitons. Additionally, κ l are frequencies ofthe two solitons, ω l are the wave numbers, while θ l are the phase constants.

iqt a1qxx b1 q 2 c1 r 2+⎝ ⎠⎛ ⎞ q d1 q 4 e1 q 2 r 2 f1 r 4+ +⎝ ⎠

⎛ ⎞ q

iλ1qx is1 q 2q⎝ ⎠⎛ ⎞

xiμ1 q 2

⎝ ⎠⎛ ⎞

xq iθ1 q 2qx iγ1qxxx

+ + + +

+ + + + + 0=

irt a2rxx b2 r 2 c2 q 2+⎝ ⎠⎛ ⎞ r d2 r 4 e2 r 2 q 2 f2 q 4+ +⎝ ⎠

⎛ ⎞ r

iλ2rx is2 r 2r⎝ ⎠⎛ ⎞

xiμ2 r 2

⎝ ⎠⎛ ⎞

xr iθ2 r 2rx iγ2rxxx

+ + + +

+ + + + + 0=

q x t,( ) A1P1 η x t,( ) iφ1 x t,( )exp=

r x t,( ) A2P2 η x t,( ) iφ2 x t,( )exp=

Optical solitons in birefringent fibers... 401

Substituting (3) and (4) into (1) and (2), and separating the real and imaginary parts,respectively, one obtains

(5)

(6)

for l = 1, 2 and = 3 – l.

2. Riccati equation expansion method

Assume that Pl(η) satisfies

(7)

where a and b are the nonzero real constants. Equation (7) is the famous Riccati equa-tion [15–17], the solutions of which are listed in Table 1.

Substituting the assumption (7) into Eqs. (5) and (6) yields

(8)

(9)

ωl λlκl– alκl2 γlκl

3+ +⎝ ⎠⎛ ⎞ Pl– cl Al

2Pl Pl2 dl Al

4Pl5 el Al

2 Al2 Pl

3 Pl2

fl Al4 Pl P

l4 bl slκl θlκl+ +( )Al

2Pl3 al 3γlκl+( )B2Pl''

+ + + +

+ + + 0=

λl 2alκl– 3γlκl2– v–⎝ ⎠

⎛ ⎞ Pl' 3sl 2μl θl+ +( ) Al2 Pl

2 Pl' γl B2Pl'''+ + 0=

l

Pl' η( ) a bPl2 η( )+=

T a b l e 1. Solutions to the Riccati equation (7).

ab > 0

ab < 0

Pl η( )abb

------------- ab η( )tan=

Pl η( )abb

-------------– ab η( )cot=

Pl η( )a– bb

----------------– a– b η( )tanh=

Pl η( )a– bb

----------------– a– b η( )coth=


3+ +⎝ ⎠⎛ ⎞ Pl– cl Al

2Pl Pl2 dl Al

4Pl5 el Al

2 Al2 Pl

3 Pl2

fl Al4 Pl Pl

4 bl slκl θlκl+ +( )Al2Pl

3 al 3γlκl+( )B2 2abPl 2b2Pl3+⎝ ⎠

⎛ ⎞

+ + + +

+ + + 0=


⎛ ⎞ a bPl2+⎝ ⎠

⎛ ⎞ 3sl 2μl θl+ +( ) Al2 Pl

2 a bPl2+⎝ ⎠

⎛ ⎞

γl B2 2a2b 8ab2Pl2 6b3Pl

4+ +⎝ ⎠⎛ ⎞

+ +

+ 0=

402 QIN ZHOU et al.

Then using the homogeneous balance principle, from Eqs. (8) and (9), setting the co-efficients of each power of Pl(η) to zero gives:

(10)

(11)

(12)

(13)

(14)

(15)

It needs to be noted that upon equating the two values of the solitons velocitiesfrom (13) and (14) also yields the same relation as given by (15).

Equating the two values of the soliton velocity v, for l = 1, 2, from Eq. (13) givesthe width of the soliton as

(16)

which introduces the constraint condition

(17)

From Eq. (15), the amplitude of the solitons are given by

(18)

with the constraint condition

(19)

Additionally, Equations (11) and (12) pose other two constraint conditions that aregiven by

ωl λlκl alκl2– γlκl

3– 2ab al 3γlκl+( )B2+=

bl slκl θlκl+ +( ) Al2 2b2 al 3γlκl+( )B2 cl Al

2+ + 0=

dl Al4 el Al

2Al2 fl Al

4+ + 0=

v λl 2alκl– 3γlκl2– 2abγl B2+=

v λl 2alκl– 3γlκl2– 8abγl B2 a 3sl 2μl θl+ +( )

b-----------------------------------------------Al

2+ +=

3sl 2μl θl+ +( ) Al2 6b2γl B2+ 0=

Bλl λ

l–( ) 2 alκl a

lκ

l–( )– 3 γlκl

2 γlκ

l2–( )–

2ab γl γl–( )------------------------------------------------------------------------------------------------------------------

1/2

=

ab γl γl

–( ) λl λl

–( ) 2 alκl alκ

l–( )– 3 γlκl

2 γlκ

l2–( )– 0>

Al

3bγl λl λl

–( ) 2 alκl alκ

l–( )– 3 γlκl

2 γlκ

l2–( )–

a 3sl 2μl θl+ +( ) γl γl–( )----------------------------------------------------------------------------------------------------------------------------------–

⎩ ⎭⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪⎪ ⎪⎧ ⎫1/2

=

γl 3sl 2μl θl+ +( ) 0<


(20)

(21)

Hence, finally the singular solutions, dark and singular soliton solutions for the bi-refringent fibers with parabolic law nonlinearity are obtained, which are listed as fol-lows.

Case 1 – when ab > 0, Eqs. (1) and (2) admit the singular periodic solutions thatare given by

(22)

(23)

(24)

(25)

Case 2 – when ab < 0, Eqs. (1) and (2) admit the dark soliton solutions that aregiven by

(26)

(27)

and the singular soliton solutions that are given by

(28)

(29)

where the amplitude and width of the solitons are given by Eqs. (18) and (16) respec-tively, while the velocity of the solitons are given by Eq. (13) or (14) and finally

3γl bl slκl θlκl+ +( )3sl 2μl θl+ +

-------------------------------------------------------3clγl

3sl 2μl θl+ +------------------------------------------+ al 3γl κl+=

dlγl2

3sl 2μl θl+ +( )2-----------------------------------------

elγl γl

3sl 2μl θl+ +( ) 3sl 2μl θl+ +( )----------------------------------------------------------------------------------

flγl2

3sl

2μl

θl

+ +( )2---------------------------------------------+ + 0=

q x t,( ) abb

------------A1 ab B x vt–( ) i κ1x– ω1t θ1+ +( )exptan=

r x t,( ) abb

------------A2 ab B x vt–( ) i κ2x– ω2t θ2+ +( )exptan=

q x t,( ) abb

------------– A1 ab B x vt–( )cot i κ1x– ω1t θ1+ +( )exp=

r x t,( ) abb

------------– A2 ab B x vt–( )cot i κ2x– ω2t θ2+ +( )exp=

q x t,( ) a– bb

----------------– A1 a– b B x vt–( )tanh i κ1x– ω1t θ1+ +( )exp=

r x t,( ) a– bb

----------------– A2 a– b B x vt–( )tanh i κ2x– ω2t θ2+ +( )exp=

q x t,( ) a– bb

----------------– A1 a– b B x vt–( )coth i κ1x– ω1t θ1+ +( )exp=

r x t,( ) a– bb

----------------– A2 a– b B x vt–( )coth i κ2x– ω2t θ2+ +( )exp=

404 QIN ZHOU et al.

the wave numbers are given by Eq. (10). The constraint conditions for analytical so-lutions to exist are given by Eqs. (17) and (19)–(21).

3. Jacobian elliptic equation expansion method

Assume that Pl (η ) satisfies

(30)

where g0, g2 and g4 are the nonzero real constants. Eq. (30) is Jacobian elliptic equation,the solutions of which are listed in [2, 18–20].

Substituting the assumption (30) into Eqs. (5) and (6) yields

(31)

(32)

Then using the homogeneous balance principle, from Eqs. (31) and (32), settingthe coefficients of each power of Pl (η ) to zero gives

(33)

(34)

(35)

(36)

(37)

(38)

It needs to be noted that equating the two values of the solitons velocities from (36)and (37) also yields the same relation as given by (38).

Pl'2 η( ) g0 g2 Pl

2 η( ) g4 Pl4 η( )+ +=


3+ +⎝ ⎠⎛ ⎞Pl– cl Al

2Pl Pl2 dl Al

4Pl5 el Al

2 Al2 Pl

3Pl2

fl Al4 Pl P

l4 bl slκl θlκl+ +( )Al

2Pl3 al 3γlκl+( )B2 g2Pl 2g4Pl

3+⎝ ⎠⎛ ⎞

+ + + +

+ + + 0=


⎛ ⎞2 2 λl 2alκl– 3γlκl2– v–⎝ ⎠

⎛ ⎞ 3sl 2μl θl+ +( ) Al2 Pl

2

3sl 2μl θl+ +( )2Al4Pl

4

+ +

+ γl2B4 g2 6g4Pl

2+⎝ ⎠⎛ ⎞2

=

ωl g2 al 3γlκl+( )B2 λlκl alκl2– γlκl

3–+=

bl slκl θlκl+ +( ) Al2 cl A

l2 2g4 al 3γlκl+( )B2+ + 0=

dl Al4 el Al

2Al2 fl Al

4+ + 0=

v λl 2alκl– 3γlκl2– g2γl B2+=

v λl 2alκl– 3γlκl2–

6g2g4γl2B4

3sl 2μl θl+ +( )Al2

---------------------------------------------------–=

3sl 2μl θl+ +( ) Al2 6g4γl B2=

Optical solitons in birefringent fibers...

405

T a b l e 2. Jacobian elliptic periodic traveling wave solutions to Eqs. (1) and (2).

T a b l e 3. Trigonometric periodic solutions to Eqs. (1) and (2).

g0 g2 g4 q(x, t) r (x, t )

λ2E 2 –λ2(1 + m2) λ2m2/E 2

λ2E 2(1 – m2) λ2(2m2 – 1) –λ2m2/E 2

–λ2E 2(1 – m2) λ2(2 – m2) –λ2/E 2

λ2m2E 2 –λ2(1 + m2) λ2/E 2

–λ2m2E 2 λ2(2m2 – 1) λ2(1 – m2)/E 2

–λ2E 2 λ2(2 – m2) –λ2(1 – m2)/E 2

λ2E 2 λ2(2 – m2) λ2(1 – m2)/E 2

λ2E 2 λ2(2m2 – 1) –λ2m2(1 – m2)/E 2

λ2E 2(1 – m2) λ2(2 – m2) λ2/E 2

λ2E 2 –λ2(1 + m2) λ2m2/E 2

–λ2m2(1 – m2)E 2 λ2(2m2 – 1) λ2/E 2

λ2m2E 2 –λ2(1 + m2) λ2/E 2

g0 g2 g4 q (x, t) r(x, t )

λ2E 2 –λ2 0

λ2E 2 –λ2 0

EA1sn λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2sn λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1cn λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2cn λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1dn λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2dn λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1ns λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2ns λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1nc λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2nc λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1nd λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2nd λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1sc λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2sc λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1sd λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2sd λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1cs λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2cs λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1cd λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2cd λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1ds λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2ds λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1dc λB x vt–( ) i κ1x– ω1t θ1+ +( )exp EA2dc λB x vt–( ) i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )sin i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )sin i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )cos i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )cos i κ2x– ω2t θ2+ +( )exp

406Q

IN ZH

OU et al.

T a b l e 4. Unbounded solutions to Eqs. (1) and (2).

T a b l e 5. Singular periodic solutions to Eqs. (1) and (2).

T a b l e 6. Singular, dark and bright soliton solutions to Eqs. (1) and (2).

g0 g2 g4 q(x, t) r(x, t )

–λ2E 2 λ2 0

λ2E 2 λ2 0

g0 g2 g4 q (x, t ) r(x, t)

0 –λ2 λ2/E 2

0 –λ2 λ2/E 2

λ2E 2 2λ2 λ2/E 2

λ2E 2 2λ2 λ2/E 2

g0 g2 g4 q (x, t ) r (x, t)

λ2E 2 –2λ2 λ2/E 2

0 λ2 λ2/E 2

λ2E 2 –2λ2 λ2/E 2

0 λ2 –λ2/E 2

EA1 λB x vt–( )cosh i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )cosh i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )sinh i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )sinh i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )csc i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )csc i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )sec i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )sec i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )tan i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )tan i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )cot i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )cot i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )coth i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )coth i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )csch i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )csch i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )tanh i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )tanh i κ2x– ω2t θ2+ +( )exp

EA1 λB x vt–( )sech i κ1x– ω1t θ1+ +( )exp EA2 λB x vt–( )sech i κ2x– ω2t θ2+ +( )exp


Equating the two values of the soliton velocity v, for l = 1, 2, from Eq. (36) givesthe width of the soliton as

(39)

which poses the constraint condition

(40)

From Eq. (38), the amplitudes of the solitons are given by

(41)

with the constraint condition

(42)

Additionally, Equations (34) and (35) pose other two constraint conditions that aregiven by

(43)

(44)

Hence, finally the explicit Jacobian elliptic periodic traveling wave solutions forthe birefringent fibers with parabolic law nonlinearity are constructed (see Table 2).The amplitude and width of the solitons are given by Eqs. (41) and (39), respectively,while the velocity of the solitons are given by Eq. (36) or (37) and finally the wavenumbers are given by Eq. (33). The constraint conditions for analytical solutions toexist are given by Eqs. (40) and (42)–(44).

It needs to be noted that when the modulus m = 0 and m = 1, the Jacobian ellipticperiodic traveling wave solutions become trigonometric periodic solutions (see Table 3),unbounded solutions (see Table 4), singular solutions (see Table 5), singular, brightand dark soliton solutions (see Table 6).

Bλl λl–( ) 2 alκl al κl–( )– 3 γlκl

2 γl κl2–( )–

g2 γl γl

–( )------------------------------------------------------------------------------------------------------------------

1/2

=

g2 γl γl–( ) λl λl–( ) 2 alκl al κl–( )– 3 γlκl2 γl κl

2–( )– 0>

Al

6g4γl λl λl–( ) 2 alκl al κl–( )– 3 γlκl2 γl κl

2–( )–

g2 3sl 2μl θl+ +( ) γl γl–( )---------------------------------------------------------------------------------------------------------------------------------

⎩ ⎭⎪ ⎪⎪ ⎪⎨ ⎬⎪ ⎪⎪ ⎪⎧ ⎫1/2

=

g4γl 3sl 2μl θl+ +( ) 0>

3γl bl slκl θlκl+ +( )3sl 2μl θl+ +

-------------------------------------------------------3clγl

3sl 2μl θl+ +------------------------------------------ al 3γl κl+( )+ + 0=

dlγl2

3sl 2μl θl+ +( )2-----------------------------------------

elγl γl

3sl 2μl θl+ +( ) 3sl 2μl θl+ +( )----------------------------------------------------------------------------------

flγl2

3sl

2μl

θl

+ +( )2---------------------------------------------+ + 0=

408 QIN ZHOU et al.

4. Conclusion

The Hirota equation, describing the propagation of optical solitons through birefrin-gent fibers with Hamiltonian perturbations and parabolic law nonlinearity, is studiedanalytically by employing the Riccati equation expansion method and Jacobian ellipticequation expansion method. We report the Jacobian elliptic periodic traveling wavesolutions, periodic solutions, unbounded solutions, singular solutions, singular, brightand dark soliton solutions. We obtain the constraint conditions for these solutions toexist.

Acknowledgements – The work of the second author (Q.P. Zhu) was supported by the Scientific ResearchFund of Hubei Provincial Education Department under Grant No. B2013193.

References

[1] BISWAS A., KONAR S., Introduction to Non-Kerr Law Optical Solitons, Boca Raton, FL, 2006. [2] QIN ZHOU, DUANZHENG YAO, XIAONA LIU, FANG CHEN, SIJING DING, YAFANG ZHANG, FENG CHEN,

Exact solitons in three-dimensional weakly nonlocal nonlinear time-modulated parabolic law media,Optics and Laser Technology 51, 2013, pp. 32–35.

[3] QIN ZHOU, DUANZHENG YAO, FANG CHEN, WEIWEI LI, Optical solitons in gas-filled, hollow-corephotonic crystal fibers with inter-modal dispersion and self-steepening, Journal of Modern Optics60(10), 2013, pp. 854–859.

[4] AGRAWAL G.P., Nonlinear Fiber Optics, New York, 2007. [5] PAN WANG, BO TIAN, YAN JIANG, YU-FENG WANG, Integrability and soliton solutions for an inhomo-

geneous generalized fourth-order nonlinear Schrödinger equation describing the inhomogeneousalpha helical proteins and Heisenberg ferromagnetic spin chains, Physica B: Condensed Matter 411,2013, pp. 166–172.

[6] SAVESCU M., ALSHAERY A.A., BHRAWY A.H., HILAL E.M., MORARU L., BISWAS A., Optical solitonsin birefringent fibers with coupled Hirota equation and spatio-temporal dispersion, Wulfenia 21(1),2014, pp. 35–43.

[7] MILOVIĆ D., BISWAS A., Bright and dark solitons in optical fibers with parabolic law nonlinearity,Serbian Journal of Electrical Engineering 10(3), 2013, pp. 365–370.

[8] BHRAWY A.H., ALSHAERY A.A., HILAL E.M., SAVESCU M., MILOVIĆ D., KHAN K.R., MAHMOOD M.F.,JOVANOSKI Z., BISWAS A., Optical solitons in birefringent fibers with spatio-temporal dispersion,Optik – International Journal for Light and Electron Optics 125(17), 2014, pp. 4935–4944.

[9] BISWAS A., KHAN K.R., RAHMAN A., YILDIRIM A., HAYAT T., ALDOSSARY O.M., Bright and darkoptical solitons in birefringent fibers with Hamiltonian perturbations and Kerr law nonlinearity,Journal of Optoelectronics and Advanced Materials 14(7–8), 2012, pp. 571–576.

[10] MENYUK C.R., Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,Optics Letters 12(8), 1987, pp. 614–616.

[11] BARAD Y., SILBERBERG Y., Polarization evolution and polarization instability of solitons in a bire-fringent optical fiber, Physical Review Letters 78(17), 1997, p. 3290.

[12] MANI RAJAN M.S., HAKKIM J., MAHALINGAM A., UTHAYAKUMAR A., Dispersion management andcascade compression of femtosecond nonautonomous soliton in birefringent fiber, The EuropeanPhysical Journal D 67(7), 2013, article 150.

[13] YAN JIANG, BO TIAN, WEN-JUN LIU, KUN SUN, PAN WANG, Mixed-type solitons for the coupled higher--order nonlinear Schrödinger equations in multi-mode and birefringent fibers, Journal of ModernOptics 60(8), 2013, pp. 629–636.


[14] ISLAM M.N., POOLE C.D., GORDON J.P., Soliton trapping in birefringent optical fibers, Optics Letters14(18), 1989, pp. 1011–1013.

[15] VITANOV N.K., Application of simplest equations of Bernoulli and Riccati kind for obtaining exacttraveling-wave solutions for a class of PDEs with polynomial nonlinearity, Communications inNonlinear Science and Numerical Simulation 15(8), 2010, pp. 2050–2060.

[16] QI WANG, YONG CHEN, HONGQING ZHANG, A new Riccati equation rational expansion method andits application to (2+1)-dimensional Burgers equation, Chaos, Solitons and Fractals 25(5), 2005,pp. 1019–1028.

[17] ZHENYA YAN, The Riccati equation with variable coefficients expansion algorithm to find moreexact solutions of nonlinear differential equations, Computer Physics Communications 152(1),2003, pp. 1–8.

[18] BELIĆ M., PETROVIĆ N., WEI-PING ZHONG, RUI-HUA XIE, GOONG CHEN, Analytical light bulletsolutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation, Physical ReviewLetters 101(12), 2008, article 123904.

[19] QIN ZHOU, DUANZHENG YAO, FANG CHEN, Analytical study of optical solitons in media with Kerr andparabolic-law nonlinearities, Journal of Modern Optics 60(19), 2013, pp. 1652–1657.

[20] QIN ZHOU, DUAN-ZHENG YAO, ZHIHAI CUI, Exact solutions of the cubic-quintic nonlinear opticaltransmission equation with higher-order dispersion terms and self-steepening term, Journal ofModern Optics 59(1), 2012, pp. 57–60.

Received June 10, 2014in revised form July 17, 2014


Optical generation of ultra-wideband signals with a reconfigurable spectral notch-band

PENG XIANG*, YINFANG CHEN, DALEI CHEN, JIYONG ZHAO

College of Communications Engineering, PLA University of Science and Technology, 210007, Nanjing, China


A novel method for optical generation of ultra-wideband signals with a reconfigurable spectralnotch-band is proposed. In the proposed system, ultra-wideband signals are generated in the opticaldomain and an optical tunable delay line is deployed to introduce a notch-band to the spectralprofile of the generated ultra-wideband signals, which can effectively avoid the signal interferencebetween ultra-wideband signals and pre-planned narrowband wireless signals used in wireless localarea networks (WLAN). A theoretical model describing the proposed system is derived; the opticalgeneration and fiber transmission of ultra-wideband signals with a reconfigurable notch-band aredemonstrated via computer simulations.

Keywords: ultra-wideband (UWB), ultra-wideband over fiber, notch-band, interference avoidance.

1. IntroductionUltra-wideband (UWB) has attracted a lot of attention due to its potential applicationsin a wide variety of fields such as high speed wireless communication systems, per-sonal area networks, sensor networks and radar systems [1]. It is well-known thatthe UWB signals are regulated by the Federal Communications Commission (FCC) ofthe United States in the frequency range of 3.1–10.6 GHz band (i.e., baseband) and22–29 GHz band (i.e., millimeter-wave band) for short range communications and ve-hicular radar respectively [2]. One of the key concerns in the application of UWB tech-nology is the generation of UWB signals that satisfy the FCC specified spectral mask.In recent years, photonic generation of UWB signals has attracted extensive researchinterests due to the advantages offered by modern photonics such as low loss, highbandwidth and immunity to electromagnetic interference. More importantly, photonicgeneration of UWB signals can provide good compatibility with the UWB-over-fibertechnology, which is widely regarded as a promising solution to enable UWB wirelessreach extension [3].

In the past few years, optical generation of UWB signals, both in baseband andmillimeter-wave band, has attracted great research interests [2–8]. And all of the ex-

412 PENG XIANG et al.

iting works demonstrated optical generation of UWB signals with spectral profile sat-isfying the FCC spectral mask. However the issue about interference avoidancebetween UWB signals and other pre-planned narrowband wireless signals has not beenfully addressed in these works. UWB signals, especially in baseband (3.1–10.6 GHz),can unavoidably overlap with the pre-planned narrowband radio signals such as the veryprevalent wireless fidelity (Wi-Fi) signals used in WLAN, which typically operates inthe frequency band around 5 GHz [9]. In order to realize the interference avoidancebetween the UWB and Wi-Fi signals, electronic UWB filters and antennas with narrownotch-band around 5 GHz were designed and fabricated [10, 11]. However, theseelectronic components usually have a fixed notch-band and lack of tunability, whichlimits their usage in more complicated environment. In UWB over fiber systems,the interference avoidance issue is highly desirable to be addressed in the optical do-main, to fully explore the advantages offered by modern photonics. Very recently,a band-notched UWB pulse generator has been proposed based on a nonlinear operatedpolarization-to-intensity converter [12]. Microwave photonic filtering and a notch--band were introduced in the generated UWB power spectra to realize the interferenceavoidance.

In this paper, a novel method to generate baseband UWB signals with a reconfig-urable spectral notch-band in the optical domain is proposed. The proposed methodcan generate UWB signals with an expected spectral notch-band around 5 GHz, withits power spectrum matching with FCC spectral mask. And the notch-band can be flex-ibly turned in a wide frequency range. The proposed method is verified via both math-ematical models and computer simulations.

2. Principle and theoretical analysisFigure 1 shows the schematic diagram of the proposed system, which consists of a laserdiode (LD), a polarization modulator (PolM), an optical bandpass filter (OBPF), a tun-

Fig. 1. Schematic diagram of the proposed UWB signal generation system. LD – laser diode, PolM – po-larization modulator, OBPF – optical bandpass filter, PBS – polarization beam splitter, PBC – polarizationbeam combiner, PC – polarization controller, TODL – tunable optical delay line, PD – photodetector;insert – ideal response of an OBPF.

H(ω)

ωL – Δω ωL ωH ωH + Δωω

LDPC1

PolM OBPFPC2

TODL

PBS PBC PD

Gaussian pulses Fiber transmission

GeneratedUWB signal

Optical generation of ultra-wideband signals... 413

able optical delay line (TODL), two polarization controllers (PC), a polarization beamsplitter (PBS) and a polarization beam combiner (PBC).

A light wave from the LD is sent to the PolM which is driven by an electronicGaussian pulse source. The PolM is a special phase modulator that can support bothTE (transverse electronic) and TM (transverse magnetic) modes with however oppositephase modulation indices [13].When a linearly polarized incident light is oriented withan angle of 45° to one principal axis of the PolM, complementary phase modulatedoptical fields at the output of the PolM along the two principal axes can be expressed as

(1)

where ωc is the angular frequency of the optical carrier, β is the phase modulation in-dex, and ϕ (t) is the modulating (driving) signal.

The frequency response of an OBPF can be modeled as trapezium shape with twolinear slopes, as shown in the insert of Fig. 1. Mathematically, its response can be writ-ten as [3]:

(2)

where K is the slope of the filter (K > 0). If the phase modulated optical signal fromPolM has a narrow bandwidth and the optical carrier is properly selected to be locatedat one of the linear slope, the impulse response of this OBPF can be approximated as:

(3)

where the group delay derived from the linear phase response is neglected, δ (t) isthe unit impulse, and δ '(t) is the first-order derivative of the unit impulse. Afterthe signals from PolM passing through the OBPF, the phase modulated optical signalsalong two polarization axes will be converted into intensity modulated optical signals.Assuming the optical signals are located at the left-slope of the OBPF, then the opticalfields outputing from the OBPF can be expressed as:

(4)

Ex t( )

Ey t( )jωc( )

jβϕ t( )exp

j– βϕ t( )expexp=

H ω( )

Kω K ω L ωΔ–( ),– ω L ωΔ– ω ω L≤ ≤

K ω ,Δ ω L ω ωH≤ ≤

K ωH ωΔ+( ) Kω ,– ωH ω ωH ωΔ+≤ ≤⎩⎪⎨⎪⎧

=

h t( )

K– ω L ωΔ–( )δ t( ) jKδ' t( ),– left slope

K ωδ t( ),Δ centerK ωH ωΔ+( )δ t( ) jKδ ' t( ),+ right slope⎩

⎪⎨⎪⎧

=

ex1 t( )

ey1 t( )

Ex t( )

Ey t( )*hleft slope t( )

Ex t( ) K ω c ωL ωΔ+–( ) Kβϕ ' t( )+

Ey t( ) K ω c ωL ωΔ+–( ) Kβϕ' t( )–≈=


where * denotes the convolution operation, and ϕ '(t) is the first-order derivative ofthe modulating signal ϕ (t). It can be seen from Eq. (4), when ϕ (t) is selected asGaussian pulse, its first-order derivative, namely UWB monocycle shaped signals inthe optical domain, can be acquired along both polarization axes.

Next, these two orthogonally polarized signal components are separated by a PBSand sent to its two outputs, with one component delayed by an TODL. Then they arecombined by a PBC with their polarization state maintained, which can be written as

(5)

The signals are fed to a PD for optical-to-electrical conversion. Since these twosignal components are orthogonally polarized, the problem associated with coherenceinterference in PD detection is avoided, and the photocurrent at the output of the PDcan be written as

(6)

Note that in Eq. (6), the DC (direct current) and quadratic terms are neglected.The quadratic terms are usually very small compared with their linear counterpart un-der the assumption of small-signal modulation. And the DC component can be elimi-nated easily by a DC blocker. Therefore, the generated radio-frequency signals havea power spectral density (PSD) profile as follows:

(7)

where F [ϕ '(t)] is the Fourier transform of ϕ '(t), and has a spectral shape of monocyclesignals, as inferred from Eq. (4). As can be seen from Eq. (7), the system outputRF signals show a PSD profile of UWB monocycle signals multiplied by a cosine-basedfunction. Since a cosine function is periodic, notch-bands are introduced to the signalspectrum, with a frequency spacing determined by Δ fnotch = 1/τ, which can be easilyreconfigured by turning the TODL. It is very straightforward to choose the notch-bandat fnotch = 1/τ to be the expected spectral notch for the generated UWB signals.

3. Simulation results and discussionsFigure 2 shows the simulation model of the proposed optical UWB signal generationsystem using a commercial software package Virtual Photonic Incorporation (VPI)Transmission maker. The simulation model is based on the schematic diagram inFig. 1, where the light wave from the LD is sent to the PolM with its polarization stateoriented with an angle of 45° to one principal axis of the PolM. Its center wavelengthis adjusted to match the left slope of the OBPF frequency response. An electronic pulse

ex2 t( )

ey2 t( )

ex1 t( )

ey1 t τ–( )=

iPD ex2 t( ) 2 ey2 t( ) 2+ PK 2 ω c ωL ωΔ+–( )β ϕ ' t( ) ϕ ' t τ–( )–∝=

Sout f( ) F ϕ ' t( )2

1 2π f τ( )cos–∝


source which generates Gaussian pulses with a full-width at half-maximum (FWHM)pulsewidth of 60 ps is used to drive the PolM.

Firstly, optical generation of UWB signals with a notch-band located at 5 GHz isdemonstrated by the simulation, where the TODL induced delay is set as τ = 200 ps.Figure 3 shows the generated UWB signals and their power spectrum. The power spec-trum peak is controlled to be –41.3 dBm by properly adjusting the LD output power,and compared with the FCC spectral mask.

As can be seen from Fig. 3a, the power spectrum of the generated UWB signal hasan obvious notch-band at 5 GHz, and can fit into the FCC mask well. The notch-band

LD PC1

Data Gaussian pulses

PolM OBPF PC2 PBS

TODL

PBC EDFA

Fiber

PD DC block

transmission

Fig. 2. Simulation model of the proposed system.

FCC mask

–40

–80

–120

0 5 10 15 20

0.4

0.2

0.0

–0.2

–0.4

–300 –200 –100 0 100 200 300

Pow

er [d

Bm

]

Frequency [GHz]

Time [ps]

Rel

ativ

e am

plitu

de

a

b

Fig. 3. The generated UWB signals with a spectral notch-band at 5GHz. Signal power spectrum (a), andUWB signal waveform (b).

Notch depth >35 dB at 5 GHz


depth reaches more than 35 dB calculated from the spectral peak, which can signifi-cantly reduce the signal interference between UWB and Wi-Fi signals. As seen fromFig. 3b, the generated UWB signal is composed of two polarity reversed monocycles,which can be explained by Eq. (6).

Secondly, the tunability of the notch-band in the generated UWB signal spectrumis demonstrated, where 5 frequency locations are chosen, namely: 4.5, 5.15, 5.8, 6.5,and 8 GHz. Accordingly, in these cases the time delay is set as 222, 194, 172, 154 and125 ps, respectively. The simulation results are shown in Fig. 4.

As can be seen from Fig. 4a, the tuning of the expected notch-band in the generatedUWB signal spectrum is successfully realized. Therefore the interference betweenUWB signals and other narrowband signals, including WLAN signals located at5.1–5.8 GHz [10], can be avoided in a flexible manner.

In practical systems, the frequency tuning range and the precision of the spectralnotch-band are determined by the time delay tuning range and the step size of the de-ployed TODL. Since TODL with a tuning range of 0–600 ps and a step size of less than1 ps is commercially available, accurate frequency tuning of the expected notch-bandwithin the total frequency band of UWB signals (namely 3.1–10.6 GHz) can be realized.

It is also noticed from Fig. 4a that when the expected notch-band is set at 4.5 GHz(τ = 222 ps), a second notch-band around 9 GHz will also be induced in the UWB pow-er spectrum due to the periodicity of the notches as indicated in Eq. (7). Indeed, mul-tiple notch-bands can be possibly introduced to UWB power spectrum when the timedelay is set as τ > 200 ps. However this may lead to unwanted notch-bands.

Figure 4b shows the corresponding UWB signal waveform when the time delay τis set as 222, 194, 172, 154 and 125 ps, respectively. As can be seen, the generatedUWB signal waveforms have longer time duration when τ is larger. The time durationof the generated UWB signals increases from 490 to 586 ps, as is increased from 125to 222 ps.

For a practical UWB over fiber system, the generated UWB signals are usuallyrequired to be coded and transmitted over a distance of an optical fiber link [14]. Inthe third simulation scenario, the generated UWB signals are on-off-keying (OOK)coded by coding the electronic Gaussian pulse source, and transmitted over a span ofan fiber-optic link. The transmission fiber is a span of polarization maintain fiber,which can be inserted before the PD in the system as indicated in the dashed box shownin Figs. 1 and 2. The simulation results are shown in Fig. 5, where the fiber link lengthis set as 0, 10 and 30 km. Signal bit rate is set as 1 Gbps, and pseudorandom binarysequence (PRBS) bit pattern is used. The signal spectral notch-band is chosen asfnotch = 5 GHz to avoid interference with Wi-Fi signals, and an erbium-doped fiberamplifier (EDFA) is deployed to compensate the fiber transmission loss.

As seen from Fig. 5a, the expected notch-band at 5 GHz remains after signal codingand fiber transmission. Discrete spectral lines with a frequency spacing of 1 GHz ap-pear on the UWB signal power spectrum, which is corresponding to the bit rate of

Optical generation of ultra-w

ideband signals... 417

FCC mask

–40

–80

–120

0 5 10 15 20

Pow

er [d

Bm

]

Frequency [GHz]

a0.4

0.2

0.0

–0.2

–0.4

–300 –200 –100 0 100 200 300Time [ps]

Rel

ativ

e am

plitu

de

b

fnotch [GHz]4.5

τ [ps]125154171194222

Fig. 4. Frequency tuning of expected spectral notch-band of UWB signals. Signal power spectrum (a), and UWB signal waveform (b).

0 km trans–40

–80

–120

0 5 10 15 20

Pow

er [d

Bm

]

Frequency [GHz]

a

0.4

0.2

0.0

–0.2

–0.4

0 2 4 6 8Time [ns]

Rel

ativ

e am

plitu

de

b

Fig. 5. The OOK coded UWB signals after 0, 10 and 30 km fiber transmission (trans). Signal power spectrum (a), and UWB signal waveform (b).

10 km trans30 km trans

0 km trans10 km trans30 km trans

5.155.86.58

1 1 1 0 1 0 0 1


1 Gbps. These spectral lines can interfere with the notch-band of UWB spectrum ifone of them happens to reach the notch-band frequency. This may weaken the inter-ference avoidance function of the expected notch-band at 5 GHz. This problem can beeasily eliminated by properly choosing the system bit rate, such as 2 Gbps [15],781 Mbps [16], etc., so that the spectral lines never overlap with the spectral notch-band.

As seen from Fig. 5b, the generated UWB signals suffer some minor distortionsdue to the fiber dispersion. Proper dispersion compensation techniques can be used tosolve this problem. However, as indicated by the simulation results, when the fibertransmission distance is not very long (such as less than 10 km, typically the case forindoor application [2]), dispersion compensation may not be necessary.

In the proposed system, the coding processes are relatively independent ofthe UWB signal generation, so other coding schemes such as pulse-amplitude-modu-lation (PAM) and pulse-position-modulation (PPM) can also be easily implementedby properly coding the Gaussian pulse source.

4. Conclusion A novel method for the generation of UWB signals with a reconfigurable notch-bandin the optical domain is proposed and simulatively demonstrated. The notch-band canbe widely tuned within the UWB spectrum by properly adjusting the TODL in the sys-tem, which can effectively realize the interference avoidance between UWB signalsand existing narrowband radio signals, such as Wi-Fi signals used in WLAN systems.The proposed system can effectively exploit the benefits offered by modern photonics,and has great potential for application in UWB over fiber systems.

Acknowledgements – This work is supported by Jiangsu Province Natural Science Foundation undergrant BK20140069 and National Nature Science Foundation of China (NSFC) under grant No. 61032005.

References

[1] PORCINO D., HIRT W., Ultra-wideband radio technology: potential and challenges ahead, IEEE Com-munications Magazine 41(7), 2003, pp. 66–74.

[2] WEI LI, WEN TING WANG, WEN HUI SUN, JIAN GUO LIU, NING HUA ZHU, Generation of FCC-compliantand background-free millimeter-wave ultrawideband signal based on nonlinear polarization rotationin a highly nonlinear fiber, Optics Express 22(9), 2014, pp. 10351–10358.

[3] JIANPING YAO, FEI ZENG, QING WANG, Photonic generation of ultrawideband signals, Journal ofLightwave Technology 25(11), 2007, pp. 3219–3235.

[4] WEI LI, WEN TING WANG,WEN HUI SUN, LI XIAN WANG, NING HUA ZHU, Photonic generation ofbackground-free millimeter-wave ultra-wideband pulses based on a single dual-drive Mach–Zehndermodulator, Optics Letters 39(5), 2014, pp. 1201–1203.

[5] MING-JIANG ZHANG, TIE-GEN LIU, AN-BANG WANG, JIAN-YU ZHENG, LI-NA MENG, ZHAO-XIA ZHANG,YUN-CAI WANG, Photonic ultrawideband signal generator using an optically injected chaoticsemiconductor laser, Optics Letters 36(6), 2011, pp. 1008–1010.

[6] YUAN YU, JIANJI DONG, XIANG LI, XINLIANG ZHANG, Ultra-wideband generation based on cascadedMach–Zehnder modulators, IEEE Photonics Technology Letters 23(23), 2011, pp. 1754–1756.


[7] YANG YUE, HAO HUANG, LIN ZHANG, JIAN WANG, JENG-YUAN YANG, YILMAZ O.F., LEVY J.S., LIPSON M.,WILLNER A.E., UWB monocycle pulse generation using two-photon absorption in a silicon wave-guide, Optics Letters 37(4), 2012, pp. 551–553.

[8] PENG XIANG, XIAOPING ZHENG, HANYI ZHANG, YUQUAN LI, JINTIAN XIONG, A novel approach to all-op-tical generation of ultra-wideband signals, Fiber and Integrated Optics 32(3), 2013, pp. 222–232.

[9] YOUNG JUN CHO, KI HAK KIM, DONG HYUK CHOI, SEUNG SIK LEE, SEONG-OOK PARK, A miniatureUWB planar monopole antenna with 5-GHz band-rejection filter and the time-domaincharacteristics, IEEE Transactions on Antennas and Propagation 54(5), 2006, pp. 1453–1460.

[10] BAHADORI K., RAHMAT-SAMII Y., A miniaturized elliptic-card UWB antenna with WLAN bandrejection for wireless communications, IEEE Transactions on Antennas and Propagation 55(11),2007, pp. 3326–3332.

[11] MONDAL P., YONG LIANG GUA, A coplanar stripline ultra-wideband bandpass filter with notch band,IEEE Microwave and Wireless Components Letters 20(1),2010, pp. 22–24.

[12] JIANYU ZHENG, NINGHUA ZHU, HUI WANG, YUANXIN DU, LIXIAN WANG, JIANGUO LIU, Photonic-as-sisted ultrawideband pulse generator with tunable notch filtering based on polarization-to-intensityconversion, IEEE Photonics Journal 5(3), 2013, article 7900909.

[13] SHILONG PAN, JIANPING YAO, Performance evaluation of UWB signal transmission over optical fiber,IEEE Journal on Selected Areas in Communications 28(6), 2010, pp. 889–900.

[14] SHILONG PAN, JIANPING YAO, UWB-over-fiber communications: modulation and transmission,Journal of Lightwave Technology 28(16), 2010, pp. 2445–2455.

[15] ADRAHA S.T., OKONKWO C.M., KOONEN A.M., TANGDIONGGA E., Experimental demonstration of2 Gbps IR-UWB over fiber using a novel pulse generation technique, Presented at the Conferenceon Access Network and In-house Communications 2010, Karlsruhe, Germany, June 21–24, 2010,paper AthA5.

[16] XIANBIN YU, GIBBON T.B., MONROY I.T., Experimental demonstration of all-optical 781.25-Mb/sbinary phase-coded UWB signal generation and transmission, IEEE Photonics Technology Letters21(17), 2009, pp. 1235–1237.

Received May 3, 2014in revised form July 17, 2014


Theoretical analysis of a hollow laser beam transmitting in an off-axis Cassegrain optical antenna system

CONGWEI MI, PING JIANG*, HUAJUN YANG, SHASHA KE, BO LI, JIANHUA LIU

College of Physical Electronics, University of Electronic Science and Technology of China, Sichuan Province 610054, China


The optical model of a Cassegrain optical antenna with a confocal double-parabolic reflectorstructure has been designed, and the propagation characteristics of a hollow laser beam, whichcould avoid the loss of energy caused by the subreflector center reflection in the optical antenna,has been researched in this paper. By detailed analysis and numerical calculations of a receivingCassegrain antenna with different deflection angles, the coupling efficiency curve and 3-D distri-butions of the receiving light intensity for different inclined angles have been obtained.

Keywords: Cassegrain optical antenna, off-axis hollow laser beam, receiving efficiency.

1. IntroductionWith the rapid advancement of space laser communications technology and opticaldevices, optical communication has developed much faster in recent years [1]. Plentyof studies have been accomplished and much more manpower and material resourceshave been and will be invested in those researches [2]. Gaussian optical beams havealso attracted much attention when designing the high power of SLED, and they havebeen widely used in optical communication systems [3, 4]. A double-parabolic reflec-tor Cassegrain optical antenna structure, which possesses many advantages, includingthe bigger aperture, less aberration and more choices of different wavelengths, has beenoften employed in space optical communication systems [5]. However, the loss of en-ergy caused by the subreflector center reflection in the transmitting Cassegrain opticalantenna and the off-axis error of a receiving antenna have seriously hindered the trans-mission efficiency in the space optical communication system [6]. Therefore, a hollowbeam could almost avoid the loss of energy caused by the subreflector center reflection,which can be seen from the calculation results.

In this work, the effect of the off-axis antenna structure on the hollow beampropagation efficiency has been investigated. The results will offer the fundamental

422 CONGWEI MI et al.

research for the propagation efficiency enhancement of the free space optical commu-nication.

2. The comparison between the transmitting Gaussian beam and hollow beam

The Cassegrain antenna is mainly made up of a primary reflector and a subreflector.We chose the aperture diameters of the primary reflector and the subreflector as2a = 150 mm and 2b = 30 mm, respectively. The distance between the vertices oftwo reflectors is d = 300 mm. The transmitting antenna and the receiving antenna witha symmetrical structure are shown in Fig. 1.

Because those two antennas are symmetric, only the parameters of the transmittingantenna were considered in this paper. According to the properties of the double-par-abolic reflection Cassegrain system, the geometric optical paths of the transmitting op-

Fig. 1. The Cassegrain antenna system in space optical communication. The structure of a transmittingoptical antenna (a). The structure of a receiving optical antenna (b).

a b

y

x

y2 = 2p1x

y2 = 2p2(x – d)a

d

b

F

HG

E

A

BO

D

C2R

Fig. 2. The geometric optical path of transmitting Cassegrain antenna.

Theoretical analysis of a hollow laser beam... 423

tical Cassegrain antenna are shown in Fig. 2. The primary mirror satisfies the equationy 2 = 2p1x, and the equation of the subreflector is y 2 = 2p2(x – d )

(1)

In the triangle ΔABC,

(2)

(3)

(4)

It can be deduced that

(5)

By solving two simultaneous equations (Eqs. (1) and (5)), the radius of the lightwhich was reflected backward at the center of the subreflector is

(6)

In the triangles ΔDEG and ΔFHG

(7)

By solving Eqs. (1) and (7), the focal length of the primary reflector could be written as

(8)

and the focal length of the subreflector is

(9)

According to Eqs. (8) and (9), Eq. (6) can be simplified as

R = b2/a (10)

dp1

2-----------

p2

2----------–=

AC b2

2p1-------------

p1

2-----------+

⎝ ⎠⎜ ⎟⎛ ⎞ R2

2p2-------------

p2

2----------+

⎝ ⎠⎜ ⎟⎛ ⎞

– b2

2p1------------- R2

2p2------------- d+–= =

BC R2

2p2------------- d b2

2p1-------------–+=

AB b R–=

b2

2p1------------- R2

2p2------------- d+–

⎝ ⎠⎜ ⎟⎛ ⎞

2R2

2p2------------- d b2

2p1-------------–+

⎝ ⎠⎜ ⎟⎛ ⎞

2

b R–( )2+=

Rp2

p1----------b=

HGEG

--------------- FHDE

---------------=p2 2⁄ b2 2p2⁄–

p1 2⁄ a2 2p1⁄–------------------------------------------⇒ b

a-------=

p1

2---------- a

a b–----------------- d=

p2

2---------- b

a b–----------------- d=


Supposing the incident light is a Gaussian beam with a wavelength of λ = 830 nm.From the theoretical analysis, the light intensity of the beam is [5]

(11)

where

(12)

representing the spot radius of the Gaussian beam, z denotes the propagation distance,and ω0 is the light waist of the Gaussian beam.

From Eq. (6), the power attenuation of the Gaussian beam can be written as

(13)Because of the properties of the Gaussian beam, ω (z) denotes the radius of a spot

reaching the subreflector. Supposing ω (z) = b and R = b2/a = 3 mm, the incident lightis expanded and aligned to match with the antenna. Therefore,

(14)

which showed that the power attenuation was as much as 8.89%. If the incident beamis a dark hollow laser beam whose dark-part radius was R, by theoretical conclusion,the light intensity of the beam is [6]

(15)

where

(16)

I1 r z,( ) C 2

ω 2 z( )-------------------- 2r 2

ω 2 z( )--------------------–exp=

ω z( ) ω 0 1 λzπω0

2---------------⎝ ⎠⎜ ⎟⎛ ⎞ 2

+=

P1

P-----------

C 2

ω 2 z( )-------------------- dθ 2r 2

ω 2 z( )--------------------–exp rdr

0

R

∫0

2π

∫C 2

ω 2 z( )-------------------- dθ 2r 2

ω 2 z( )--------------------–exp rdr

0

ω z( )

∫0

2π

∫-------------------------------------------------------------------------------------------------------------

2r 2

ω 2 z( )--------------------–exp

0

R

2r 2

ω 2 z( )--------------------–exp

0

ω z( )-----------------------------------------------------------= =

P1

P-----------

2r 2

b2-------------–exp

0

3

2r 2

b2--------------–exp

0

15------------------------------------------------ 0.0889= =

I r z,( )P0

πω 2 z( )------------------------

2 r R0–( )2

ω 2 z( )--------------------------------–exp=

ω z( ) ω0 1z r R0–( )2 θ( )tan⁄+

2

z02

------------------------------------------------------------------+=


(17)

and L denotes the length of the double cone prism which is used to create a hollowbeam, θ is the vertex angle of the double cone prism, z means the propagation distance,and n stands for the refractive index of the double cone prism.

The power attenuation can be written as

(18)

Supposing, ω (z) = (b – R) /2 = 6 mm, R0 = (b + R) /2 = 9 mm. By calculation,

(19)

which suggested that the power attenuation was only 0.94%. In comparison, it wasmuch more efficient to transmit the hollow beam than the Gaussian beam.

3. Analysis of power and coupling efficiency of an antenna with an inclined optical axis

Assuming the transmitting Cassegrain antennas are precisely aligned and the inclinedangle between the receiving Cassegrain antenna and the optical axis is γ, the schematicdiagram of the off-axis antenna system is as shown in Fig. 3.

R0 L 2θ( ) 1 θ( )sin

n2 cos2 θ( )–---------------------------------------------–sin=

P'1P

-----------

P0

πω 2 z( )------------------------ πR2e 2–

dθ I r z,( )rdrR

b

∫0

2π

∫-------------------------------------------------=

P'1P

-----------

P0

π62-------------- πR2e 2–

dθP0

π62-------------- 2 r 40–( )2

62------------------------------–exp rdr

9

15

∫0

2π

∫----------------------------------------------------------------------------------------------------------- 0.0094= =

Primary reflectorof the receiving

Cassegrain antenna

Fig. 3. The schematic diagram of an off-axis antenna system.

Subreflectorof the receiving

Cassegrain antenna

Primary reflectorof the transmitting

Cassegrain antenna

The cross-sectionof emitting hollow

laser beam

The cross-sectionof collimated hollow

laser beam

Subreflectorof the transmitting

Cassegrain antenna

The deflectionangle γ

d

L


Supposing the incident beam is a hollow laser beam that is parallel to the opticalaxis of the system, the light intensity distribution of the hollow beam in the radial di-rection can be obtained, as shown in Fig. 4. The 3-D image light intensity distributionof the hollow beam is shown in Fig. 5.

By the theoretical analysis, when transmitting a hollow beam, the receiving powerhas been obtained [7].

As shown in Fig. 6a, when γ ≥ atan(2a/d ), there is no light received, hence Pr = 0.As shown in Fig. 6b, when atan[(a + b)/d ] ≤ γ < atan(2a/d ), the receiving power is

(20)

1.0

0.8

0.6

0.4

0.2

–15 –10 –5 0 5 10 15x [mm]

Pow

er in

tens

ity d

istri

butio

nof

hol

low

bea

m in

radi

cal d

irect

ion

Fig. 4. The light intensity distribution of a hollow beam in the radical direction.

1.0

0.8

0.6

0.4

0.2

0.0

100

–10 –100

10y [mm] x [mm]

Pow

er in

tens

ity d

istri

butio

nof

hol

low

bea

m

Fig. 5. The 3-D image light intensity distribution of a hollow beam.

Pr I x y,( )dydxd γ( ) /2tan

a2 x2–

∫a2 d γ( ) /2tan[ ]2––

a2 d γ( )tan /2[ ]2–

∫

I x y,( )dydxd γ( )tan a2 x2––

d γ( ) /2tan

∫a2 d γ( ) /2tan[ ]2––

a2 d γ( ) /2tan[ ]2–

∫

+

+

=


As shown in Fig. 6c, when atan[(a – b)/d ] ≤ γ < atan[(a + b)/d ], the receivingpower is

Fig. 6. The distribution of a hollow beam light spot on the receiving plane (see text for explanation).

140

100

60

20

–20

–60

–100 –50 0 50 100x [mm]

y [m

m]

c 100

60

20

–20

–60

–100 –50 0 50 100x [mm]

y [m

m]

d

20

–60

–100 –60 –20 20 60 100x [mm]

y [m

m]

e 60

20

–20

–60

–100 –60 –20 20 60 100x [mm]

y [m

m]

f60

–20

200

150

100

50

0

–50

–150 –50 50 150x [mm]

y [m

m]

a 150

100

50

0

–50

–150 –50 50 150x [mm]

y [m

m]

b


a2 x2–

∫a2 d γ( ) /2tan[ ]2––

a2 d γ( ) /2tan[ ]2–

∫


d γ( ) /2tan

∫a2 d γ( ) /2tan[ ]2––

a2 d γ( ) /2tan[ ]2–

∫

+

+ +

=


(21)

where and .

As shown in Fig. 6d, when atan(2b/d ) ≤ γ < atan[(a – b)/d ], the receiving power is

(22)

As shown in Fig. 6e, when 0 ≤ γ < atan(2b/d ), the receiving power is

(23)

I x y,( )dydxy1

a2 x2–

∫a2 y1

2––

a2 y12–

∫– I x y,( )dydxd γ( )tan b2 x2––

y1

∫a2 y1

2––

a2 y12–

∫–

I x y,( )dydxy2

d γ( )tan a2 x2––

∫a2 y2

2––

a2 y22–

∫– I x y,( )dydxb2 x2–

y2

∫a2 y2

2––

a2 y22–

∫–

+

y1a2 b2– d 2tan2 γ( )+

2d γ( )tan------------------------------------------------------= y2

b2 a2– d 2tan2 γ( )+2d γ( )tan

------------------------------------------------------=


a2 x2–

∫a2 d γ( ) /2tan[ ]2––

a2 d γ( ) /2tan[ ]2–

∫


d γ( ) /2tan

∫a2 d γ( ) /2tan[ ]2––

a2 d γ( ) /2tan[ ]2–

∫

I x y,( )dydxb2 x2––

b2 x2–

∫b–

b


d γ( )tan b2 x2–+

∫b–

b

∫–

+

+ +

=


a2 x2–

∫a2 d γ( ) /2tan[ ]2––

a2 d γ( ) /2tan[ ]2–

∫


d γ( ) /2tan

∫a2 d γ( ) /2tan[ ]2––

a2 d γ( ) /2tan[ ]2–

∫

I x y,( )dydxb2 x2––

b2 x2–

∫b–

b


d γ( )tan b2 x2–+

∫b–

b

∫–

I x y,( )dydxd γ( ) /2tan

b2 x2–

∫b2 d γ( ) /2tan[ ]2––

b2 d γ( ) /2tan[ ]2–

∫

I x y,( )dydxd γ( )tan b2 x2––

d γ( ) /2tan

∫b2 d γ( ) /2tan[ ]2––

b2 d γ( ) /2tan[ ]2–

∫

+

+ +

+

+ +

+

=


Because the integration is non-integrable, the receiving efficiencycurve was shown in Fig. 7 by numerical calculation and simulation. In this paper, wechose the normalized amplitude of I(x, y) and ω (z) = (a + b) /2, which kept the inten-sity distribution of the receiving spot on the receiving plane the same with the idealhollow beam’s.

It is clear that the receiving power will be zero, if the deflection angle is more than0.38 rad. The receiving power is less than 80% of the total power, when the deflection

e r R–( )2rdr∫

1.0

0.8

0.6

0.4

0.2

0.00.0 0.1 0.2 0.3 0.4 0.5

Deflection angle [rad]

Rec

eivi

ng e

ffici

ency

Pr/

P

Fig. 7. The receiving efficiency curve.

1.0

0.0

50

0

–50–60

060

x [mm]

y [mm]

a

Pow

er in

tens

ity d

istri

butio

nof

hol

low

bea

m in

off-

axis

1.0

0.0

60

0

–60 –60

0

60

x [mm]y [mm]

b

Pow

er in

tens

ity d

istri

butio

nof

hol

low

bea

m in

off-

axis

1.0

0.0

60

0

–60 –60

0

60

x [mm]

y [mm]

c

Pow

er in

tens

ity d

istri

butio

nof

hol

low

bea

m in

off-

axis

1.00.0

60

0

–60 –60

0

60

x [mm]y [mm]

d

Pow

er in

tens

ity d

istri

butio

nof

hol

low

bea

m in

off-

axis

Fig. 8. The 3-D images of light intensity distribution with inclined angles γ = 0 rad (a), γ = 0.0997 rad (b),γ = 0.1974 rad (c) and γ = 0.2915 rad (d).


angle is more than 0.05 rad. And it can be seen that the ratio of power attenuationwhen the inclined angle is γ ∈ [0, 0.2] fiercer than the case when the inclined angleγ ∈ [0.2, 0.5]. Meanwhile, the 3-D images of light intensity distribution with severaldifferent inclined angles are shown in Fig. 8.

By the theoretical analysis of an off-axis Cassegrain optical system, we found thatthe distance of the centers of the small circle and ellipse satisfied the equation

Therefore, we changed the distance to get the images ofFig. 8, and the inclined angles were calculated according to the equation

4. Conclusion

The characteristics of a double-parabolic reflector Cassegrain optical antenna has beenanalyzed, and the relationships among the focal length of a primary reflector and sub-reflector (0.5p1, 0.5p2), the aperture of two reflectors (a, b), and the distance of tworeflectors d have been obtained. This work will provide some theoretical referencesfor those manufacturing Cassegrain optical antennas. When the inclined angle is lessthan 0.05 rad, the receiving power is beyond 80%, which is satisfied with the Strehlstandard. To keep the receiving efficiency higher than 80%, the inclined angle mustbe kept less than 0.05 rad. Therefore, the technology of aligning the optical systemneeds to be improved much more. From the receiving power curve, we can adjustthe antennas to make the off-axis Cassegrain optical system aligned more precisely ac-cording to the receiving power. The investigation results will offer the fundamentalresearch for the propagation efficiency enhancement of the free space optical commu-nication.

Acknowledgements – This work is supported by the National Natural Science Foundation of China underGrant No. 61271167 and No. 61307093. It was also supported by the Research Foundation of the GeneralArmament Department of China under Grant No. 9140A07040913DZ02106, and the FundamentalResearch Funds for the Central Universities under Grant No. ZYGX2013J051.

References

[1] HAN SUN, HUAJUN YANG, YI PENG, 3-D simulation research for off-axis Cassegrain optical antennaand coupling systems, Optoelectronics and Advanced Materials – Rapid Communications 6(1–2),2012, pp. 284–287.

[2] HUILIN JIANG, GUOJUN LIU, FUCHANG YIN, ZHI LIU, Laser communications technology with airborneplatform, Proceedings of SPIE 6031, 2005, article 603102.

[3] ZHIGANG ZANG, MINATO T., NAVARETTI P., HINOKUMA Y., DUELK M., VELEZ C., HAMAMOTO K., Highpower (>110 mW) superluminescent diodes by using active multimode interferometer, IEEE PhotonicsTechnology Letters 22(10), 2010, pp. 721–723.

[4] ZHIGANG ZANG, MUKAI K., NAVARETTI P., DUELK M., VELEZ C., HAMAMOTO K., Thermal resistancereduction in high power superluminescent diodes by using active multi-mode interferometer, AppliedPhysics Letters 100(3), 2012, article 031108.

OO' d γ( )tan .= OO'

γ OO' d⁄( ).atan=


[5] POSYNIAK M., STACEWICZ T., MIERNECKI M., JAGODNICKA A.K., MALINOWSKI S.P., Multiwavelengthmicropulse lidar for atmospheric aerosol investigation, Optica Applicata 40(3), 2010, pp. 623–632.

[6] KAI HUANG, HUAJUN YANG, TUOHUI LI, CHENGHONG LI, QUAN XU, KANG XIE, Analysis of spaceoff-axis and performance of Cassegrain optical antenna system, Optik – International Journal forLight and Electron Optics 121(18), 2010, pp. 1688–1692.

[7] ZIHAO CHEN, HUAJUN YANG, XINYANG WANG, JING WANG, XIAOPING HUANG, Theoretical analysis andtest for off-axis Cassegrain optical antenna, Optik – International Journal for Light and ElectronOptics 123(3), 2012, pp. 268–271.

Received January 15, 2014in revised form May 29, 2014


Monitoring and identification of marine oil spills using advanced synthetic aperture radar images

ZAKARYA MIHOUB1*, ABDELATIF HASSINI1, 2

1Institute of Maintenance and Industrial Safety, University of Oran, B.P.05, Airport Road Es-Senia, Oran, Algeria

2Laboratory of Analysis and Application of Radiation LAAR, Faculty of Physics USTOMB, El M’nouer B.P.1505 Oran, Algeria


The aim of this study is to propose and test a new methodology for detection of oil spills in the worldoceans from advanced synthetic aperture radar imagery embedded in ENVISAT satellite(ENVISAT-ASAR). The proposed and applied methodology includes four levels: data acquisition,dark spots detection, features extraction and dark spots classification for discrimination betweenoil spills and look-alikes. Level 1 contains the ENVISAT-ASAR wide swath mode data acquisi-tion. Level 2 begins with a visual interpretation based on experience and a priori information con-cerning location, external information about weather conditions, differences in shape, and contrastto surroundings between oil spills and look-alikes, then filtering and segmentation. Level 3 con-tains extraction of features from the detected dark spots. Level 4 aim is to discriminate oil spillsfrom look-alikes using the features extracted by means of object-based fuzzy classification. Asa result, oil slicks are discriminated from look-alikes with an overall accuracy classification of 91%for oil slicks and 86% for look-alikes. Finally, to validate our results, the method has been testedby comparing the areas of the automatically detected oil spills (object-based fuzzy classification)with the areas of the manually detected oil spills (region of interest), by means of area ratios.

Keywords: sea pollution, remote sensing, oil spills detection, ENVISAT-ASAR images.

1. IntroductionOil slicks on sea surface can have different sources such as man-made slicks from illegaldischarges of ships or spills resulting from ship accidents, slicks originated from bio-logical activities such as photo-oxidation processes or by planktons, and geologicalslicks originated as natural hydrocarbon seeps from a reservoir. Including every kindof slick, 10% of ocean surface is estimated to be covered by slicks [1]. Natural seepagedetection is considered to be one of the significant preliminary works for offshorepetroleum exploration. However, it does not explain the whole petroleum system by

434 Z. MIHOUB, A. HASSINI

itself, and it should be combined with regular exploration techniques such as seismicinterpretation, sample collection from the sea bottom, and geological survey. The oil slickdetection and mapping are becoming one of the standard tools for hydrocarbon explo-ration activities and have been applied to most of the hydrocarbon basins in the worldsuch as Gulf of Mexico [2], Santa Barbara Channel, California [3], Australian Shelf [4],and South Caspian Sea [5].

Radar systems are extensively used for the dark formation detection in the marineenvironment, as they are not affected by local weather conditions and cloudiness andwork day and night [3]. They emit their own energy in the microwave range, which isthen reflected from the sea surface and received back at the sensor. A radar image isa representation of the backscatter return and is mainly proportional to the surfaceroughness at the scale of the radar wavelength (few centimeters) [6]. Synthetic apertureradar (SAR) capabilities are widely well demonstrated, and thus it still turns out to bethe most efficient and superior satellite sensor in oil spill detection [7]. Parameters usedto detect oil slicks are functions of radar configuration, slick nature, meteorologicaland oceanic conditions like the height of the waves, the amount of oil that has beenreleased, and the speed of the wind [1, 8]. SARs have some limitations, as the presenceof natural phenomena that can give false oil spill detections (look-alikes), such as oilspills from oil-rigs, leaking pipelines, passing vessels as well as bottom seepages,while look-alikes do include natural films/slicks, grease ice, threshold wind speedareas (wind speed <3 m/s), wind sheltering by land, rain cells, shear zones, internalwaves, etc. [8].

Detection of oil spills from SAR imagery can be divided into three steps: 1) detectionof dark spots (suspicious slicks), 2) extraction of features from the detected dark spots,and 3) classification of the dark spots (oil spills/look-alikes) [7]. This can be done man-ually or automatically. In manual detection, a trained operator has to go through the entireimage, find possible oil spills and discriminate between the oil spills and the look-alikes.Though a trained operator is able to detect oil spills from SAR images with some con-fidence, it is time-consuming. It is also labor-intensive given the large number of SARimages that must be analyzed in a short period of time for effective oil-spill monitoring,especially after the launch of constellations like Sentinel-1A and 1B and the RCM(RADARSAT Constellation Mission). For some areas and in sight of a local groundstation, products can be delivered within one hour [9]. The first Sentinel-1A satellitewas launched on April 3, 2014, it will ensure the continuity of the C-band SAR datafrom the ERS-1/2 and ENVISAT missions, with the second Sentinel 1-B following in2016. For further reading ESA websites are recommended (https://earth.esa.int/web/guest/missions/esa-future-missions/sentinel-1). In addition, manual detection is con-strained by the knowledge and experience of operators, whose results are subjective.

Discriminative features of oil spills and look-alikes are basically geometrical, ra-diometric, textural, and temporal [7, 10]. Natural oil slicks originated from subsurfaceshould be permanent, and temporally many different slicks should be present in a close

Monitoring and identification of marine oil spills... 435

neighborhood with a repetitive manner. However, orientation, shape, and texture canbe different because of the weather conditions at the time of image acquisition [10, 11].Thus, studies have been undertaken to develop fast, reliable and automated oil-spilldetection systems. Several classifiers have been employed for the discrimination ofoil spills and look-alikes: Bayesian classification scheme by combining prior knowl-edge, Gaussian densities and rule-based density corrections [12, 13], linear discrimi-nate analysis (LDA) approach basing on the Mahalanobis distance [14], a multiple linearregression method for oil-spill classification [15], the artificial neural network (ANN)approach to approximate the relation between dark-spot features and the class labels [16],the support vector machine (SVM) [17], object-based fuzzy classification [11], bun-dling, bagging, boosting and the generalized additive model (GAM) [18].

In this paper, we propose a multi-level methodology for detection of oil slicks usingENVISAT-ASAR imagery and apply our methodology in a variety of conditions, in-cluding different regions of the planet, and different dates. We establish that the methodcan be used to support the identification of hydrocarbon seeps.

2. Materials – satellite sensor description and input data

Microwave sensors are the most applicable tools for oil slick monitoring since theyare not affected by clouds, haze, weather conditions, and day/night differences. Syntheticaperture radar is the most common method to detect offshore oil slicks. Parametersused to detect oil slicks are functions of radar configuration, slick nature, meteoro-logical and oceanic conditions like the height of the waves, the amount of oil that hasbeen released, and the speed of the wind [1, 19].

The advanced synthetic aperture radar (ASAR) sensor rides aboard the ENVISATsatellite and provides radar imagery of the earth for studying oceans, atmosphere,ice, and land [19]. ASAR was operational since the launch of the satellite on March1, 2002 [19, 20], and the mission operated until April 8, 2012 [20]. The processing andarchiving of data from ESA’s (European Space Agency) ERS-2 and ENVISAT mis-sions were unified in the ESA multi-mission facility infrastructure (MMFI). Since thenthe MMFI served both missions until their end, for ERS-2 in July 2011 and ENVISATin April 2012. Nevertheless, the mission data are still being archived and are frequentlyrequested by users, with MMFI still serving those needs. It and the attendant processingwere transferred from the former mission-specific payload ground segments to a mod-ern processing infrastructure [21].

ASAR has five mutually exclusive modes of operation: image mode (IM), alternatepolarization (APM), wide swath (WSM), wave (WM), global monitoring (GMM).Image mode, has 30 m resolution, similar to ERS SAR, 7 possible mutual exclusiveswaths and 2 possible mutual exclusive polarizations (VV or HH). Alternate polariza-tion mode, has 30 m resolution, 7 possible mutual exclusive swaths and 3 possible mu-tual exclusive polarizations (HH/VV, HH/HV or VV/VH). Wide swath mode, 150 m


resolution, has 1 unique swath (400 km) and 2 possible mutual exclusive polarizations(VV or HH) [22]. In the literature, for oil slick detection VV polarized, C-band withlow incidence angle data is considered preferable [1, 8, 23–25]. The methodology pro-posed has been applied on a dataset of 10 ENVISAT-ASAR images of wide swathmode (WSM) [26].

3. Methods The proposed and applied methodology in this study is an implementation of pre-ex-isting techniques, with a new approach, to 4 differing contextual levels, as shownin Figure 1:

– ENVISAT-ASAR data acquisition, – dark spots detection,– feature extraction from the detected dark spots,– classification of dark spots to discriminate oil spills from look-alikes.

3.1. Level 1: ENVISAT-ASAR data acquisition

The ENVISAT-ASAR data are downloaded from the ESA (European Space Agency)websites (https://earth.esa.int/web/guest/data-access) [26]. In this study, the wide

Level 1ENVISAT-ASAR data acquisition

Visual interpretation Filtering

Segmentation

Features extraction

Object-based fuzzy classification Manual classification

Comparison results to validate

Final results

Level 2

Level 3

Level 4

Fig. 1. Representative framework of the methodology.


swath mode, level 1b ASA_WSM_1P are used. The study area is covered by 10 dif-ferent ENVISAT-ASAR images. The details of the dataset containing the informationabout the region, date and start time of acquisition are given in Table 1.

3.2. Level 2: dark spots detection

The capability of ASAR in detecting oil slicks over the sea surface is well-knownand proven by several studies aiming at oil spill detection and discrimination usingENVISAT-ASAR images [1, 6, 7, 13, 17, 27, 28]. Most of these studies are primarilybased on the dark spots detection; it is a preliminary task when detecting oil spills; itis a critical and fundamental step prior to feature extraction and classification. There-fore, unless an oil spill can be detected at this first step, it can never be detected ata later step. Furthermore, the accuracies of feature extraction and classification greatlyrely on the accuracy of dark-spot detection. This level includes three steps.

Visual interpretation – Visual interpretation starts with a pre-processing stagewhere artifacts (if applicable) resulting in different contrast trends across the images(range falloff, gain control effects, etc.) have been determined and removed [29].The de-trended images with balanced contrast have been scanned visually to determinethe target dark spots. The human eye is superior in observing a slick in the context ofthe surrounding sea, and a trained human interpreter can discriminate oil slicks andlook-alikes based on experience and a priori information concerning location, externalinformation about weather conditions, differences in shape, and contrast to surround-ings between oil slicks and look-alikes [12]. If the surroundings are homogeneous,the human observer will have more belief in that the spot is an oil slick than withheterogeneous surroundings [12]. With heterogeneous surroundings, the human eyecan easily determine if the spot is separated from the surroundings based on contrastor orientation [27]. In this study the images have been thoroughly analyzed by different

T a b l e 1. List of images used.

Environment Date and time of acquisition Region Image A (image reference) 17/11/2002 at 10:44 UTC Northwest coast of Spain

Image B 25/11/2011 at 12:12 UTC Northeast of Rio De Janeiro Brazil coast Image C 28/04/2010 at 03:45 UTC Gulf of MexicoImage D 09/05/2010 at 15:48 UTC Gulf of Mexico Image E 27/08/2008 at 09:20 UTC Northeast coast of Algeria Image F 31/03/2005 at 12:13 UTC Coast of South Africa Image G 07/12/2007 at 01:40 UTC South Korea coastImage H 30/07/2004 at 20:08 UTC Southeast of the Baltic SeaImage I 09/08/2006 at 09:54 UTC Lebanese coastImage J 10/04/2004 at 01:55 UTC East China Sea


experts using visual photo-interpretation techniques, furthermore the subset images areextracted based on target areas containing dark spots on the bases of contrast level tothe surroundings, homogeneity of the surroundings, wind patterns, nearby bright spotsof ships, edge, and shape characteristics for natural slicks. Closely spaced, a numberof dark spot groups or large individual ones are limiting the subsets spatially.

Filtering – Image filtering step aims to reduce speckle and to enhance the image [30].Adaptive filtering methods are used to discriminate high contrast areas representingpossible oil discharges in the images. In general, the filter of image with noise removal:Lee, Gamma, Frost or Kuan and two pass filters (3×3 median filter and 5×5 low passfilter) are used in different oil spill discrimination studies [31, 32]. It is also observedthat these filters minimize the loss of information boundaries of high and low contrast-ed areas. Filtering of the image with noise removal filters gives a clear output for dis-crimination of dark areas from the remaining heterogeneous background [19, 33]. Inthis study the Lee (3×3) filter is used.

Thresholding and segmentation – In segmentation neighboring pixels are com-pared and they are merged into regions if they are similar. It runs iteratively to mergethe resulting regions. Two neighboring regions, Ri and Rj, are merged if they satisfythe three following conditions:

1. Thresholding condition: dist(Ri , Rj) ≤ T;2. Neighborhood condition 1: Rj ∈ N(Ri) and dist(Rj , Ri) ≤ dist(Rk, Ri), Rk ∈ N(Ri);3. Neighborhood condition 2: Rk ∈ N(Ri) and dist(Ri, Rj) ≤ dist(Rk , Rj), Rk ∈ N(Rj). In the above, T is the chosen similarity threshold, dist(Ri , Rj) is the Euclidean dis-

tance between the mean grey levels of the regions. Also, regions smaller than the cho-sen area threshold are removed by merging them with their most similar neighbor [34].In this approach, a detection window is passed through the ASAR image. An intensitythreshold segmentation algorithm is implemented for each window. Pixels with inten-sities below the intensity threshold are regarded as potential dark-spot pixels whilethe others are potential background pixels [35].

3.3. Level 3: features extraction for dark spots After segments have been created, features need to be extracted as an input to classifiers.The features proposed by the researchers can be categorized into four groups: 1) phys-ical and textural properties, 2) geometric shape, 3) contrast with background, and4) contextual information [7]. Different researchers employed different features. Forexample, TOPOUZELIS et al. (2007) adopted 10 features to train a neural network clas-sifier [16], FISCELLA et al. (2000) used 11 features [14] and SOLBERG et al. (2007) used13 features [13].

Although most classifiers relied predominantly on limited features, they tended topresent different patterns on feature ranking and permutation-based variable accuracyimportance (PVAI) values [18]. The importance of a variable may show great variation,depending on which evaluation criterion is used. As a result, features that are uselessfor a particular classifier may be of great help for another, while features that are usefulfor one classifier may become useless for another. Some shape features and a contex-


tual feature have very high PVAI values in most of the classifiers [18]. In this study,we intend not to use all the features proposed by other researchers, because it will in-crease the dimensionality of the dataset, thus the risk of over fitting. Therefore, we se-lect 11 features out of all the available features as a classifier input. The selected11 features related to: intensity value of pixels (layer values) (predictors no. 1 to 3),shape (no. 4 to 7), to texture (no. 8 to 11) [27], see Table 2.

The selected features in this study are used for defining the boundaries of the mem-bership functions while making object-based fuzzy classification [27]. The index pa-rameters are selected to identify the geometric shape of the dark spot and spectralsimilarity of the neighboring pixels (background). Features related to shape (A, P, C,Com and S ) are defining the geometric properties of the dark spot, because the darkspot related with natural oil slicks should have larger width with respect to slicks cre-ated by oil tankers or large ships. Similarly they should have less rounded shapes withrespect to low-wind areas and the algae or biological dampening effects. Secondly, fea-tures related to texture (H, C and D) and intensity value of pixels (OSd, BMe and BSd)are used to define spectral properties of dark spots.

3.4. Dark spots classificationThis level includes two steps: 1) automatic classification (object-based fuzzy classifi-cation) and 2) manual classification (region of interest).

Automatic classification (object-based fuzzy classification). Several classifiers havebeen used for classification of dark formations to oil spills or look-alikes, i.e., statisticalapproach through computation of probabilities, neural networks, fuzzy logic, etc.

T a b l e 2. Summary statistics of features for oil spills and look-alikes separately.

OSd – standard deviation of gray-scale intensity values of the object; BMe – average intensity value ofthe background area; BSd – standard deviation of the intensity value of the background; A – target area(in number of pixels); P – target perimeter (in number of pixels); C = P2/A – complexity measure;Com – compactness; S – spreading measure (the ratio between the target width and length); H – homo-geneity; Con – contrast; D – dissimilarity.

No. Features Oil spill (min–max) Look-alikes (min–max)1 OSd 8.1–42.2 31.5–71.82 BMe 31.6–161.7 42.2–194.03 BSd 10.1–56.6 21.5–76.14 A 17–16.619 325–170.3845 P 64–2011 106–28076 C = P2/A 20.4–510.8 15.2–325.97 Com 2.1–2.4 1.5–2.58 S 72.1–100 54.9–99.99 H 0.024–0.040 0.038–0.042

10 Con 1.324–2.140 1.230–1.69011 D 25–35 23–27


The last stage includes defining membership functions based on extracted object fea-tures [10]. In this paper an object-based fuzzy classification scheme is used for dis-criminating dark spots, with a simple empirical class hierarchy consisting of twoclasses which are “clear sea water” and “dark spots”. “Dark spots” class includes twosubclasses, namely “probable oil slicks” and “probable look-alikes”. Fuzzification de-scribes the transition from a crisp system to a fuzzy system. The fuzzy rule can havea single condition or can consist of a combination of conditions that have to be fulfilledfor a dark object to be assigned to a probability class [11]. A membership function as-signs a membership degree or value between 0 and 1 to each feature. Boundaries ofmembership functions are determined based on feature value intervals from randomlyselected representative segments that are supposed to belong to a specific class. In mostof the cases, “Boolean range function” is used, which assigns a value of “1” betweenspecific values and assigns “0” for the rest, in order to achieve sharp distinction of“probable oil slick” and “probable look-alike” classes [27]. As a final stage of this clas-sification, an accuracy assessment is performed by classification stability (CS) and bestclassification result (BCR) methods, apart from comparisons of level 1 visual inter-pretation results. CS explores differences in degrees of membership between the bestand the second best class assignments of each object, which can give evidence aboutthe ambiguity of an object’s classification. On the other hand, BCR determines whetherthe object has memberships in more than one class. In the accuracy assessment of clas-sification schemes, basic statistical information describing the classes like number ofimage objects, mean, standard deviation, minimum value, and maximum value hasbeen calculated [27].

Manual classification (region of interest). Regions of interest (ROIs) are portionsof images, either selected graphically or selected by other means such as thresholding.The regions can be irregularly-shaped and are typically used to extract statistics forclassification, masking, and other operations. ENVI (the Environment for VisualizingImages, Research Systems, Inc., Boulder, USA) allows selection of any combinationof polygons, points, or vectors as a region of interest. Multiple regions of interest canbe defined and drawn in any of the main image, scroll, or zoom windows. Regions ofinterest can be grown to adjacent pixels that fall within a specified pixel value thresh-old. As done for the training dataset, each oil spill signature present in ENVISAT--ASAR data was manually digitized via ENVI’s region of interest (ROI) tool and savedto oil spill position text files. ROIs were used as reference oil spill regions [6, 26, 28].Lastly, to validate our results, the methodology has been tested with computing a suc-cess percentage by comparing the areas of the automatically detected oil spills withthe areas of the manually detected oil spills, by means of area ratios.

4. Results and discussion

In our case, we have used wide swath mode level 1b images with spatial resolutionof 150 m. This class of filenames begins with the following convention:ASA_MOF_1PXPDEyyyymmdd_hhmmss, where ASA denotes the sensor (ASAR),


MOF is the functioning mode (IM, APM, WSM, WM, GMM), yyyymmdd is the year,the month (01–12) and the day (01–31), respectively, hh is the hour (UTC) whenthe sensor began collecting the scene’s data (00–23), mm is the minute (00–59), andss is the second (00–59).

Image A (reference image) is used to process oil spill pixels covering the SpainCoast from the Prestige accident (2002). Because of the important number of oil spillpixels on this image, it is considered like the reference image in this work (image Aof Fig. 2). The file of this image named ASA_WSM_1PXPDE20021117_104431_000000672011_00180_03741_0009.N1 was received from an official source(https://earth.esa.int/web/guest/data-access). In this case, our image was received onthe 17/02/2002 at 10:44:31 UTC, with wide swath mode, 00180 frame number and03741 orbit number.

The other event, on November 14, 2011; US energy giant Chevron said Mondayit has suspended drilling following an oil spill in waters off Rio de Janeiro state.The image of this event (image B of Fig. 3) is acquired by an advanced synthetic ap-erture radar (ASAR) sensor from the ENVISAT satellite, and covers the oil spill pixels

Num

ber o

f pix

els

Intensity0 128 255

Probable oil slicksProbable look-alikes a b

Fig. 2. Visual analyses of the image A (a), and the histogram (b).

Fig. 3. Visual analyses of the image B.

Probable oil slicksProbable look-alikes


in the northeast coast of Brazil. The file of this image named ASA_WSM_1PXPDE20111125_121304_000026293109_00052_50928_0009.N1 was acquiredon November 25, 2011 with wide swath mode, 00052 frame number and 50928 orbitnumber at 12:13:04 UTC. This image is used to corroborate our research.

Firstly, in the visual interpretation step, the ten images are manually interpretedand Lee 3×3 noise removal filter is applied. Filtering of the image with noise removalfilters gives a clear output for discrimination of dark areas from the remaining hetero-geneous background. ASAR imagery is highly speckled and the dark spot may havedifferent contrasts relative to its background under different conditions. If the spatialdistribution of intensity is considered, the dark spot and the background can be sepa-rated further. Before addressing this idea in detail, it is necessary to clarify our termi-nology to avoid any confusion [35].

In this paper, pixels with intensities below the intensity threshold are referred as“probable dark-spot pixels” or “dark pixels”. Pixels with intensities above the intensitythreshold are referred as “probable background pixels” or “light pixels”. For eachimage, we used the histogram to present intensity pixels distribution for each imagecombination selected (number of pixels/intensity [0–255]), and to define the density(number of pixels) of different intensity pixels (dark and light). We can observe thatdark pixels distribution in Fig. 2b (histogram of image A) presents a larger part com-pared to light pixels, especially for the values in the range 20–50, because of the im-portant number of dark spots in image A.

We applied these interpretations on other images (image B to image J in Table 1)and the results are shown in Fig. 4. Based on these interpretations, 21 subset imagesare selected and 65 dark spots are detected to be investigated in further stages. Figures 2and 3 present the visual analyses of images A and B, respectively; the square presentspossible oil slicks and the ellipse presents the possible look-alike.

For the segmentation of images, the segment scale parameter is decided as 20 afterseveral trials. Shape factor is set to 0.4. Smoothness parameter is set to 0.7 yieldingcompactness to be automatically 0.3. Figures 5a and 6a present the detection of darkspots to identify the oil spill pixels from image A and B, respectively, using automatic

Oil spills probabilityLook-alikes probabilityBackground probability

1.0

0.8

0.6

0.4

0.2

0.00 50 100 150 200 250

Pro

babi

lity

Intensity

Fig. 4. Probability of detecting oil spills, look-alikes and background.


segmentation conditions 1–3. We can observe a number of dark spots detected. Majorpart of these dark spots detection problem is found to be connected with distinguishingoil spills from other natural phenomena (look-alikes), e.g., low wind area, wind frontarea and natural slicks that create dark patches in ENVISAT-ASAR images.

After segmenting subsets images, the specific features related to “layer values”,“shape”, and “texture” are automatically calculated for each segment. Sample seg-ments are selected randomly, which are supposed to belong to one specific class.The interval of feature values is determined and tabulated, as shown in Table 2.

Based on the extracted features tabulated (Table 2), the membership functions aredefined for the class hierarchy. For class “dark spot”, a Boolean range membershipfunction is defined using standard deviation of gray-scale intensity (OSd) values. Since“probable oil slick” and “probable look-alike” classes are subclasses of “dark spot”class, this membership function appears to be an inherited function for them, andthe rules are valid for the subclasses as well. The image is classified based on the mem-bership functions, but some segments are found to be unclassified. In order to correctthe unclassified areas, the membership function and logical operators are modified and

a b

Fig. 5. Segmented subset image, simple scene for image A (a), representing the discrimination of twodark spot classes (b).

a b

Fig. 6. Segmented subset image, simple scene for image B (a), representing the discrimination of twodark spot classes (b).


tweaked for intersecting boundaries of feature values. At last, the resultant classifiedimage is obtained. The applied methodology combines pixel-based filtering, supervi-sion of human interpreter, object-based segmentation, and fuzzy classification. In ob-ject-based classification, the pixels are grouped to segments based on the two differentinput data. Membership functions helped to adjust the specific character of every in-dividual subset. The algorithm converts every segment to a binary object with the helpof Boolean range membership functions.

Standard deviation of gray-scale intensity (OSd) values in image A are in the range0–255 where the oil spills values are 7.3–40.1 and the look-alikes are 32.3–70.3, andon other hand, OSd values in image B are in the range 0–255, where the oil spills valuesare 10.1–54.3 and the false alarms are 33–69.2. Starting from the OSd values andthe target area (A), we can estimate the oil spill (OS) quality and quantity, for examplefrom image A, the number of common OSd values between the oil spill and false alarmsis small, so it is easy to discriminate between them because of the big quantity ofa heavy oil spill (Prestige accident). But in image B the common OSd values intervalis large because of the small quantity of an oil spill (natural or operational oil spill caus-es). In addition to that, we can estimate the look-alikes nature, such as low wind, windfront, etc.

Figure 5b presents classification results for the subset image A and Fig. 6b forthe image B, representing the discrimination of two dark spot classes (oil slicks andlook-alikes). Oil spills locations have been enhanced and edged in red color, greencolor presents probable look-alikes and white color presents clear sea water.

For the accuracy assessment, CS and BCR method is used to evaluate the accuracyof the classes. In this respect, the classification accuracy is calculated from CS andBCR, in which they show the basic statistics and probability of segments belonging tothe classes that they are assigned by the fuzzy logic defined by the membership func-tions. Since there is neither training set for class definition nor control set for absoluteaccuracy assessment, only the consistency of classes within themselves could be meas-ured. However, it should be kept in mind that there is always a risk of obtaining wrongresults even if class stability results show high level of consistency.

As a result of “classification stability”, 89 segments out of 9.527 are classified as“probable oil slicks” with an accuracy of 91%, 191 segments are classified as “probablelook-alikes” with an accuracy of 86% and 9.092 segments are classified as “clear seawater” with an accuracy of 96%. Moreover, BCR showed that 97% of segments be-longing to “probable oil slicks” has only one class; similarly, probability of segmentsbelonging to “probable look-alikes” and “clear sea water” are 96% and 98%, respec-tively.

As done for the training dataset, each oil spill signature presents in ENVISAT-ASARdata was manually digitized via ENVI’s ROI tool and saved to oil spill position textfiles. ROIs were used as reference oil spill regions. Dark formations are usually clas-sified as potential oil spills according to the following criteria: dark homogeneousspots in a uniform windy area and linear dark areas, not extremely large, with abruptturns. And they are usually classified by visual interpretation as look-alikes according


to the following criteria: low wind areas; coastal zones due to wind sheltering and elon-gated dark areas with smooth turnings in spiral shape [26, 28].

Lastly, to validate our results, the methodology has been tested with computinga success percentage by comparing the areas of the automatically detected oil spillswith the areas of the manually digitalization of oil spills via ROI, by means of arearatios.

An example of this procedure is shown in Figs. 7 and 8 from image A and B, re-spectively. Figures 7 and 8 show the representative steps to validate the oil spills de-tection methodology. The input images (image A and B) contain oil spills to be detected.Applying the oil spills automatic detection (fuzzy classification) to the inputs image,we obtain the result shown in Figs. 7a and 8a, where black regions in red ellipse/squarerepresent all candidate oil spills and green ellipse represents look-alikes. Manual digi-talization of the oil spill (ROI) is shown in Figs. 7b and 8b, depicted by the green re-gion. Finally, Figs. 7c and 8c show the comparison result in terms of an area ratio bythe percentage of success, red pixels are common pixels belonging to both automaticdetected pixels (in red ellipse (a)) and manually digitized pixels (in green region (b)).

a b c

Fig. 7. Comparison result (c) of automatic classification (fuzzy classification) (a), and manuallydigitalized (ROI) (b) from image A.

a b c

Fig. 8. Comparison result (c) of automatic classification (fuzzy classification) (a), and manuallydigitalized (ROI) (b) from image B.


Figures 7c and 8c show that oil pills areas detected by the algorithm are in general dif-ferent than those manually digitalized.

This is not surprising since the manual digitalization of an expert operator can ofteninclude water pixels at the border of an oil spill contour and can connect disjoint regionsseparated by few pixels. This implies an overestimation of the actual area covered bythe oil and a subsequent decreasing in the success percentage. The area ratio percentageis 93% and 90% from image A (reference image) and B, respectively, so the appliedmethodology can discriminate oil spills from look-alikes with good percentage in theseimages (image A and B). The proposed oil spill classification method is tested witheight other scenes of images (image C to image J in Table 3).

Table 3 summarizes results of the application of the procedure described above tothe entire validation dataset of 89 oil spills. The overall percentage of correct identi-fication of the area covered by the 21 subset images analyzed is 84.5%. In general,these results are very encouraging and promising, because the method can detect max-imum pixels of dark spots pixels and discriminate oil slicks from look-alikes.

In some images, the percentage of correct identification is obviously lower thanthe percentage derived analyzing only the number of identified regions. Since this meth-od compares the overall area classified as oil by the automatic system with the ROI areafor each event, the limited decrease in percentage resulting from Table 3 indicates thatthe system detected the presence of oil region despite the ambiguity of the area in whichoil and water are not really separated in some subsets.

On the one hand, the smallest values are observed in some images (e.g., image E:78%, image F: 79%, image I: 77%), because of:

– a small area of oil spills in this scene of image (operational or natural causes),– a large area of look-alikes caused mainly by biogenic slicks and low-wind areas

(less than 3 m/s or superior to 12 m/s).

T a b l e 3. Area ratio comparison procedure applied to the validation oil spills (OS) dataset.

Location/OS source Number of subset images OS area/ROI areaImage A 2 93%Image B 3 91%Image C 2 83%Image D 2 84%Image E 1 78%Image F 3 79%Image G 2 80%Image H 2 91%Image I 1 77%Image J 3 89%Total 21 84.5%


On the other hand, the largest values are observed in a number of images (e.g., im-age A: 93%, image B: 91%) because of the important number of oil spill pixels in theseimages (accidental causes).

5. Conclusion

This paper presents an overview of environmental phenomena: oil spills. SAR sensorsare commonly used by oil spill monitoring systems due to their well demonstrated ca-pability of detection. ASAR deployed on satellites is today an important tool in oil spillmonitoring due to its wide area coverage and day and night all-weather capabilities.In this paper, an adapted methodology for detection of oil slicks in ENVISAT-ASARimages is presented.

Major part of the oil slick detection problem is found to be connected withdistinguishing oil slicks from other natural phenomena that create dark patches inthe ENVISAT-ASAR image. The methodology worked satisfactorily in different casesof oil slicks, by combining different approaches. The discriminative power of humaninterpreter at the starting phase with the optimization of sea state conditions throughnoise removal filters yielded a good basis for further segmentation steps. False clas-sifications due to pixel-based approaches are minimized with the object-based ap-proach, and further discrimination between oil slicks and look-alikes becameapplicable through segmentation, fuzzy membership functions, and classification al-gorithms. The accuracy of classification is different for different images. The overallaccuracy obtained by averaging 21 subsets of 10 images is 91% for oil slicks, 86% forlook-alikes and 96% for clear sea water.

Finally, we tested and validated the proposed methodology with computing a suc-cess percentage by comparing the areas of the automatically detected oil spills (fuzzyclassification) with the areas of the manually digitalization of oil spills (region of in-terest) by means of area ratios. Using an independent dataset of 89 oil spills events,the overall percentage of correct identification of the area covered by 21 subsets ana-lyzed is 84.5%. We have established that the method can detect the maximum of darkspots pixels and discriminate oil slicks from look-alikes

There are some efforts which must be undertaken in future works. They are as fol-lows:

– An improvement of our results with in situ measurements to validate our work;– A comparative study of different classification techniques;– A comparative study between ASAR and optical sensors (e.g., SeaWiFS, MODIS),

to eliminate look-alikes from ASAR images;– How to use classification results (possible oil spills) in the alert system of oil spills.

Acknowledgements – This work is performed as a part of a PhD study funded by the Institute ofMaintenance and Industrial Security, University of Oran, Algeria. The authors would like to thankthe European Space Agency (ESA), for the ASAR scenes used for illustration purposes.


References

[1] GIRARD-ARDHUIN F., MERCIER G., GARELLO R., Oil slick detection by SAR imagery: potential andlimitation, [In] OCEANS 2003, Proceedings, Vol. 1, 2003, pp. 164–169.

[2] FRIEDMAN K.S., PICHEL W.G., CLEMENTE-COLON P., XIAOFENG LI, GoMEx – an experimentalGIS system for the Gulf of Mexico region using SAR and additional satellite and ancillary data,[In] IEEE International Geoscience and Remote Sensing Symposium, IGARSS ’02, Vol. 6, 2002,pp. 3343–3345.

[3] LEIFER I., LUYENDYK B., BRODERICK K., Tracking an oil slick from multiple natural sources: CoalOil Point, California, Marine and Petroleum Geology 23(5), 2006, pp. 621–630.

[4] O’BREIN G.W., LAWRENCE G.M., WILLIAMS A.K., GLENN K., BARRETT A.G., LECH M., EDWARDS D.S.,COWLEY R., BOREHAM C.J., SUMMONS R.E., Yampi Shelf, Browse Basin, North-West Shelf, Australia:A test-bed for constraining hydrocarbon migration and seepage rates using combinations of 2D and3D seismic data and multiple independent remote sensing technologies, Marine and PetroleumGeology 22(4), 2005, pp. 517–549.

[5] WILLIAMS A., LAWRENCE G., The role of satellite seep detection in exploring the South Atlantic’sultra deep water, [In] Schumacher D., LeSchack L.A. [Eds.], Surface Exploration Case Histories:Applications of Geochemistry, Magnetics and Remote Sensing, AAPG Studies in Geology No. 48,SEG Geophysical References Series No. 11, 2002, pp. 327–344.

[6] PISANO A., Development of oil spill detection techniques for satellite optical sensors and theirappilcation to monitor oil spill disharge in the mdditeranean sea, PhD Thesis, Department of Controland Management of Natural Resources, University of Bologna, Italy, 2011.

[7] BREKKE C., SOLBERG A.H.S., Oil spill detection by satellite remote sensing, Remote Sensing ofEnvironment 95(1), 2005, pp. 1–13.

[8] ESPEDAL H.A., Detection of oil spill and natural film in the marine environment by spacebornesynthetic aperture radar, PhD Thesis, Department of Physics, University of Bergen and NansenEnvironment and Remote Sensing Center, Norway, 1998.

[9] HORNÁČEK M., WAGNER W., SABEL D., HONG-LINH TRUONG, SNOEIJ P., HAHMANN T., DIEDRICH E.,DOUBKOVÁ M., Potential for high resolution systematic global surface soil moisture retrieval viachange detection using Sentinel-1, IEEE Journal of Selected Topics in Applied Earth Observationsand Remote Sensing 5(4), 2012, pp. 1303–1311.

[10] TOPOUZELIS K.N., Oil spill detection by SAR images: dark formation detection, feature extractionand classification algorithms, Sensors 8(10), 2008, pp. 6642–6659.

[11] KARATHANASSI V., TOPOUZELIS K., PAVLAKIS P., ROKOS D., An object-oriented methodology to detectoil spills, International Journal of Remote Sensing 27(23), 2006, pp. 5235–5251.

[12] SOLBERG A.H.S., STORVIK G., SOLBERG R., VOLDEN E., Automatic detection of oil spills in ERS SARimages, IEEE Transactions on Geoscience and Remote Sensing 37(4), 1999, pp. 1916–1924.

[13] SOLBERG A.H.S., BREKKE C., HUSØY P.O., Oil spill detection in radarsat and envisat SAR images,IEEE Transactions on Geoscience and Remote Sensing 45(3), 2007, pp. 746–755.

[14] FISCELLA B., GIANCASPRO A., NIRCHIO F., PAVESE P., TRIVERO P., Oil spill detection using marineSAR images, International Journal of Remote Sensing 21(18), 2000, pp. 3561–3566.

[15] NIRCHIO F., SORGENTE M., GIANCASPRO A., BIAMINO W., PARISATO E., RAVERA R., TRIVERO P.,Automatic detection of oil spills from SAR images, International Journal of Remote Sensing 26(6),2005, pp. 1157–1174.

[16] TOPOUZELIS K., KARATHANASSI V., PAVLAKIS P., ROKOS D., Detection and discrimination betweenoil spills and look-alike phenomena through neural networks, ISPRS Journal of Photogrammetryand Remote Sensing 62(4), 2007, pp. 264–270.

[17] BREKKE C., SOLBERG A.H.S., Classifiers and confidence estimation for oil spill detection in ENVISATASAR images, IEEE Geoscience and Remote Sensing Letters 5(1), 2008, pp. 65–69.

[18] LINLIN XU, LI J., BRENNING A., A comparative study of different classification techniques for marine oilspill identification using RADARSAT-1 imagery, Remote Sensing of Environment 141, 2014, pp. 14–23.


[19] WAGNER W., PATHE C., SABEL D., BARTSCH A., KUNZER C., SCIPAL K., Experimental 1 km soilmoisture products from ENVISAT ASAR for Southern Africa, Proceedings of ENVISAT Symposium,Montreux, Switzerland, 2007, SP-636.

[20] RAMOS-FUERTES A., MARTI-CARDONA B., BLADÉ E., DOLZ J., Envisat/ASAR images for the calibrationof wind drag action in the Doñana wetlands 2D hydrodynamic model, Remote Sensing 6(1), 2014,pp. 379–406.

[21] SPARWASSER N., KRAUS T., HASCHBERGER P., Multi-temporal radar image mosaic from the MekongRiver Delta (ENVISAT ASAR© ESA), Status Report 2007–2013, German Remote Sensing DataCenter, Oberpfaffenhofen, September 2013, pp. 64–65.

[22] SHENGLI HUANG, POTTER C., CRABTREE R.L., HAGER S., GROSS P., Fusing optical and radar data toestimate sagebrush, herbaceous and bare ground cover in Yellowstone, Remote Sensing ofEnvironment 114(2), 2010, pp. 251–264.

[23] FINGAS M.F., BROWN C.E., Review of oil spill remote sensing, Spill Science and Technology Bulletin4(4), 1997, pp. 199–208.

[24] MOUCHE A.A., HAUSER D., DALOZE J.-F., GUERIN C., Dual-polarization measurements at C-bandover the ocean: results from airborne radar observations and comparison with ENVISAT ASARdata, IEEE Transactions on Geoscience and Remote Sensing 43(4), 2005, pp. 753–769.

[25] GIRARD-ARDHUIN F., MERCIER G., COLLARD F., GARELLO R., Operational oil-slick characterization bySAR imagery and synergistic data, IEEE Journal of Oceanic Engineering 30(3), 2005, pp. 487–495.

[26] MIHOUB Z., HASSINI A., Oil spill detection technique from RADAR and optical satellite data,The Second International Conference on Signal, Image, Vision and their Application SIVA ’13,November 18–20, 2013, Algeria, pp. 169–174.

[27] SERTAC AKAR, MEHMET LUTFI SÜZEN, NURETDIN KAYMAKCI, Detection and object-based classifica-tion of offshore oil slicks using ENVISAT-ASAR images, Environmental Monitoring and Assessment183(1–4), 2011, pp. 409–423.

[28] MIHOUB Z., HASSINI A., Oil spill monitoring and classification technique from ENVISAT-ASAR data,International Conference on Engineering of Industrial Safety and Environment ICISE ’14, January26–27, 2014, Algeria.

[29] WACKERMAN C.C., Digital SAR image formation, [In] CARSEY F.D. [Ed.], Microwave Remote Sensingif Sea Ice, Geophysical Monograph 68, Washington, 1992, pp. 105–110.

[30] HASSINI A., DÉJEAN S., BENABADJI N., HASSINI N., BELBACHIR A.H., Forest fires smoke monitoringfrom sea-viewing wide field-of-view sensor images, Optica Applicata 38(4), 2008, pp. 737–754.

[31] MARGHANY M., RADARSAT automatic algorithms for detecting coastal oil spill pollution,International Journal of Applied Earth Observation and Geoinformation 3(2), 2001, pp. 191–196.

[32] ÖZKAN C., SUNAR F., Comparisons of different semi-automated techniques for oil-spill detection: a casestudy in Lebanon, 27th EARSel Symposium, June 4–7, 2007, Bolzano, Italy.

[33] RUSS J.C., The Image Processing Handbook, CRC Press, Boca Raton, United States,1992, p. 445.[34] ESPINDOLA G.M., CAMARA G., REIS I.A., BINS L.S., MONTEIRO A.M., Parameter selection for region-

-growing image segmentation algorithms using spatial autocorrelation, International Journal ofRemote Sensing 27(14), 2006, pp. 3035–3040.

[35] YUANMING SHU, LI J., YOUSIF H., GOMES G., Dark-spot detection from SAR intensity imagery withspatial density thresholding for oil-spill monitoring, Remote Sensing of Environment 114(9), 2010,pp. 2026–3035.

Received March 3, 2014in revised form June 1, 2014


Deflectometry for phase retrieval using a composite fringe

TONGCHUAN LIU1, CANLIN ZHOU1*, YEPENG LIU1, SHUCHUN SI1, ZHENKUN LEI2

1School of Physics, Shandong University, Jinan 250100, China

2Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China


An improved deflectometry for wavefront measurement using a composite fringe is proposed toreduce the projection fringes and improve the accuracy. The single composite fringe containsfour fringes in different directions. It goes through the tested objects and then is captured bya CCD camera. Two high frequency orthogonal fringe patterns and two single period orthogonalfringe patterns can be obtained from the composite fringe by fast Fourier transform. The unwrap-ping of the wrapped phase of the high frequency fringe is accomplished by the corresponding singleperiod fringe using a heterodyne method. The wavefront is reconstructed by the integration of par-tial derivatives. Using only one fringe, the proposed method is more applicable to dynamic wavefrontmeasurement. The experimental results demonstrate that the proposed method can retrieve the com-plex wavefronts more accurately.

Keywords: wavefront measurement, fringe analysis, phase retrieval, fast Fourier transform (FFT), multi-frequency heterodyne principle.

1. IntroductionMany methods for wavefront measurement have been presented so far. They measurethe phase directly or measure the wavefront slope. Measuring the phase directly hasa high accuracy, but it is not suitable for measuring objects with complex shapes. Mea-suring the wavefront slope can solve the problem, but it requires coherent illuminationand a precise positioning of the optical setup.

A simple technique for measuring the wavefront slopes, consisting of a LCD mon-itor and a CCD camera, has been developed in the last decade [1, 2]. The conventionalfringe algorithms are used to extract the deflections introduced by the tested objectmodifying the reference fringe pattern. However, for the general wavefront, two partialderivatives of the phase are needed to recover the desired wavefront. Two fringe pat-terns are displayed and captured successively in orthogonal directions. It is not suitablefor dynamic measurements. FLORES et al. proposed to utilize a two-dimensional additive

452 TONGCHUAN LIU et al.

fringe to extend the one-dimensional deflectometry to two-dimensional case [3]. It hasan advantage of measuring smooth wavefront slopes by one-shot deflectometry. Butphase unwrapping must be carried out before wavefront information can be deducedfrom the partial derivatives of the phase. Encountering an object with a complex shape,phase unwrapping will become a difficult procedure. CANABAL and ALONSO [1] em-ployed the TPU (temporal phase unwrapping) method [4–6], where the unwrapping iscarried out along the time axis. CASTILLO et al. [7] proposed the technique for wavefrontmeasurement of flame flux by combining the color fringe pattern and the temporalphase unwrapping method [8]. These methods need the manipulation of various im-ages, which do not meet the requirements of dynamic measurement.

Inspired by GARCÍA-ISÁIS and OCHOA [9], we get four fringe patterns from a com-posite fringe to solve this problem. Different from the method proposed by García-Isáis,we develop a single composite fringe containing four fringes in different directions.By calculating, we get two high frequency orthogonal fringe patterns and two singleperiod orthogonal fringe patterns. Making use of a heterodyne principle [10–13], weget simultaneously two accurate wavefront slope components from the orthogonalfringe patterns. After integration, we can obtain the results with a high accuracy.Though our method resembles the one proposed in [9], it is extended to the two-direc-tion from the original one-direction, which meets the requirements of phase unwrap-ping in the wavefront measurement.

The paper is organized as follows. Section 2 introduces the principle of the system.Section 3 shows the procedure of the experiment. Section 4 presents the experimentalresults. Section 5 discusses different results and summarizes this paper.

2. Fringe analysisSuppose that we have a fringe pattern displayed in a LCD across the plane (x, y) withfringes along the y-direction. The optical path lengths will change if we place a purephase object in front of the fringe pattern. The rays will be deflected by an angleα = ∂W (x, y)/∂x, if the phase is inhomogeneous in the x-direction; W(x, y) is the opticalpath length accumulated by a ray traveling through the phase object at the position (x, y).

Fig. 1. One-dimensional deflectometry.

x

P

y

d

T

α

Deflectometry for phase retrieval using a composite fringe 453

The fringes will appear shifted in the x-direction by a distance α d ≈ (∂W (x, y)/∂x)dwhile the distance of the test object to the displayed pattern is d (as shown in Fig. 1).

Without loss of generality, we can suppose the undistorted fringe pattern is as fol-lows:

(1)

where f is the carrier frequency. The intensity distribution seen through the phase ob-ject will be as follows:

(2)

However, to reconstruct the wavefront W (x, y), we need to obtain the partial de-rivatives ∂W (x, y)/∂x and ∂W (x, y)/∂y.

Using a computer, we generate a composite pattern to be displayed in a LCD given by

(3)

where f is the carrier frequency, G is the constant that represents the amplitude value,(x, y) are the normalized pixel coordinates, and I (x, y) is the image with its gray levelsin the range [0, G]. We can see that the pattern given by Eq. (3) comprises the sum offour fringe patterns: one with vertical fringes, another with horizontal fringes, andthe last two with fringes almost at 45° and 135°. If the carrier terms are written as fol-lows:

(4)

(5)

(6)

then the following relations hold,

(7)

(8)

The cosines in formulas (7) and (8) are one period vertical and horizontal fringes.

I x y,( ) I0 1 2πfx( )cos+=

I x y,( ) I0 1 2πfx 2πfd ∂W x y,( )∂x

--------------------------+⎝ ⎠⎜ ⎟⎛ ⎞

cos+=

I x y,( ) G8

-------- 4 2πfx( )cos 2πfy( )cos

2π 1 f–( )x 2πfy+cos 2πfx 2π 1 f+( )y+cos

+ + +

+ +

⎩

⎭

⎨

⎬

⎧

⎫

=

cx x y,( ) 2πfx,= cy x y,( ) 2πfy=

cxy1 x y,( ) 2π 1 f–( )x 2πfy+=

cxy2 x y,( ) 2πfx 2π 1 f+( )y+=

cxy1 x y,( ) cx x y,( ) cy x y,( )–+ 2πx=

cxy2 x y,( ) cx x y,( ) cy x y,( )–– 2πy=


The intensity profile that we will obtain after the fringe in Eq. (3) goes throughthe object will be given by

(9)

where a and b are the background and amplitude terms that depend on the LCD, re-spectively, ϕ x, ϕ y, ϕ xy1 and ϕ xy2 are the phase functions related to the wavefront.

As presented in [9], the Fourier transform of Eq. (9) can be expressed as

(10)

where (u, v) are the frequency coordinates. It consists of nine spectra centered onfrequencies (0, 0), ( f , 0), (0, f ), (1 – f, f ), ( f , f + 1), (–f, 0), (0 , –f ), ( f – 1, –f ) and(–f, –f – 1).We only choose Dx, Dy, Dxy1 and Dxy2 to filter. We can separate these termsaccurately by a band-pass filter, and then transform them into the space domain bythe inverse Fourier transform. By computing the phase angle of these quantities, wecan obtain the phase maps of four fringe patterns as follows:

(11a)

(11b)

(11c)

(11d)

The wrapped differences of φ xy1, φ xy2, φ x and φ y are shown as:

(12)

i a b cx ϕ x+( )cos cy ϕ y+( )cos cxy1 ϕ xy1+( )cos cxy2 ϕ xy2+( )cos+ + ++=

I u v,( ) A 0 0,( ) Dx u f– v,( ) Dy u v f–,( )Dxy1 u f 1–+ v f–,( ) Dxy2 u f– v f– 1–,( )Dx

* u f+ v,( ) Dy* u v f+,( )

Dxy1* u f– 1+ v f+,( ) Dxy2

* u f+ v f 1+ +,( )

+ + ++ + ++ + ++ +

=

φ x Cx ϕ ' x+mod 2π

arctanIm Dx u f– v,( )

Re Dx u f– v,( )-----------------------------------------------

⎩ ⎭⎪ ⎪⎨ ⎬⎪ ⎪⎧ ⎫

= =

φ y Cy ϕ ' y+mod 2π

arctanIm Dy u v f–,( )

Re Dy u v f–,( )------------------------------------------------

⎩ ⎭⎪ ⎪⎨ ⎬⎪ ⎪⎧ ⎫

= =

φ xy1 Cxy1 ϕ ' xy1+mod 2π

arctanIm Dxy1 u f 1–+ v f–,( )

Re Dxy1 u f 1–+ v f–,( )-----------------------------------------------------------------------

⎩ ⎭⎪ ⎪⎨ ⎬⎪ ⎪⎧ ⎫

= =

φ xy2 Cxy2 ϕ ' xy2+mod 2π

arctanIm Dxy2 u f– v f– 1–,( )

Re Dxy2 u f– v f– 1–,( )-----------------------------------------------------------------------

⎩ ⎭⎪ ⎪⎨ ⎬⎪ ⎪⎧ ⎫

= =

φ 1w arctan

φ xy1 φ x φ y–+( )sin

φ xy1 φ x φ y–+( )cos--------------------------------------------------------=


(13)

As presented in Eqs. (7) and (8), each of the wrapped differences consists of onlyone period and is within the range 0 to 2π. To get φ1 and φ2, the unwrapped function ofthe low frequency wrapped function and the following relations are satisfied:

(14)

(15)

Using Eq. (7) and Eq. (8) in Eq. (14) and Eq. (15), we obtain

(16)

(17)

where ϕ E1 = ϕ xy1 + ϕ x – ϕ y and ϕ E2 = ϕ xy2 + ϕ x – ϕ y represent the equivalent phasesof the phase differences. Then, what we have obtained are two single period fringe pat-terns [9].

The multifrequency heterodyne principle can provide an accurate phase map be-cause it can calculate the phase value of every pixel independently [13]. The un-wrapped phase φ (x) is calculated by adding the phase function φ 1(x) and the orderfunction O1(x) multiplied by 2π

(18)

Since we have the phase maps of two single period fringe patterns and two relatedhigh frequency fringe patterns, we can get two accurate orthogonal phase maps byEq. (18). They are the partial derivatives ∂W (x, y)/∂x and ∂W (x, y)/∂y.

Two accurate components of the ray deflection are obtained, then we can re-construct the wavefront because it will be the solution of a Poisson equation withthe source term ∂2W/∂x2 + ∂2W/∂y2 resulting from the derivation of the vector(∂W (x, y)/∂x, ∂W (x, y)/∂y).

The integration of the partial derivatives ∂W (x, y)/∂x and ∂W (x, y)/∂y is equivalentto finding the function f (x, y) that is the solution of the Poisson equation ∇2f (x, y) == g(x, y) [3], while f (x, y) can be written as

(19)

where

(20)

φ 2w arctan

φ xy2 φ x– φ y–( )sin

φ xy2 φ x– φ y–( )cos-------------------------------------------------------=

φ 1w φ 2

w,

φ1 cxy1 cx cy–+( ) ϕ xy1 ϕ x ϕ y–+( )+=

φ2 cxy2 cx– cy–( ) ϕ xy2 ϕ x– ϕ y–( )+=

φ1 x y,( ) 2πx ϕ E1 x y,( )+=

φ2 x y,( ) 2πy ϕ E2 x y,( )+=

φ x( ) φ1 x( ) O1 x( ) 2π×+=

f x y,( ) Lπ

-------⎝ ⎠⎛ ⎞2 dkn

n2 k 2+---------------------- πkx

L-------------⎝ ⎠⎛ ⎞ πny

L---------------⎝ ⎠⎛ ⎞sinsin

n 1=

L∑k 1=

L∑–=

dkn1

L2----------- g x y,( ) πkx

L-------------⎝ ⎠⎛ ⎞ πny

L---------------⎝ ⎠⎛ ⎞ dx dysinsin

0

2L

∫0

2L

∫=


3. ExperimentsNow, we will describe some experiments and practical suggestions for the above pro-cedure.

The two-dimensional composite fringe pattern described by Eq. (3) was displayedin a LCD. We set f = 20 and G = 255. Our tested object was a convex lens with a di-ameter of 7 cm as shown in Fig. 2. The lens was 5 cm distant from the LCD. The cameraused for acquiring the images was at a distance of the order of 100 cm from the LCD.

Figure 3 shows the frequency spectrum of the acquired pattern. The nine bright spotsare clearly visible, therefore it is easy to locate their position. Multiplying the FFT re-sult with a Hanning filter of radius 10, centered on the frequency coordinates (30, 0),(0, 23), (–30, 23) and (30, 23) shown in the circles, and calculating the four inverseFFTs, we have obtained four wrapped phases given by Eq. (7) and shown in Fig. 4.

Using Eqs. (16) and (17), we obtain the phase maps of two fringe patterns withoutunwrapping as follows:

cx(x, y) = 2πx, cy(x, y) = 2πy (21)

Taking advantage of the multifrequency heterodyne principle, we can obtainthe accurate phase maps of two orthogonal fringe patterns with the phase maps of twosingle period fringe patterns and two related high frequency fringe patterns.

Fig. 2. The tested convex lens.

150

200

250

300

350

400

200 250 300 350 400 450 500 550

Pix

els

Y

Pixels XFig. 3. Frequency spectrum of the acquiredpattern.


In order to avoid boundary effects, we choose a region in the middle as shownin Fig. 2. The unwrapped maps of ∂W (x, y)/∂x and ∂W (x, y)/∂y are shown in Fig. 5.

As presented in Section 2, with the value of the vector (∂W (x, y)/∂x, ∂W (x, y)/∂y),obtained above, we can calculate ∇2W (x, y). Basing on the result of the numerical inte-gration of the Poisson equation with ∇2W (x, y), we reconstructed the wavefront W (x, y).

4. ResultsWe reconstruct the wavefronts by Flores algorithm, García-Isáis algorithm andthe proposed algorithm separately. As shown in Figs. 6a–6c, the central areas corre-sponding to the convex lens are smooth and similar. By comparison of the results, wecan see that all the methods can retrieve the wavefronts of the convex lens well.

a b

c d

Fig. 4. Wrapped phase components obtained from the Fourier spectrum. Horizontal (a), vertical (b), slopeupper right (c), and slope bottom right (d).

Fig. 5. The unwrapped maps of ∂W (x, y)/∂x (a), and ∂W (x, y)/∂y (b).

a b


The contrasts are not obvious when the tested object has a simple shape. The compu-tational times are 0.7216, 0.7286 and 0.7360 s. There is little difference among them.

The 3D display of the wavefronts recovered by the proposed algorithm is shownin Fig. 6d. It conforms to the shape of the tested lens. This confirms the practicabilityof the proposed algorithm.

Lacking the theoretical value, we simulate the above experiment by MATLAB. Wechoose an area in the center of the convex lens to measure. After being normalized,the mean square errors obtained by Flores algorithm, García-Isáis algorithm andthe proposed algorithm are 0.3153, 0.3063 and 0.3005. The computational times are0.2843, 0.2872, and 0.2896 s. At the longest computational time, the proposed algo-rithm has the highest accuracy. The comparisons of them are not obvious. To contrastthe three algorithms distinctly, we do another experiment on a complex bottle as shownin Fig. 7.

Since the pattern in the middle of the bottle is a semicircle and the matter is isotropic,the wavefronts should have the same structure in the middle. The differences in the struc-tures of the wavefronts obtained by Flores algorithm, García-Isáis algorithm andthe proposed algorithm are shown in Figs. 8a–8c, respectively. The contrasts among

300

250

200

150

100

50

50 100 150 200 250 300

0 1000 2000 3000

Pix

els

Y

Pixels X

[μm]

a 300

250

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50

50 100 150 200 250 300

0 1000 2000 3000

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els

Y

Pixels X

[μm]

b

300

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50 100 150 200 250 300

0 1000 2000 3000

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els

Y

Pixels X

[μm]

c

–1000

–10000

100200

300

Pixels X0100

200300

Pixels Y

×103

Wav

efro

nts

[μm

] 4

2

0

–2

d

Fig. 6. Wavefronts obtained by Flores algorithm (a), by García-Isáis algorithm (b), and by the proposedalgorithm (c). 3D display of the wavefronts recovered by the proposed algorithm (d).


the figures are obvious. The contour lines in Fig. 8a are nearly rectangles which arevery different from the bottle. The contour lines in Fig. 8b are rounder. García-Isáisalgorithm is more accurate. The contour lines in Fig. 8c are the roundest. The proposedalgorithm is the most accurate. The 3D display of the wavefronts recovered by the pro-posed algorithm is shown in Fig. 8d. It also conforms to the structure of the bottle.The computational times are 0.7241, 0.7312 and 0.7364 s. The complexity of the tested

Fig. 7. The tested complex bottle.

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50 100 150 200 250 300

0 1000 2000 3000

Pixe

ls Y

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[μm]

a 300

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ls Y

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[μm]

b

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[μm]

c

–10000

100200

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200300

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×103

Wav

efro

nts

[μm

] 6

2

0

–2

d

Fig. 8. Phase change obtained by Flores algorithm (a), by García-Isáis algorithm (b), by the proposedalgorithm (c). 3D display of the wavefronts recovered by the proposed algorithm (d).

4000

4000

4


object influences the computational times little, however, it influences the accuracyobviously. The experiment demonstrates that the proposed method can retrieve the com-plex wavefronts more accurately.

The proposed algorithm unwraps the wrapped phases ∂W (x, y)/∂x and ∂W (x, y)/∂yby the multifrequency heterodyne method. García-Isáis algorithm unwraps the wrappedphases ∂W (x, y)/∂x in the same way, however, it unwraps the wrapped phases∂W (x, y)/∂y by the general spatial method. Since ∂W (x, y)/∂y has errors, the recon-structed wavefronts ∇2W (x, y) have a low accuracy. The accuracy of Flores algorithmis much lower. It is because the algorithm only separates two orthogonal fringes fromthe composite fringe by FFT, and the unwrapping procedure of a wrapped phase is verysimple. When the object has a complex shape, the accuracy reduces most.

The more complex the algorithm is, the more computational time it uses. The dif-ferences in computational times are small. Taking advantage of multi-threading andparallel processing, GPU (graphic processing unit) algorithm can speed up the processesof the multifrequency heterodyne method [14]. Then the proposed algorithm will useless computational time and apply to the dynamic wavefront measurement better.

Using only one fringe, the proposed method makes it possible to measure dynamicwavefronts. In general, it can retrieve the wavefronts quickly and accurately. Espe-cially, when the tested object has a complex shape, the proposed method can improvethe accuracy greatly.

5. Conclusions

By a composite fringe containing four fringe patterns, we get the accurate phase mapsof two accurate orthogonal fringe patterns. Basing on the phase maps, we obtainthe accurate wavefront patterns. The proposed algorithm is more applicable to dynamicwavefront measurement. It can retrieve the complex wavefronts more accurately.

Acknowledgments – This work was supported by the National Nature Science Foundation of China(No. 11172054), the support is gratefully acknowledged.

References

[1] CANABAL HA., ALONSO J., Automatic wavefront measurement technique using a computer displayand a charge coupled device camera, Optical Engineering 41(4), 2002, pp. 822–826.

[2] LEGARDA-SAENZ R., ESPINOSA-ROMERO A., Wavefront reconstruction using multiple directionalderivatives and Fourier transform, Optical Engineering 50(4), 2011, article 040501.

[3] FLORES J.L., BRAVO-MEDINA B., FERRARI J.A., One-frame two-dimensional deflectometry for phaseretrieval by addition of orthogonal fringe patterns, Applied Optics 52(26), 2013, pp. 6537–6542.

[4] YANJUN FU, YONGLONG WANG, JIANFENG WU, GUANGYU JIANG, Dual-frequency fringe Fouriertransform profilometry based on defocusing, Optics Communications 295, 2013, pp. 92–98.

[5] YAJUN WANG, LAUGHNER J.I., EFIMOV I.R., SONG ZHANG, 3D absolute shape measurement of liverabbit hearts with a superfast two-frequency phase-shifting technique, Optics Express 21(5), 2013,pp. 5822–5832.


[6] KAI LIU, YONGCHANG WANG, LAU D.L., QI HAO, HASSEBROOK L.G., Dual-frequency pattern schemefor high-speed 3-D shape measurement, Optics Express 18(5), 2010, pp. 5229–5244.

[7] CASTILLO O.E., LEGARDA-SÁENZ R., FLORES J.L., GARCIA-TORALES G., Measurement of phase objectsby the use of color phase-shifting technique, Proceedings of SPIE 8867, 2013, pp. 886710–886716.

[8] HUNTLEY J.M., SALDNER H., Temporal phase-unwrapping algorithm for automated interferogramanalysis, Applied Optics 32(17), 1993, pp. 3047–3052.

[9] GARCÍA-ISÁIS C.A., OCHOA N.A., One shot profilometry using a composite fringe pattern, Optics andLasers in Engineering 53, 2014, pp. 25–30.

[10] YANMING CHEN, YUMING HE, ERYI HU, HONGMAO ZHU, Deformation measurement using dual-fre-quency projection grating phase-shift profilometry, Acta Mechanica Solida Sinica 21(2), 2008,pp. 110–115.

[11] CHAO ZUO, QIAN CHEN, GUOHUA GU, SHIJIE FENG, FANGXIAOYU FENG, RUBIN LI, GUOCHEN SHEN,High-speed three-dimensional shape measurement for dynamic scenes using bi-frequencytripolar pulse-width-modulation fringe projection, Optics and Lasers in Engineering 51(8), 2013,pp. 953–960.

[12] ZHENZHONG XIAO, OICHOO CHEE, ANAND ASUNDI, An accurate 3D inspection system using heterodynemultiple frequency phase-shifting algorithm, Physics Procedia 19, 2011, pp. 115–121.

[13] REICH C., RITTER R., THESING J., White light heterodyne principle for 3D-measurement, Proceedingsof SPIE 3100, 1997, pp. 236–244.

[14] KARPINSKY N., HOKE M., CHEN V., ZHANG S., High-resolution, real-time three-dimensional shapemeasurement on graphics processing unit, Optical Engineering 53(2), 2014, article 024105.

Received March 9, 2014in revised form July 12, 2014


Luminescence of hydrothermally fabricated PbF2:Er3+ particles and their application in bifacial silicon solar cells

FANG YANG1, CHENYANG WU2, XIULI HAO1, YONGSHENG CHEN1*, JINGXIAO LU1, SHI-E YANG1

1Key Lab of Material Physics, Department of Physics, Zhengzhou University, Zhengzhou 450052, China

2Yingli Solar, 3399 Chaoyang North Road, Baoding, China

We report the synthesis of PbF2:Er3+ particles using a hydrothermal method. The structure andupconversion emission properties of the products are investigated by scanning electron microsco-py, X-ray diffractometer, Raman spectrophotometer and fluorescence spectrometry. An increasein Er3+ concentration in the crystals changes the PbF2 structure from a mixed phase to a cubic phaseand decreases the grain size to nanoscale levels. Enhanced upconversion efficiency is achievedafter annealing resulted from the formation of the cubic phase and the increase of grain size.The optimal Er3+ concentration is found to be 4% after annealing, and applied to the back of a bi-facial silicon solar cell, maximum external quantum efficiencies of 0.38% and 0.79% are respec-tively obtained under 0.77 W/cm2 laser excitation (1560 nm) and AM1.5 + laser co-excitation.

Keywords: PbF2:Er3+ particles, hydrothermal method, upconversion.

1. Introduction

The upconversion (UC) luminescence of lanthanide-doped fluorides has attractedsignificant attention because of their low phonon energy and good optical performance[1–3]; these fluorides are widely used in lasers, sensors, and fluorescence bimolecularmarkers [4–6]. PbF2, a highly transparent material that allows a wide range of light topass through it without much attenuation in luminescence, has many advantages as a hostmatrix for Ln3+ ions. The phonon energy of PbF2 is <250 cm–1, which is significantlylower than that of NaYF4 (~360 cm–1) [7]. In addition, PbF2 undergoes orthorhom-bic (α ) to cubic (β ) phase transition at temperatures >335°C, a characteristic thatmakes the material an interesting subject for structure-property studies [8].

Many investigations on lanthanide-doped transparent glass ceramics containingPbF2 nanocrystals have been reported [7, 9–11]; in these reports, doping of PbF2 andglass ceramic formation are simultaneously completed using PbF2 and LnF3 or Ln2O3as raw materials and Ln3+-doped PbF2 nanoparticle synthesis through chemical etching

464 FANG YANG et al.

of the bulk glass ceramics. In 2010, GANGQIANG ZHU et al. [12] reported the fabricationof PbF2 microstructures via a simple hydrothermal method and found that treatmenttime, amount of cetyltrimethyl ammonium bromide used, and F/Pb molar ratio signif-icantly affect the resultant PbF2 shape and phase structures. SARKAR et al. [13] reportedthe synthesis of PbF2:Dy3+ nanocrystals by a hydrothermal method. In the presentstudy, we fabricate PbF2:Er3+ nanoparticles using a hydrothermal method and inves-tigate the effects of doping concentration and high-temperature annealing on the lu-minescence properties of the products. The fabricated materials are then applied toa bifacial silicon (c-Si) solar cell, and improvements in near-infrared responses are dis-cussed.

2. Experiment

Er2O3 was dissolved in dilute HNO3 (1:1 volume ratio) with heating and stirring toprepare an Er(NO3)3 stock solution (0.1 mol/dm3). A certain amount of Pb(C2H3O2)2was dissolved in 5 cm3 of deionized water. After mixing these two solutions at differentEr3+ to Pb2+ mole ratios, NH4HF2 solution was gradually added to the mixture to forma white suspension. A certain amount of citric acid was then added to the white sus-pension. The resulting solution was stirred for approximately 10 min and then trans-ferred into a 100 cm3 Teflon vessel. The vessel was filled with deionized water up to60% of the total volume and then sealed tightly. Thereafter, the solution was heatedat 200°C for 8 h and then slowly cooled to room temperature. The solution was cen-trifuged, and the obtained products were thoroughly washed with deionized water anddehydrated alcohol. The products were dried in air at approximately 100°C for 2 h. Toimprove the emission intensity of the product, high-temperature annealing was imple-mented for 1 h.

The crystalline structure and morphologies of the products were characterized usinga scanning electron microscope with an energy-dispersive spectrometer (SEM-EDS,JEOL-JSM-6700F/INCA-ENERGY), a transmission electron microscope (TEM,JEM-2100), a Raman spectrophotometer (Renishaw-2000 within the range of 200 to880 cm–1; the laser source at 514 nm was used as the excitation source, and the laserpower level was 5 mW) and an X-ray diffractometer (XRD, Philips PANAlyticalX’pert) with Cu Kα radiation. The UC spectra of the products were recorded by a spec-trophotometer (Fluoromax-4, Horiba Jobin Yvon) under 1560 nm laser excitation.

A c-Si solar cell with an area of 2.6 cm×2 cm was used to verify the enhanced solarcell response from the UC process. Under AM1.5G illumination (2000AAA,Crowntech, Inc.), the solar cell without phosphor exhibited approximately 20% and17% efficiency when illuminated from the front and rear, respectively. PbF2:Er3+ pow-der was attached to the rear of the solar cell by dissolution in cyclohexane and thenspin-coating to yield a UC layer thickness of 500 μm. The laser beam was not focusedwith a diameter of 5 mm, and the intensity was measured using a power meter(VPL-2W, Beijing Viasho Technology Co., Ltd.). The short circuit current of the solarcell was measured using a galvanometer (Keithley, 6517).

Luminescence of hydrothermally fabricated PbF2:Er3+ particles... 465

3. Results

Representative XRD patterns of the as-prepared samples are shown in Fig. 1. All ofthe diffraction peaks of the undoped PbF2 sample can be readily indexed to an or-thorhombic (α ) phase (JCPDS Card No. 41-1086), and no diffraction peak correspond-ing to any impurity or allotropic phase is found. By contrast, mixed orthorhombic andcubic (β ) phases (JCPDS Card No. 06-0251) are observed in the doped samples. Asthe Er3+ concentration in the crystals is increased, the peaks corresponding to the cubicphase are enhanced whereas those corresponding to the orthorhombic phase are weak-ened.

Typical SEM and TEM images of the samples are shown in Fig. 2. In Fig. 2a,the undoped PbF2 sample shows a spherical form with sizes ranging from 4 to 6 μm.After doping, the size of the particles (Fig. 2b) decreases to approximately 100 nm, andan elemental composition including F, Pb, and Er is observed (Fig. 2c). TEM images(Fig. 2d) also indicate the formation of spherical nanocrystals with sizes between50 and 100 nm. The diffraction pattern (Fig. 2e) corresponds to the face-centered cubicfluorite lattice [14].

The phase transition behavior of PbF2 has been studied in various experimentsusing high-pressure and theoretical techniques [12, 15–17]. While phase transition be-haviors can be qualitatively explained by Ostwald ripening and oriented attachment [18],these explanations mainly focus on undoped PbF2 growth conditions. In the currentsystem, the size modification and phase transition caused by Er3+ doping originate fromthe surface charge redistribution of the crystal nucleus, which is induced by inner elec-tron charge transfer between dopant ions and lattice cations [19].

6%

5%

4%

3%

2%

0%

β-PbF2

α-PbF2

(111

)

(200

)

(220

)

(311

)

(222

)

(400

)

(331

)

(420

)

(422

)

Inte

nsity

[a. u

.]

2θ [deg]20 30 40 50 60 70 80

Fig. 1. XRD patterns of samples with different Er3+ concentrations.


The upconversion emission spectra of the as-prepared samples excited at 300 mW,1560 nm laser are presented in Fig. 3. A major infrared emission corresponding tothe 4I11/2 → 4I15/2 Er3+ transition is found at 970 nm. Weaker infrared, red, and greenemissions, which correspond to 4I9/2 → 4I15/2, 4F9/2 → 4I15/2, and 2H11/2(4S3/2)→ 4I15/2transitions, are found at approximately 800, 650, and 540 nm, respectively. The emis-sion intensity significantly increases with increasing Er3+ concentration from 2% to 5%;

Fig. 2. SEM image of the undoped sample (a), SEM (b), comparison spectra (c), TEM (d) and selectedarea electron diffraction pattern (e) of PbF2:Er(6%) sample.

c

e

ba

d

F Er Pb

Pb

Er Er

0 2 4 6 8Full scale 2432 cts [keV]


further increases in Er3+ concentration, however, decrease the emission intensity.Therefore, the optimum Er3+ doping concentration for the as-prepared samples is 5%.

Upconversion (UC) nanomaterials generally have low emission efficiencies partlybecause of structural defects, such as interstitial anions and cation vacancies, and partlybecause of their large surface area, which features various quenchers induced by solv-ers or surface defects such as absorbed contaminants [20, 21]. Therefore, high-tem-perature annealing is used to enhance the emission efficiency. The XRD spectra ofPbF2:Er3+(4%) samples annealed under different temperatures for 1 h in air are shownin Fig. 4. The proportion of cubic phase particles increases with increasing annealingtemperature, which indicates that the cubic phase is thermodynamically stable. In ad-dition, the full width at half-maximum decreases with increasing annealing tempera-ture, which indicates that the grain size increases after annealing. This finding isdemonstrated by the SEM images in Fig. 5. With the increase in annealing temperature,

Wavelength [nm]Er concentration [%

]

3+

Inte

nsity

[a. u

.]

Fig. 3. Er3+ concentration-dependent emission intensity of the as-prepared samples.

500 600 700 800 900 10006

54

32

2H11/2(4S3/2)→ 4I15/2

4I11/2 → 4I15/2

4I9/2 → 4I15/24F9/2 → 4I15/2

500°C

400°C

300°C

As-prepared

20 30 40 50 60 70 80

Inte

nsity

[a. u

.]

2θ [deg]

Fig. 4. XRD patterns of the annealed PbF2:Er3+(4%) samples under different temperature.


the grain aggregation occurs and micro-grade particles are formed after annealing at500°C, which may contribute to the increase in UC emission.

The UC emission spectra of the annealed samples under different temperature areshown in Fig. 6 excited at 60 mW, 1560 nm laser. It is conformed that with the increasein annealing temperature, the UC emission intensity increases due to the increase in

Fig. 5. SEM images of the annealed PbF2:Er3+(4%) samples under different temperature: 300°C (a),400°C (b), and 500°C (c).

ba

c

×5500°C400°C300°CAs-prepared

500 600 700 800 900 1000

Inte

nsity

[a. u

.]

Wavelength [nm]

Fig. 6. The UC emission spectra of the annealed PbF2:Er3+(4%) samples under different temperature.The signals corresponding to the emissions at 540, 650, and 800 nm are amplified 5.0 times.


the grain size and the formation of the cubic phase. Figure 7 shows the Raman spectraof the samples annealed at 500°C for 1 h with varying Er3+ concentration. For the un-doped sample, one dominating peak accompanied by three weak and broad peaks arefound at about 304, 435, 580, and 704 cm–1, ascribed to the vibrational modes andthe presence of electronic centers [22]. With the addition of Er3+, two weak peaks areshown around 370 and 483 cm–1. The emission spectra of the samples annealed at500°C for 1 h with different doping concentrations are presented in Fig. 8. The varia-tion in emission intensity of samples as a function of Er3+ concentration showsthe same change tendency as that of as-prepared samples. However, the optimum dop-ing concentration of Er3+ decreases to 4%.

The UC emission intensities of the PbF2:Er3+(4%) sample observed after annealingat 500°C were recorded as a function of excitation power in log–log plots (Fig. 9).The intensities of the green, red, and infrared emissions increase with increasing ex-citation power and eventually reach saturation. The slope of the infrared emission is

304 370 435 483 580 704

200 300 400 500 600 700 800

6%

5%

4%

3%

2%

0%

Inte

nsity

[a. u

.]

Raman shift [cm–1]

Fig. 7. The Raman spectra of samples annealed at 500°C for 1 h with varying Er3+ concentration.

500 600 700 800 900 1000

23

45

6

Wavelength [nm] Er concentration [%

]

3+

Inte

nsity

[a. u

.]

Fig. 8. Emission intensities of samples annealed at 500°C for 1 h with varying Er3+ concentration.


approximately 2 under low pumping power, indicating a well-known two-photon mech-anism. In addition, the slopes of the green and red emissions are approximately 3, cor-responding to a three-photon emission process.

The PbF2:Er3+(4%) powders annealed at 500°C for 1 h were applied to the rear ofthe c-Si solar cell with a typical bandgap of 1.1 eV. The log–log plot of the short-circuitcurrent as a function of excitation power is shown in Fig. 10. Similar to the UC emis-sions shown in Fig. 9, the short-circuit current increases with increasing excitationpower and reaches saturation, thereby indicating a direct relationship between the cur-rents and the UC emission intensities. The slope of the short-circuit current under lowpower is similar to that of infrared emission, which suggests that the photon-generatedcarriers are derived mainly from infrared excitation. The external quantum efficiency(EQE) of the solar cell, which is defined as the ratio between the number of generatedelectron–hole pairs caused by the UC emission and the number of incident infraredphotons, can be calculated as follows [23]:

where Isc is the short-circuit current, q is the electron charge, Pin is the excitation power,and hγ is the energy of the laser photon. The calculated EQE values withthe corresponding excitation power are presented in Fig. 10. EQE increases with increas-ing, reaches a maximum (0.38%) at 150 mW (0.77 W/cm2), and then decreases withfurther increases in excitation power because of Isc saturation. This maximum valueis comparable with reported values obtained at 2305 W/m2 for NaYF4:Er3+(20%) ina c-Si solar cell system at 1523 nm (0.64%) [24] and at 37 mW (235 μm×235 μm) forEr3+-Yb3+ co-doped fluoroindate glasses at 1480 nm (0.4%) [25]. Therefore, PbF2 isan excellent host material for high-efficiency UC processes.

In actual application processes, photons from sun irradiation and UC emission areabsorbed simultaneously by solar cells. Thus, the response of solar cells under this con-

7.2

6.8

6.4

6.0

5.6

5.21.8 2.0 2.2 2.4 2.6

Slope = 1.7

Slope = 2.5

Slope = 3.0540650970

log(

inte

nsity

[a. u

.])

log(excited power [mW])

Fig. 9. Excitation power-dependent UC intensities of the PbF2:Er3+(4%) sample after annealing at 500°C.

EQEIsc

Pin q hγ⁄----------------------------=


dition differs significantly from that observed under laser excitation only. However,to the best of our knowledge, few experiments and theoretical calculations have studiedthis difference [1]. The influence of laser power on the properties of c-Si (Eg = 1.12 eV)solar cells under AM1.5 and laser co-excitation was evaluated (Fig. 11); here, all ofthe incident lights are perpendicular to the solar cell and the UC layer. The open-circuitvoltage Voc remains nearly constant with increasing power because of the logarithmicdependence on light intensity. Isc increases linearly with increasing laser power, andan EQE of 0.79% may be obtained, which is higher than the 0.38% shown in Fig. 10.This result is due to the saturation of carrier recombination under co-excitation, whichenhances the collection of electron–hole pairs generated by UC emissions and leadsto an increase in a fill factor. Therefore, the efficiency of the solar cell increases withincreasing laser power, and 0.5% enhancement is achieved at 400 mW.

0.2

0.0

–0.2

–0.4

–0.6

–0.81.8 2.0 2.2 2.4 2.6

0.36

0.32

0.28

0.24Slope = 1.3lo

g(sh

ort-c

ircui

t cur

rent

[mA]

)

EQ

E [%

]

log(excited power [mW])

Fig. 10. Log–log diagrams of short-circuit current and the EQE as a function of excitation power.

0.208

0.204

0.68

0.67

0.66

0.6576.0

75.8

75.6

21.0

20.5

0 100 200 300 400

I sc [A

]FF

[%]

Voc

[V]

Effi

cien

cy [%

]

Excited power [mW]

Fig. 11. Solar cell properties as a function of excitation power at 1560 nm under co-excitation condition.


4. Conclusions

PbF2:Er3+ particles are synthesized in this study using a hydrothermal method. Trans-formation from the mixed phase to cubic phase occurs with increasing dopant concen-tration, and high-temperature annealing contributes to the formation of the cubic phaseand the increase in the grain size as well as improvements in UC emission. The optimaldoping concentration (4%) is obtained after annealing. When the PbF2:Er3+(4%) par-ticles are applied in c-Si solar cells, a maximum EQE of 0.38% is achieved under150 mW, 1560 nm excitation. However, under co-excitation with AM1.5 and laser ir-radiation, an EQE of 0.79% is obtained, resulting in a 0.5% enhancement in efficiencyat 400 mW excitation power. The results of this study indicate that PbF2 is a good can-didate host material for UC applications.

Acknowledgements – This work was supported by the National Key Basic Research Program of China(2011CBA00706).

References

[1] TRUPKE T., GREEN M.A., WÜRFEL P., Improving solar cell efficiencies by up-conversion of sub-band-gap light, Journal of Applied Physics 92(7), 2002, pp. 4117–4122.

[2] RODRÍGUEZ V.D., TIKHOMIROV V.K., MÉNDEZ-RAMOS J., DEL-CASTILLO J., GÖRLLER-WALRAND C.,Measurement of quantum yield of up-conversion luminescence in Er3+-doped nano-glass-ceramics,Journal of Nanoscience and Nanotechnology 9(3), 2009, pp. 2072–2075.

[3] SONGJUN ZENG, GUOZHONG REN, CHANGFU XU, Intense blue photoluminescence of the Tm3+/Yb3+

co-doped single-crystalline hexagonal phase NaYF4 nanorods, Journal of Alloys and Compounds509(5), 2011, pp. 2540–2543.

[4] NGUYEN D.C., FAULKER G.E., DULICK M., Blue-green (450-nm) upconversion Tm3+:YLF laser,Applied Optics 28(17), 1989, pp. 3553–3555.

[5] DOWNING E.A., HESSELINK L., MACFARLANE R.M., KLEIN J.R., EVANS D., RALSTON J., A laser-diode--driven, three-color, solid-state 3-D display, [In] Summaries of papers presented at the Conferenceon Lasers and Electro-Optics, CLEO ’96, Vol. 9, 1996, pp. 89–90.

[6] GUANGSHUN YI , HUACHANG LU, SHUYING ZHAO, YUE GE, WENJUN YANG, DEPU CHEN, LIANG-HONG

GUO, Synthesis, characterization, and biological application of size-controlled nanocrystallineNaYF4:Yb, Er infrared-to-visible up-conversion phosphors, Nano Letters 4(11), 2004, pp. 2191–2196.

[7] TIKHOMIROV V.K., ADAMO G., NIKOLAENKO A.E., RODRIGUEZ V.D., GREDIN P., MORTIER M.,ZHELUDEV N.I., MOSHCHALKOV V.V., Cathodo- and photoluminescence in Yb3+-Er3+ co-dopedPbF2 nanoparticles, Optics Express 18(9), 2010, pp. 8836–8846.

[8] PORTELLA K.F., RATTMANN K.R., DE SOUZA G.P., GARCIA C.M., CANTAO M.P., MUCCILLO R.,Characterization of α ↔ β PbF2 phase transition by several techniques, Journal of MaterialsScience 35(13), 2000, pp. 3263–3268.

[9] FANQING ZENG, GUOZHONG REN, XIANNIAN QIU, QIBIN YANG, JINGWU CHEN, The effect of PbF2 contenton the microstructure and upconversion luminescence of Er3+-doped SiO2-PbF2-PbO glass ceramics,Journal of Non-Crystalline Solids 354(29), 2008, pp. 3428–3432.

[10] SILVA M.A.P., BRIOIS V., POULAIN M., MESSADDEQ Y., RIBEIRO S.J.L., SiO2-PbF2-CdF2 glasses andglass ceramics, Journal of Physics and Chemistry of Solids 64(1), 2003, pp. 95–105.

[11] MORTIER M., Nucleation and anionic environment of Er3+ in a germanate glass, Journal ofNon-Crystalline Solids 318(1–2), 2003, pp. 56–62.


[12] GANGQIANG ZHU, PENG LIU, HOJAMBERDIEV M., JIAN-PING ZHOU, XIJIN HUANG, Synthesis of or-thorhombic and cubic PbF2 by hydrothermal method, Journal of Materials Science 45(7), 2010,pp. 1846–1853.

[13] SARKAR S., HAZRA C., CHATTI M., SUDARSAN V., MAHALINGAM V., Enhanced quantum efficiency forDy3+ emissions in water dispersible PbF2 nanocrystals, RSC Advances 2(22), 2012, pp. 8269–8272.

[14] TIKHOMIROV V.K., MORTIER M., GREDIN P., PATRIARCHE G., GÖRLLER-WALRAND C., MOSHCHALKOV V.V.,Preparation and up-conversion luminescence of 8 nm rare-earth doped fluoride nanoparticles,Optics Express 16(19), 2008, pp. 14544–14549.

[15] EHM L., KNORR K., MÄDLER F., VOIGTLÄNDER H., BUSETTO E., CASSETTA A., LAUSI A., WINKLER B.,High-pressure X-ray diffraction study on α-PbF2, Journal of Physics and Chemistry of Solids 64(6),2003, pp. 919–925.

[16] ALOV D.L., RYBCHENKO S.I., Luminescence of orthorhombic PbF2, Journal of Physics: CondensedMatter 7(7), 1995, pp. 1475–1482.

[17] THANGADURAI P., RAMASAMY S., KESAVAMOORTHY R., Raman studies in nanocrystalline lead (II)fluoride, Journal of Physics: Condensed Matter 17(6), 2005, pp. 863–874.

[18] GILBERT B., HENGZHONG ZHANG, FENG HUANG, FINNEGAN M.P., WAYCHUNAS G.A., BANFIELD J.F.,Special phase transformation and crystal growth pathways observed in nanoparticles, GeochemicalTransactions 4, 2003, p. 21.

[19] XIANGFU WANG, YANYAN BU, YANG XIAO, CAIXIA KAN, DI LU, XIAOHONG YAN, Size and shapemodifications, phase transition, and enhanced luminescence of fluoride nanocrystals induced bydoping, Journal of Materials Chemistry C 1(18), 2013, pp. 3158–3166.

[20] FENG WANG, JUAN WANG, XIAOGANG LIU, Direct evidence of a surface quenching effect on size-de-pendent luminescence of upconversion nanoparticles, Angewandte Chemie International Edition49(41), 2010, pp. 7456–7460.

[21] FENG WANG, XIAOGANG LIU, Recent advances in the chemistry of lanthanide-doped upconversionnanocrystals, Chemical Society Reviews 38(4), 2009, pp. 976–989.

[22] RAMASAMY S., SMITH D.J., THANGADURAI P., RAVICHANDRAN K., PRAKASH T., PADMAPRASAD K.,SABARINATHAN V., Recent study of nanomaterials prepared by inert gas condensation using ultrahigh vacuum chamber, Pramana – Journal of Physics 65(5), 2005, pp. 881–891.

[23] DE WILD J., RATH J.K., MEIJERINK A., VAN SARK W.G.J.H.M., SCHROPP R.E.I., Enhanced near-infra-red response of a-Si:H solar cells with β -NaYF4:Yb3+ (18%), Er3+ (2%) upconversion phosphors,Solar Energy Materials and Solar Cells 94(12), 2010, pp. 2395–2398.

[24] GOLDSCHMIDT J.C., FISCHER S., LÖPER P., KRÄMER K.W., BINER D., HERMLE M., GLUNZ S.W.,Experimental analysis of upconversion with both coherent monochromatic irradiation and broadspectrum illumination, Solar Energy Materials and Solar Cells 95(7), 2011, pp. 1960–1963.

[25] HERNÁNDEZ-RODRÍGUEZ M.A., IMANIEH M.H., MARTÍN L.L., MARTÍN I.R., Experimental enhancementof the photocurrent in a solar cell using upconversion process in fluoroindate glasses excitingat 1480 nm, Solar Energy Materials and Solar Cells 116, 2013, pp. 171–175.

Received February 13, 2014in revised form April 8, 2014


Miniaturized ultraviolet sources driven by dielectric barrier discharge and runaway electron preionized diffuse discharge

MIKHAIL EROFEEV1, 2*, EUGENII BAKSHT1, VICTOR TARASENKO1, 2

1Institute of High Current Electronics, Akademichesky Avenue 2/3, 634055 Tomsk, Russia

2National Research Tomsk Polytechnic University, Lenina Avenue 30, 634050 Tomsk, Russia


In this work we have studied the energy and spectral characteristics of miniaturized dielectricbarrier discharge KrCl-, XeCl-, XeBr-, and Xe2-excilamps of various designs as well as short pulsepoint-like light sources based on runaway electron preionized diffuse discharge. The maximumultraviolet power density was 20 mW/cm2, which is comparable with the densities of ordinarydielectric barrier discharge excilamps, whereas the maximum efficiencies of the excilamps werenot greater than 2.5%. The causes for the low radiation efficiency of the compact dielectric barrierdischarge driven excilamps were analyzed. It is found that at an electron concentration ofne > 1014 cm–3, the efficiency decreases due to enhanced quenching of excited atoms or moleculesin dissociation by electron impact. The spectral characteristics of a runaway electron preionizeddiffuse discharge formed between two pointed electrodes in atmospheric pressure air inan inhomogeneous electric field at a gap shorter than 8 mm were investigated. It is shown thatthe radiation spectrum of the discharge consists of bands of the second positive nitrogen system,and as the discharge transforms to a spark, lines of the electrode material appear in the spectrum.At a gap of 0.5 mm, weak X-rays from the discharge gap were detected.

Keywords: excilamps, light sources, plasma spectroscopy, runaway electron preionized diffuse discharge.

1. IntroductionThe incoherent spontaneous ultraviolet (UV) sources based on the fluorescence ofdecaying rare gases molecules and their halides in dielectric barrier discharge (or DBDexcilamps) have been intensively studied in the last 20 years and high efficiencies (tensof percent) and radiation powers (kW) have been attained [1–4]. The average radiationpower of the gas discharge plasma is increased by increasing the interelectrode gap dand/or the electrode area, which is well described by similarity laws. By this time, therehave been designed high-power and efficient UV sources, which is interesting for ap-plications dealing with surface cleaning [5, 6], microelectronics [7], microbiology [8, 9],ecology [10], and for research purposes such as calibration of optical system [11].

476 M. EROFEEV et al.

However, spectroscopy, ion sources of mass spectrometers, and devices for quantita-tive analysis require miniature gas discharge UV sources which have the same specificpower densities as ordinary DBD sources and provide spatially stable radiation outputin a wide pressure range. The miniaturization will provide lower power consumptionof the sources and make their practical use simpler and wider. In practice, the minia-turization of the sources by decreasing the interelectrode gap and increasing the oper-ating pressure under the same discharge excitation conditions faces a series ofproblems associated with violation of the similarity laws. As the gas pressure is in-creased up to hundreds of torrs, the discharge characteristics start being much affectedby the loss of electron’s energy due to decreasing of its free path. That leads to increas-ing voltage, and, as a consequence, overheating and spurious reactions the rate of whichincreases with the temperature. This impairs the discharge operation, or causes its con-traction, or the discharge is not ignited at all. High radiation powers at increased pres-sures and small gaps with no preionization can be attained with the use of nanosecondhigh-voltage discharges in an inhomogeneous electric field [12, 13]. At macro- andmicroprotrusions of the cathode surface, the electric field is amplified tens times.The electric field near the surface can thus reach critical values at which initiating elec-trons turn to the so-called runaway mode (when the electrons in the applied electricfield gain more energy than they lose in collisions) and generate slow electrons; thisgives rise to avalanches and their overlapping, and eventually provides a volume dis-charge [14]. It was proposed to term this type of discharge a runaway electron preion-ized diffuse discharge (REP DD) [15].

By now, there have been designed UV and VUV sources based on a REP DD [16, 17]excited by the RADAN nanosecond high-voltage generators [18]. With the RADAN-150generator, the UV radiation pulse width for DBD-driven XeCl-, KrCl-, XeBr-, andKrBr-excilamps was 4 ns at a peak radiation power density of up to 700 W/cm2 [19].Energy characteristics of REP DD in pulse repetition mode have been studied in [20].However, for designing miniature sources, the emitting volume and the generator volt-age should be decreased.

The objective of the work is to study the energy and spectral characteristics ofspontaneous UV radiation of the plasma of a barrier discharge and runaway electronpreionized diffuse discharge at small interelectrode gaps (less than 1 cm) in a widerange of pressures (from tens of torr to atmosphere) of inert gases, their halogenides,nitrogen, and air on microsecond and nanosecond repetitive pulsed generators and todesign miniature nanosecond repetitive pulsed UV sources.

2. Experimental setups

The compact DBD-driven emitters were made of quartz tubes of high transparency(no less than 80% at a wavelength of 170–350 nm) and had different designs (Fig. 1)which allowed to arrange coplanar or planar two barrier discharge and single barrierdischarge. Excilamp of the coplanar barrier discharge arrangement with one parallelelectrode pair located outside a tube of elliptic cross-section is shown in Fig. 1a. In

Miniaturized ultraviolet sources driven by dielectric barrier discharge... 477

the planar two barrier excilamp (Fig. 1b) and cylindrical single barrier excilamp (Fig. 1c)with outer quartz tube diameter of 2 cm, the radiation was extracted through the bulbface. The ground electrode (GE) of the coaxial two-barrier planar excilamp (Fig. 1b)was a metal grid placed on the output windows and their high-voltage (HV) electrodewas inside the inner tube. The HV electrode of the single-barrier excilamps (Fig. 1c)was either a steel spiral or a tungsten core of diameter 1 mm. Dielectric barrier dis-charge was formed in rare gases, their mixtures with halogens and in Ar-N2 mixture.The highest radiation power densities of compact excilamps was attained on Xe2

* ,KrCl*, XeCl*, XeBr* and N2 molecules. The discharge gap d was ~8 mm for all excil-amp designs.

The solid electrodes were made of Al:Mg foil and had an area of 1–5 cm2; the per-forated ground electrodes were metal grids of transparency 60%. The working mixtureswere prepared directly in the excilamp bulbs.

The radiation power densities were determined using calibrated HAMAMATSUH8025 photodetectors with a maximum spectral sensitivity at 222 and 172 nm. The com-pact excilamps were excited by unipolar and bipolar voltage generators with a pulse

AC

DC 15 V

Rectifier Stabilizer Bridge connection Excilamp

Protective

Sur

ge fi

lter

Reg

ulat

ing

Con

trol c

ircui

t

a b c

d

devi

ce

circuit

Fig. 1. Design of compact DBD-driven excilamps (a–c) and schematic diagram of the electrical circuit (d).


repetition frequency variable from 10 to 300 kHz. The voltage pulse amplitude was3–12 kV. Figure 1d shows the schematic diagram of the electrical circuit of the gen-erator loaded with two barrier excilamp described in [4]. In studies of the single-barrierXe2-excilamps, we also used a high-voltage generator producing voltage pulses ofFWHM 7.5 μs, 1.5 μs, 250 ns, and 100 ns and amplitude ~20 kV at a pulse repetitionfrequency from 340 to 1200 Hz.

The single-barrier N2-excilamps were excited by a generator with a voltage pulseamplitude in the transmission line of up to 12.5 kV at a pulse repetition frequency of370–1050 Hz, FWHM of the voltage pulse of about 1 ns, and pulse rise time of about0.2 ns at a level of 0.1–0.9 (FPG-10 generator, FID GmbH).

Volume discharges in atmospheric pressure air were formed between two elec-trodes of small curvature radius (pointed electrodes). The electrode material was stain-less steel, aluminum, copper, titanium, tantalum, niobium, and tungsten. The stainlesssteel electrodes were standard medical needles of outer diameter 0.5 mm; the otherelectrodes were made of foils of the above materials. The study was performed withgaps of 0.5, 1, 2, and 3 mm with FPG-10 generator.

The excilamp current and voltage were measured with current shunts, voltagedividers, and Tektronix TDS-3034 and DPO70604 oscilloscopes (6 GHz, 25 GS/s).The time dependence of radiation pulses was measured with a Photek PD025 LowNoise S20 photodiode. The excilamps’ radiation spectra were measured bya StellarNet EPP2000-C25 spectrometer (operating band 200–850 nm, spectral half--width of instrument function no more than 1.5 nm) and calibrated Ocean Optics B.V.HR4000 spectrometer (operating band 200–300 nm). Photos of the discharge glowwere taken with a Sony A100 digital camera and a HSFC-PRO CCD camera.

3. Results and discussion3.1. Miniaturized narrow-band UV emitters

driven by a microsecond two-barrier discharge

The working medium of two-barrier excilamps is most often excited by sinusoidal ortrapezoidal alternating voltage with an amplitude of several kilovolts and pulse repe-tition frequency from several to hundreds of kilohertz.

At voltage amplitude of 4 kV with 100 kHz pulse repetition rate, the highest radi-ation power density of the coplanar barrier discharge excilamps were obtained in mix-tures of Kr:Cl2 = 100:1 and Xe:Br2 = 18:1 at a total mixture pressure of 57 and 45 torrand were 3 and 7 mW/cm2 at a radiation efficiency to the angle 4π of 2% and 2.5%for the KrCl- and XeBr-excilamps, respectively.

The microdischarge represented a thin channel of diameter ~2 mm on the inneremitter surface, diffusely expanding under the electrodes. The position of the dischargerelative to the electrodes was invariant with time. This makes it possible to obtainuniformly light-struck regions of size up to 1 cm2 at a distance more than 1 cm fromthe excilamp surface without using additional optical elements.


In the mixtures of inert gases with halogens, the radiation of the discharge plasmaarises at the transitions between the lower excited levels and ground repulsion levelof the exciplex molecules formed at low pressures (less than 100 torr) in harpoon re-actions [3] and, at higher pressures, they can also be formed through ion–ion recom-bination [21] of a positive atomic ion or positive molecular ion of inert gas witha negative halogen ion.

The radiation spectrum of the excilamps under study (Fig. 2) contained B-X, C-A,and D-X transition bands of KrCl* and XeBr* molecules but differed somewhatfrom the spectra of capacitive, glow, and barrier discharge excilamps [22–24]. So inthe spectra of the glow and capacitive discharge KrCl- and XeBr-excilamps, the C-Aand D-X transition bands are more pronounced, and in the spectrum of the barrierdischarge excilamps, the D-X band is almost entirely absent. In the coplanar barrierdischarge excilamp, most of the radiation power is concentrated in the B-X band ofKrCl* and XeBr* molecules. The width of this band at half maximum is 3 nm forthe KrCl-excilamp and 4 nm for the XeBr-excilamp, which is 1.5 times narrower thanthat found in the capacitive and glow discharge excilamps [23, 24]. This fact is ex-plained by higher pressures used in the coplanar discharge excilamps. Moreover,the large buffer volume and proximity of the microdischarge to the wall provide bettercooling and thus increase the lifetime of this type of excilamps: after 1000-h operation,the excilamp power remained unchanged.

The average electron concentration ne was estimated by the following formula:

(1)

where j is the current density calculated from the oscillograms of the current andvoltage, e is the electron charge, wdr is the drift velocity. The electron drift velocitiesin krypton and xenon at specified electric field strengths and pressures were takenfrom the reference book [25]. For the KrCl-excilamp, the electron concentration was

1.0

0.8

0.6

0.4

0.2

0.0200 220 240 260 280 300 320 340 360

1 2

KrCl*C-A

XeBr*D-X Br*2

B-X

1 – KrCl-excilamp2 – XeBr-excilamp

I [re

l. u.

]

λ [nm]

KrCl*B-X

XeBr*B-X

XeBr*C-A

Fig. 2. Radiation spectra of the compact coplanar KrCl- and XeBr-excilamps.

ne j ewdr( ) 1–=


1012 cm–3, and for the XeBr-excilamp, it was 1013 cm–3. Note that the obtained electronconcentrations ne were two orders of magnitude lower than the electron concentrationtypical of a barrier discharge [26] for the same working molecules.

The maximum radiation power densities at the planar lamp’s surface are attainedin mixtures of Xe/Kr:Cl2 = 200:1 at a pressure of 145 torr and pulse repetition fre-quency of 100 kHz and are 20 and 10 mW/cm2 for the XeCl- and KrCl-excilamps, re-spectively. At pressures above 200 torr, the discharge transforms into a spark and itspower decreases.

In the planar excilamps, the electric field strength has uniform distribution, andthe plasma is dominated by electron collisions with neutrals; hence, the average elec-tron concentration ne can be estimated by the formula [27]:

(2)

where m and e are the electron mass and charge; νc is the electron collision frequencyequal to 25×109 Hz/torr in xenon [27]; P is the specific excitation power and E isthe maximum electric field strength which are calculated from oscillograms of the cur-rent and voltage. At optimum pressures, the electron concentration was ~2×1012 cm–3.

The spectra of the KrCl- and XeCl-excilamps (Fig. 3) represent narrow B-X bandsof the working molecules and weak C-A bands whose contribution to the total radiantflux is no more than 4.5%. The radiation pulse width of the excilamps corresponds tothe current pulses through the excilamps and lies in the range from several to tens ofmicroseconds depending on the pressure of the working medium.

3.2. Miniaturized narrow-band UV emitters driven by a microsecond single-barrier discharge

The single-barrier excilamps make it possible to form a discharge at higher mixturepressures, thus increasing the formation rate of excimer or exciplex molecules and

1.0

0.8

0.6

0.4

0.2

0.0200 240 280 320 360

I [re

l. u.

]

λ [nm]400

1 – KrCl-excilamp2 – XeCl-excilamp

1 2

KrCl*B-X

XeCl*B-X

Cl*2D-A

XeCl*C-A

Fig. 3. Radiation spectra of the compact planar KrCl- and XeCl-excilamps.

ne 2Pmν c eE( ) 2–=


the radiation power. However, the metal electrode present in the discharge region, dueto halogen-metal reaction, greatly decreases the halogen concentration in the workingmixture, and hence, the excilamp lifetime. Therefore, experiments were performed onhalogen-free single-barrier Xe2-excilamps (Fig. 1c).

At pressures of several and tens of torr, the radiation spectrum of the plasma inthe discharge in xenon is dominated by transitions of the first and second continua.The first continuum corresponds to the transitions from high vibrational levels ofthe state or to the dissociative ground state of a xenon mole-cule. The second continuum corresponds to the transitions from low vibrational levelsof both molecular states to the ground state. To determine the optimum voltage pulsewidth, we used a high-voltage generator which produced voltage pulses of amplitude~20 kV and FWHM of 7.5 μs, 1.5 μs, 250 ns, and 100 ns. Varying the voltage pulserepetition frequency of the generator from 10 to 70 kHz made it possible to varythe excitation power deposited to the discharge between 10 and 39 W. The maximumradiation power densities of the single-barrier excilamp were obtained at an excitationpulse width of 1.5 μs and xenon pressure of 300 torr which was the optimum pressurefor all excitation modes used. Figure 4 shows the dependence of the radiation powerdensity and efficiency of the single-barrier Xe2-excilamp on the power deposited tothe discharge.

It is seen from Fig. 4 that as the power deposited to the discharge is increased,the radiation power density increases almost linearly; however, the radiation efficiencyof Xe2 molecules decreases. The latter fact is explained by overheating of the workinggas and contraction due to the specific excitation power in excess of the optimum val-ues which, according to [28], are ~1 W/cm3. The main group of reactions in which en-ergy is released includes elastic collisions, dissociative recombination, predissociation,and collisional association. In this experiment, the specific excitation power was 1.8 and7.2 W/cm3 at a pulse repetition frequency of 15 and 68 kHz, respectively. The electron

1u P3 2( ) 0u+ P3 1( ) 0g

+ S1 0( )

30

25

20

15

10

5

010 15 20 25 30 35 40

0.45

0.40

0.35

0.30

0.25

0.20

0.15

Pin [W]

PV

UV [m

W/c

m2 ]

η [%

]

Fig. 4. Radiation power density and efficiency of the single-barrier Xe2-excilamp vs. the power depositedto the discharge.


concentration calculated by formula (2) for these specific excitation powers was4.2×1013 and 1.8×1014 cm–3, respectively. The increase in ne also causes a decrease inradiation efficiency due to enhanced quenching of excited xenon atoms in dissociationreactions by electron impact. Moreover, as shown [29], the rates of three-particleformation of and molecules with high vibrational statesare equal to α31 = 3.90×10–27 T–1.78cm–6s–1 and α32 = 1.34×10–27 T–1.70cm–6s–1, i.e.,these rate decrease with increasing gas temperature.

The radiation spectrum of the compact single-barrier Xe2-excilamps at the opti-mum pressures represents a band with a maximum at 172 nm and does not differ asa whole from the radiation spectra of conventional DBD-driven Xe2-excilamps.

3.3. Miniaturized narrow-band UV emitters driven by a nanosecond single-barrier discharge

Single-barrier excilamps allow a gap breakdown at lower voltages compared totwo-barrier excilamps, all other things (pressure, components ratio in gas mixture, in-terelectrode gap) being equal. Moreover, decreasing the excitation pulse width and risetime to several and tens of nanoseconds makes it possible to realize a volume dischargeat higher voltages and mixture pressures, and this increases the radiation power anddecreases the radiation pulse width.

Experiments were performed on the single-barrier excilamp (Fig. 1c) with a pointedtungsten cathode. The working medium was nitrogen, nitrogen-argon mixtures, air, andxenon. Figure 5a shows the dependences of the radiation power density in pure N2(curve 1), Ar:N2 = 50:1 (curve 2), and Ar:N2 = 200:1 (curve 3) for the FPG-10 gener-ator operating at voltage pulse amplitude of 12 kV. The highest energy characteristicswere obtained in the nitrogen-argon mixtures in which excitation of the C 3Πu state ofa nitrogen molecule from its ground state can proceed not only by electron impact

Xe2 0u+ P3 1( )[ ] Xe2 1u P3 2( )[ ]

U = 14 kV

1

2

3

1

23

160

140

120

100

80

60

40

20

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.00 50 100 150 200 250 0 25 50 75 100 125 150 175

p [torr] p [torr]

P [μ

W/c

m2 ]

τ 0.5

[μs]

a b

Fig. 5. Radiation power density (a) and its pulse width (b) of the single-barrier N2-excilamp vs. workingmixture pressure: pure nitrogen (curve 1), Ar:N2 = 50:1 (curve 2), and Ar:N2 = 200:1 (curve 3) at exci-tation pulse amplitude U = 12.5 kV.


(whose efficiency is low), but also through resonant energy transfer from metastablelevels of an argon atom. At a low nitrogen percentage (~1.5%) in the N2-Ar mixture,most of the energy deposited to the plasma is expended in excitation of the lower levelsof argon and in its ionization and is then transferred to nitrogen molecules. Therefore,in the optimum mixtures, the partial pressure of argon is much higher than the partialpressure of nitrogen. The maximum radiation power was obtained at a mixture ratioof Ar:N2 = 200:1. At pressures higher than 300 torr, the discharge in the Ar-N2 mix-tures was constricted or was not ignited at all. The radiation characteristic in air andnitrogen differed but slightly. At the voltage amplitude of 12.5 kV and its rise time of200 ps, the average UV power in the Ar-N2 mixture was 5.8 mW at a radiation effi-ciency of 1.28% to the angle 4π.

The least radiation pulse width τ1/2 (~200 ns) was found in barrier discharges inair and nitrogen (Fig. 5b). However, this width was much longer than the voltage pulsewidth of the FPG-10 generator. In nitrogen, the radiation pulse width decreased untilthe pressure reached 30 torr, whereupon it increased slightly. This can be associatedwith a change in the discharge characteristics. In the Ar:N2 = 50:1 mixture at a pressureof 180 torr, the radiation pulse width of the N2-excilamp was 210 ns. In the radiationspectrum of the Ar:N2 mixture, most of the radiation energy is concentrated in the sec-ond positive nitrogen system in which the highest intensity belongs to the band withλ = 337.1 nm. On excitation of xenon, the gap was broken down at a pressure lowerthan ~10 torr, and this led to a very low radiation efficiency of xenon dimers at 172 nm.

3.4. Short-pulse light sources driven by runaway electron preionized diffuse discharge

To create gas discharge emitters with a pulse width of several nanoseconds, we useda runaway electron preionized diffuse discharge (REP DD). The electrodes of smallcurvature radius provide electric field amplification, and this ensures the generationof runaway electrons and X-rays, preionization of the discharge gap, and diffuse char-acter of discharges in gases at increased pressures. The use of voltage pulses with a risetime of hundreds of picoseconds increases the efficiency of generation of runawayelectrons [13].

It is found that on excitation by the FPG-10 generator at a voltage pulse rise timeof 200 ps, a diffuse discharge in the form of a cylinder of height 3 mm and diameter~1 mm is formed between two pointed metal electrodes spaced by 3 mm at atmosphericpressure of air and nitrogen (Fig. 6a).

Under these conditions, the FWHM of the radiation pulse τ0.5 was 3 ns, andthe average UV radiation power to the solid angle 4π was 3.5 mW.

As the interelectrode gap was decreased, the discharge became constricted andtransformed into a spark. However, even at an interelectrode gap of ~0.5 mm, the dis-charge first assumed the volume form and then transformed to a spark. This is clearlyseen in comparing Figs. 6b and 6c which show photos of the discharge taken with


a CCD camera at different points in time. The FWHM of the radiation pulse in the sparkdischarge at a gap of 0.5 mm was ~70 ns. The radiation spectrum of the discharge wasalso studied at gaps of 3, 2, 1, and 0.5 mm. At a gap of 3 and 2 mm, the radiation spec-trum of the diffuse discharge was dominated by bands of the second positive nitrogensystem, like in [18]. As the gap was decreased from 2 to 0.5 mm, the discharge spec-trum changed: radiation of continuum in the wavelength region of 200–450 nm andadditional spectral lines of metals in the wavelength region of 700–850 nm, along withthe second positive nitrogen system, appeared in the spectrum. In this case, the radia-tion power of the second positive nitrogen system was almost unchanged, and the pow-er of broadband radiation and metal lines was increased substantially. The radiationenergy at 200–300 nm was ~40% of the total energy in the spectral range under study(200–850 nm). Figure 7 shows the radiation spectrum of the spark discharge(d = 0.5 mm) and the radiation spectrum of Fe in an arc discharge for comparison.Most of the lines in the spark spectrum coincide with the spectral lines of Fe. This sug-gests that the lines in the spark spectrum correspond to the lines of vapors of the elec-trode material; in this case, to iron. At an interelectrode gap d = 1 mm, the energyconcentrated in the continuum and spectral lines of Fe is lower than that at an intere-lectrode gap of d = 0.5 mm; that is, this case is intermediate in going from d = 2 mm

ba c

0–1 ns 15–17 ns

Fig. 6. Integral photo of the discharge (a) taken in a pulse with an interelectrode gap of 2 mm and itsphotos at different points in time (b, c) with an interelectrode gap of 0.5 mm.

Arc dischargeSpark discharge

1.0

0.8

0.6

0.4

0.2

0.0200 220 240 260 280 300

I [re

l. u.

]

λ [nm]

Fig. 7. Radiation spectra of the spark and arc discharges with stainless steel electrodes at 200–300 nm.


to d = 0.5 mm. The most interesting results were obtained with electrodes made of cop-per, niobium, and tungsten. The spectra for these electrodes are shown in Fig. 8. It isseen that the radiation of the discharge with the above electrodes contains lines of neu-tral atoms and lines of ions of these materials. In the experiments, it was found thatwith a gap of 0.5 mm, weak X-ray radiation propagated from the discharge gap. Thisradiation was detected with the scintillation detector. The presence of X-rays fromthe discharge gap owes to bremsstrahlung radiation of runaway electrons arising earlyin the formation of the discharge and providing conditions for its diffuse operation.

4. Conclusions

Based on a barrier discharge, the compact sealed-off emitters with UV power densitiescomparable with those of commercial deuterium lamps were designed. The radiationspectrum of coplanar excilamps differs from the spectrum of conventional DBD ex-cilamps by the presence of a C-A transition band, and from that of capacitive and glowdischarge excilamps, by concentration of most of the power in the narrower B-X tran-sition band. In the single-barrier discharge in Ar:N2 the energy characteristics of

1.0

0.8

0.6

0.4

0.2

0.0

200 220 240 260 280 300

I [re

l. u.

]

λ [nm]

0.8

0.6

0.4

0.2

0.0

0.8

0.6

0.4

0.2

0.0

203.

71 n

m20

4.38

nm

213.

43 n

m

219.

23 n

m22

4.7

nm

202.

93 n

m

210.

94 n

m

241.

39 n

m24

5.81

nm

269.

86 n

m27

1.66

nm

208.

45 n

m

225.

01 n

m

239.

83 n

m

248.

95 n

m

Cu II

Nb II

W I

Fig. 8. Radiation spectra of the discharge with copper, niobium, and tungsten electrodes at d = 0.5 mm.


UV radiation are the same but the radiation pulse width is shorter and is hundreds ofnanoseconds. The spectral characteristics of the REP DD in atmospheric pressure airwere studied. It is shown that this type of discharge can be used in designing compactemitters with nanoseconds radiation pulse duration whose radiation spectrum in indi-vidual regions can be varied due to the use of different electrode materials.

References

[1] KOGELSCHATZ U., Dielectric-barrier discharges: their history, discharge physics, and industrialapplications, Plasma Chemistry and Plasma Processing 23(1), 2003, pp. 1–46.

[2] MILDREN R.P., CARMAN R.J., Enhanced performance of a dielectric barrier discharge lamp usingshort-pulsed excitation, Journal of Physics D: Applied Physics 34(1), 2001, pp. L1–L6.

[3] JUN-YING ZHANG, BOYD I.W., Efficient excimer ultraviolet sources from a dielectric barrier dis-charge in rare-gas/halogen mixtures, Journal of Applied Physics 80(2), 1996, pp. 633–638.

[4] LOMAEV M.I., SKAKUN V.S., SOSNIN E.A., TARASENKO V.F., SHITTS D.V., EROFEEV M.V., Excilamps:efficient sources of spontaneous UV and VUV radiation, Physics–Uspekhi 46(2), 2003, pp. 193–209.

[5] KOGELSCHATZ U., ESROM H., ZHANG J.-Y., BOYD I.W., High-intensity sources of incoherent UV andVUV excimer radiation for low-temperature materials processing, Applied Surface Science 168(1–4),2000, pp. 29–36.

[6] TODE M., TAKIGAWA Y., IGUCHI T., MATSUURA H., OHMUKAI M., SASAKI W., Removal of carbon con-tamination on Si wafers with an excimer lamp, Metallurgical and Materials Transactions A 38(3),2007, pp. 596–598.

[7] BOYD I.W., ZHANG J.Y., KOGELSCHATZ U., Photo-Excited Process, Diagnostics and Application,Kluwer Academic Publishers, The Netherlands, 2003, pp. 161–199.

[8] EROFEEV M.V., KIEFT I.E., SOSNIN E.A., STOFFELS E., UV excimer lamp irradiation of fibroblasts:the influence on antioxidant homeostasis, IEEE Transactions on Plasma Science 34(4), 2006,pp. 1359–1364.

[9] STOFFELS E., KIEFT I.E., SLADEK R.E.J., VAN DEN BEDEM L.J.M., VAN DER LAAN E.P., STEINBUCH M.,Plasma needle for in vivo medical treatment: recent developments and perspectives, Plasma SourcesScience and Technology 15(4), 2006, pp. S169–S180.

[10] MÜHLBERGER F., WIESER J., ULRICH A., ZIMMERMANN R., Single photon ionization (SPI) via incoher-ent VUV-excimer light: robust and compact time-of-flight mass spectrometer for on-line, real-timeprocess gas analysis, Analytical Chemistry 74(15), 2002, pp. 3790–3801.

[11] YUBERO C., GARCÍA M.C., CALZADA M.D., Using a halogen lamp to calibrate an optical system forUV-VIS radiation detection, Optica Applicata 38(2), 2008, pp. 353–363.

[12] NOGGLE R.C., KRIDER E.P., WAYLAND J.R., A search for X-rays from helium and air discharge atatmospheric pressure, Journal of Applied Physics 39(10), 1968, pp. 4746–4748.

[13] TARASENKO V.F., BAKSHT E.KH., BURACHENKO A.G., KOSTYRYA I.D., LOMAEV M.I., RYBKA D.V.,High-pressure runaway-electron-preionized diffuse discharges in a nonuniform electric field,Journal of Technical Physics 55(2), 2010, pp. 210–218.

[14] TARASENKO V.F., YAKOVLENKO S.I., The electron runaway mechanism in dense gases and the pro-duction of high-power subnanosecond electron beams, Physics–Uspekhi 47(9), 2004, pp. 887–905.

[15] BAKSHT E.H., BURACHENKO A.G., KOSTYRYA I.D., LOMAEV M.I., RYBKA D.V., SHULEPOV M.A.,TARASENKO V.F., Runaway-electron-preionized diffuse discharge at atmospheric pressure and itsapplication, Journal of Physics D: Applied Physics 42(18), 2009, article 185201.

[16] LOMAEV M.I., MESYATS G.A., RYBKA D.V., TARASENKO V.F., BAKSHT E.KH., High-power short-pulsexenon dimer spontaneous radiation source, Quantum Electronics 37(6), 2007, pp. 595–596.

[17] EROFEEV M.V., TARASENKO V.F., Study of a volume discharge in inert-gas halides without preioni-sation, Quantum Electronics 38(4), 2008, pp. 401–403.


[18] ZAGULOV F.YA., KOTOV A.S., SHPAK V.G., YURIKE YA.YA., M.I. YALANDIN, RADAN – a small-sizedpulserepeating high-current electron accelerator, Pribory i Tekhnika Eksperimenta 2, 1989,pp. 146–149.

[19] EROFEEV M.V., TARASENKO V.F., XeCl-, KrCl-, XeBr- and KrBr-excilamps of the barrier dischargewith the nanosecond pulse duration of radiation, Journal of Physics D: Applied Physics 39(16),2006, pp. 3609–3614.

[20] TAO SHAO, TARASENKO V.F., CHENG ZHANG, BAKSHT E.KH., PING YAN, SHUTKO Y.V., Repetitivenanosecond-pulse discharge in a highly nonuniform electric field in atmospheric air: X-ray emissionand runaway electron generation, Laser and Particle Beams 30(3), 2012, pp. 369–378.

[21] JINZHOU XU, YING GUO, LEI XIA, JING ZHANG, Discharge transitions between glow-like and filam-entary in a xenon/chlorine-filled barrier discharge lamp, Plasma Sources Science and Technology16(3), 2007, pp. 448–453.

[22] TARASENKO V.F., CHERNOV E.B., EROFEEV M.V., LOMAEV M.I., PANCHENKO A.N., SKAKUN V.S.,SOSNIN E.A., SHITZ D.V., UV and VUV excilamps excited by glow, barrier and capacitive discharges,Applied Physics A: Materials Science and Processing 69(1 Supplement), 1999, pp. S327–S329.

[23] SOSNIN E.A., EROFEEV M.V., TARASENKO V.F., Capacitive discharge exciplex lamps, Journal ofPhysics D: Applied Physics 38(17), 2005, pp. 3194–3201.

[24] FALKENSTEIN Z., COOGAN J.J., The development of a silent discharge-driven XeBr* excimer UV lightsource, Journal of Physics D: Applied Physics 30(19), 1997, pp. 2704–2710.

[25] BABICHEV A.P., Reference Book on Physical Values, [Eds.] Grigor’ev I.S., Meilikhov E.Z.,Energoatomizdat, Moscow, 1991, (in Russian).

[26] KOGELSCHATZ U., Silent discharges for the generation of ultraviolet and vacuum ultraviolet excimerradiation, Pure and Applied Chemistry 62(9), 1990, pp. 1667–1674.

[27] ROTH J.R., Industrial Plasma Engineering, Vol. 1, IOP, Bristol, UK, 1995, p. 420.[28] LOMAEV M.I., TARASENKO V.F., TKACHEV A.N., SHITTS D.V., YAKOVLENKO S.I., Formation of coniform

microdischarges in KrCl and XeCl excimer lamps, Technical Physics 49(6), 2004, pp. 790–794.[29] MARCHAL F., SEWRAJ N., JABBOUR G., RODRIGUEZ AKERRETA P., LEDRU G., Temperature dependence

of xenon excimer formations using two-photon absorption laser-induced fluorescence, Journal ofPhysics B: Atomic, Molecular and Optical Physics 43(23), 2010, article 235210.

Received May 16, 2014in revised form June 26, 2014

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