Triple overwritten Bragg gratings based multiwavelength distributed feedback dye laser

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Journal of Luminescence 106 (2004) 321–327

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doi:10.1016/j.jlu

Triple overwritten Bragg gratings based multiwavelengthdistributed feedback dye laser

Nasrullah Khan1,*

Department of Electrical and Electronic Engineering, University Putra Malaysia, Serdang 43400, Malaysia

Received 17 March 2003; received in revised form 8 July 2003; accepted 13 November 2003

Abstract

Emission of multiple laser lines spectra due to three overwritten dynamic Bragg gratings in solution of Rhodamine

6G in ethanol is reported. The overlaid gratings were produced on dye solution by interference patterns of three pairs of

frequency doubled Nd:YAG laser. Convolution of three dynamic overwritten gratings with different periodicities gave

rise to generation of nine gratings of different periods in the interaction region. Additional gratings induced by

interaction of three main overlaid gratings were found to satisfy the Bragg scattering conditions to cause simultaneous

laser action at multiple wavelengths. Maximum number of laser lines depends upon the delay between the adjacent pairs

of the main pumping beams and their number. For one, two and three pairs of excitation beams, derived from the same

source through wave front or amplitude phase division techniques, the output lasing lines varied from 1, 5 and 9

respectively. These findings suggest a quite distinct way of generating coherent continual spectra. This work was carried

out by pumping dye solution with maximum six pulses to generate 5:4 nm wide discrete supercontinuum; consisting of

nine distinct coherent lines, but the principle may be extended to higher order spectral range; depending upon the

available gain medium and number of pumping pulses.

r 2003 Elsevier B.V. All rights reserved.

PACS: 42.55.Mv; 42.60.By; 42.79.Dj; 42.60.Mi

Keywords: DFDL; Multiple gratings; Bragg scattering and nonlinear gratings

1. Introduction

Dynamic gratings may be produced in a dye cellby interfering light beams usually derived fromsame laser source either by amplitude phasedivision or wave-front division techniques. Thelaser source must be temporally coherent for

-894-663-08; fax: +60-3-894-663-27.

ess: [email protected] (N. Khan).

m Pakistan Wapda Lahore.

e front matter r 2003 Elsevier B.V. All rights reserve

min.2003.11.006

amplitude phase division and spatially coherentfor wave-front division to form interferencepattern at dye cell. Two-beam interference pro-duces a spatially modulated light field which iscalled an interference grating.A general case of superposition of beams with

different polarizations leads to an interferencegrating with an amplitude described by an inter-ference tensor. Light from a powerful pump laseris split into two-beams A and B with the wavevector kA and kB; electric field amplitudes AA; AB;

d.

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N. Khan / Journal of Luminescence 106 (2004) 321–327322

and intensities IA and IB: The two beams intersectat an angle y at the sample and create aninterference, pattern. The grating vector q is [1]

q ¼ 7ðkA � kBÞ ð1Þ

The spatial period L ¼ 2p=q: L can be expressed interms of the pump wavelength lp and the angle y;by L ¼ lP=2 sinðy=2Þ: For small angle y; thegrating period is LElP=y for y51: It is pointedout that the wave vector ka; kb; wavelength lp andintersection angle y are measured in the materialwith refractive index n: For nearly normalincidence, l0p ¼ nlp and the intersection anglesin y0 ¼ n sin y are measured outside, therefore,LEl0P=y0 for y51: By varying the intersectionangle y0 the grating period L can be changed. Theelectric-field amplitude distribution inside theinterference region is given by [1]

A ¼ AAeþikxx þ ABe

�ikxx: ð2Þ

The intensity distribution in the interferencepattern is given by

I ¼n

2e0cðA � A�Þ

¼n

2e0cðjAAj

2 þ 2AA � A�B cos 2kxx þ jABj

2Þ

¼ IA þ 2Di cos 2kxx þ IB; ð3Þ

where Di ¼ 0:5ne0cAA � A�B is the intensity mod-

ulation amplitude and the asterisk denotes thecomplex conjugate (c.c.). Present-day mode-lockedlasers provide pulses of very short durations; say10 ps that is equivalent to a physical length of3 mm: The pulse lengths of laser used in thisexperiment were 10–20 ps: The interference of twobeams derived from such a source depends on thedelay between the pulse fractions traveling alongpath A and B. The time dependence of such pulsesis close to Gaussian with half-width tp

IA;BðtÞ ¼ #IA;B expf�½ðt7t=2Þ=tp2g; ð4Þ

where t is the delay of pulses B with regard to A,and #IA;B ¼ ð1=2Þnce0 #A2

A;B=2 is the peak intensitiesof the two pulses. The magnitude of the inter-ference tensor in this case also depends on theoverlap of the two pulses given by ratio t=tp [1].For s-polarized pulses, assuming IA ¼ IB the

intensity of interference pattern is

I ¼ 2IAð1þ cos qxÞ: ð5Þ

Thus, the intensity is fully modulated, varyingbetween zero and four times the value for singlebeam. The grating is stationary in position whenthe two beams have the same frequency. However,when two pulses of slightly different frequenciesare used then intensity distribution among fringesis also affected. Intensity dependent effects becomesignificantly considerable. A frequency offsetbetween the two excitation beams provides travel-ling grating structures [2,3].This work has been carried out using multiple

pulses induced dynamic gratings but one canpump through permanent overwritten gratings ofdifferent periods to cause multiple line spectra.This concept has previously been applied to fibreBragg lasers. This area needs further research fordye lasers. Superposition of binary gratings ofdifferent periods can give reflection spectra ofmultiple lines that intuitively refer to its nonlinearbehaviour [4]. The major parameters causingmultiple wavelength spectra may be period differ-ences, primary phase difference and overall gratinginteraction length. Overwriting of two gratings inoptical fibres has shown to produce spectra of sixlines due to creation of degenerate gratings inoverlaid gratings [5]. Superposition of three ormore gratings may cause even more number ofdegenerate gratings but the observation of oscillat-ing lines is restricted to satisfaction of Braggscattering conditions.Let us concentrate on generation of multiple

periods due to overwriting of multiple gratings ofdifferent periods as shown in Fig. 1. Overwritingof two gratings produces at least two main andthree intermediate gratings. The five gratingshave periods L1;L2;L3;L4;L5: Similarly overwrit-ing of three gratings produces three mainand six intermediate gratings of periodsL1;L2;L3;L4;L5;L6;L7;L8;L9: Present researchwas carried out on simultaneous induction of twoand three dynamic gratings in solution of R6G inethanol. Superposition of two and three gratings indye cell led to oscillation of 5 and 9 output laserlines respectively.

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Fig. 1. (a,b) Induction of 3 or 6 additional sub-gratings during writing of 2 or 3 overlaid gratings when interfering beams mutual delay

is less than pump laser pulse and coherence length.

N. Khan / Journal of Luminescence 106 (2004) 321–327 323

2. Experimental setup for overwriting Twin

gratings

In order to study the effect of an optical pathdifference (OPD) between two pairs of the pumpbeams inducing enharmonic gratings, the secondharmonic of a passively Q-switched and mode-locked Nd:YAG laser was divided into two beams.The main beam had a total available energy of700710 mJ: Two DFDLs were operated simulta-neously. The available pump energies of DFDL1

and DFDL2 were 351710 and 187710 mJrespectively. There is no special reason to choose

above pumping power, it is what was available inlaboratory. I do not think exact 50% energiesin beams can affect the results. The layout ofthe experimental arrangement is shown in Fig. 2.Some 10% (unconverted IR) from the maincavity dumped Ng:YAG laser beam wasused to trigger the streak camera and 16% waslost in the conveying optics. The net ratio ofpump beams for two DFDLs at the dye cellwas 2:1. The ratio of energy does not affectas long as the minimum energy of eachpair is more than the pump threshold energyof DFDL.

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In the first phase two DFDLs were alignedindividually with a larger OPD or mutual delaybetween the pump beam pairs and then operated

Fig. 2. Experimental set up for overwriting two gratings.

Fig. 3. Simultaneous oscillation of three, four and five lines for two pa

of 1–3 mm:

simultaneously to produce two lines. Later theOPDs between pump pairs were reduced by timedelay optics from 5 to 0 mm that resulted inmultiple gratings causing simultaneous oscillationof 3, 4 and 5 output lines as shown in Fig. 3. Allthe lines were equally spaced. Results for differentOPDs between the pumping pairs of Nd:YAGlaser pulses are shown in Table 1. The output linesand hence the number of gratings depend upon theOPD between the pump laser pulses. This delaycan be adjusted from nearly 0 to 9 mm by movablemirror carrying stages between the Nd:YAG andthe dye cell.

3. Experimental setup for overwriting triple

gratings

To investigate the effect of OPD or delay amongthree pairs of pumping beams inducing multiplegratings, the second harmonic of a passively

irs of pump beams for optical path difference or delays of order

Table 1

Relation of output laser lines to delay between pumping beams

(OPD) Laser lines

0 mmoOPDp2 mm 5

2 mmoOPDo3 mm 4

3 mmoOPDo4 mm 3

OPD > 4 mm 2

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Q-switched and modelocked Nd:YAG laser wasdivided into three main beams. The three indivi-dual DFDLs were made to operate first individu-ally and later simultaneously. The pump energiesof DFDL1; DFDL2 and DFDL3 were282:86710 mJ; 142:80710 mJ and 90710 mJ re-spectively. The experimental arrangement forwriting three overlaid gratings is shown in Fig. 4.The proportion of pump energies ofDFDL1;DFDL2 and DFDL3 were nearly 3:2:1.The pump energies of DFDLs were high enough tocause laser oscillations above the threshold. Aboveproportion was chosen based on available re-sources and it has nothing to do with overallresults as long as it is more than minimumthreshold requirements.

Fig. 4. Experimental setup for overw

The main beams dividing mirrors were mountedon moveable stages to vary the OPDs between thethree main beams causing three individual DFDLsto operate. Simultaneous operations of threeDFDLs produced multiple lasing lines dependingupon the OPDs between the pump beams. TheDFDLs lasing lines varied from three to maximumnine. The maximum number of lines was observedwhen the OPDs were less than 2 mm as shown inFig. 5. The minimum number of lines wasobtained when the OPDs between the DFDLswere more than 4 mm that was also the coherencelength of the pump laser.Simultaneous operation of two DFDLs was

conducted separately by blocking the pumpingbeams of individual DFDLs at a time. Maximum

riting three overlaid gratings.

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Fig. 5. Simultaneous oscillation of nine lines for three pair of

the pump beams for 0 mmpOPD1;2p2 mm and 0 mmpOPD2;3p2 mm:

Table 2

Oscillation of maximum nine laser lines

Optical delays among three pairs

of pumping beams

DFDL

lasing lines

DFDL2;3 DFDL1;2

0 mmpOPD2;3p2 mm 0 mmpOPD1;2p2 mm 9

2 mmoOPD2;3p3 mm 0 mmpOPD1;2p2 mm 8

5 mmoOPD2;3p4 mm 0 mmpOPD1;2p2 mm 7

0 mmpOPD2;3p2 mm 2 mmoOPD1;2p3 mm 8


3 mmoOPD2;3p4 mm 2 mmoOPD1;2p3 mm 6



5 mmoOPD2;3p9 mm 2 mmoOPD1;2p4 mm 5

OPD2;3 > 5 mm OPD1;2 > 5 3


number of output lines like twin grating experimentwas five in each case. In simultaneous operation ofthree DFDLs the fundamental lines do not changetheir location in spectrum unless angles of mainincident beams are changed. The results of triplegrating experiment are summarised in Table 2.

4. Description of results

The OPD between the three pairs of the pumpbeams were varied from 0 to 9 mm to operate

three individual DFDLs called DFDL1; DFDL2

and DFDL3: For 0pOPD1;2p2 mm and0pOPD2;3p2 mm total nine lasing lines wereobserved. Mostly nine lines were observed butsome times tenth line too appeared. The number oflaser lines in the simultaneous operation ofDFDL1 and DFDL2; DFDL2 and DFDL3; andDFDL1 and DFDL3 were five in each case. Forthree DFDLs simultaneous operation all the 9lasing lines were recorded in the spectrum. Inanother measurement the lines between 5633 to5662:9 (A were equally spaced with spectral peri-odicity of 7 (A and the lines from 5662.9 to5686:9 (A were spaced symmetrically with a differ-ent spectral periodicity of 6 (A: The two spectralspacing were very close to each other but notequal. This is due to three different pumping half-angles. The pumping half-angles for three DFDLoperations, as shown in Fig. 5, are 21:24� forDFDL1; 21:35� for DFDL2 and 21:46� forDFDL3 respectively. The half-angle differencesbetween DFDL1 and DFDL2 or DFDL2 andDFDL3 are 0:11� in this case. However, thespectral spacing between any five lines from anydirection is always similar. The spectral spacingbetween any two lines depends upon the locationof the corresponding extreme lines in the fluores-cence spectrum that in turn depends upon thepump beam half-angles. The spacing between theninth and tenth line was half of the spacingbetween other two lines. Mostly nine lines wereobserved but sometimes a tenth line appeared too.

5. Discussion of results

The location of the missing line depends uponthe relative chirping, spatial coherence and OPDbetween the interfering beams. Observed lasinglines during simultaneous operation of DFDL1

and DFDL2; DFDL2 and DFDL3; or DFDL1 andDFDL3 were always 5 for lowest delay ð271 mmÞand 2 for the longest delay ð671 mmÞ: The spacingbetween five lines depends upon the correspondinghalf-angles of the pumping pairs. In this case theinterline spacing is around 7 (A The total con-tinuum length is 5:4 nm for nine line spectra ifoperated simultaneously. It is interesting to point

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out that in some of the shots additional lines wereobserved. A sixth line in twin grating experimentand a tenth line in triple grating experiment wasobserved in some of the random shots. These linesappeared between the last two lines of highestwavelengths.Although the exact physics of multiple line

oscillation in multiple overlaid grating experimentsis not understood, however, the same mechanismseems to be responsible for additional lines.

6. Conclusions

This experimental work proves that superposi-tion of multiple gratings of different periods andphases produce several degenerate gratings re-sponsible for oscillation of multiple laser linessatisfying Bragg scattering. The number of linesdepends upon the coherence length of pump laser,number of pump beams, pulse length and length ofinteraction region in dye solution. Observation ofa sixth line in two DFDLs operation and tenth linein three DFDLs operation reveals possibility ofsome more lines at reduced inter line spacing. Theexact physics of above results is not understoodbut the overwriting of three gratings of differentperiods gives the closest answer.It appears that the two main DFDL gratings

induce a third grating that again interacts withmain gratings to produce two additional gratingsthereby giving rise to overall five lines. Sameprocess repeats itself for three grating experiment.

The middle DFDL line is common in bothinteractions so the total number of lines is nine.This by definition can happen (Ref. [1]) only whenthe delay is shorter than the pulse length andcoherence length. This work needs further researchon theoretical models to satisfy above experimen-tal results. Obviously, there is no upper limit aslong as numbers of excitation pairs of pulses areincreased and the gain medium supports lasingaction. Currently author is trying to produce 17lines by simultaneous operation of five DFDLsand planning to test it on semiconductor lasers.

Acknowledgements

This research project was sponsored by theMinistry of Science and Technology (MOST),Islamabad, Pakistan. Later some analytical workwas sponsored by Ministry of Science, Technologyand Environment (MOSTE), Putra Jaya, Malaysia.

References

[1] H.J. Eichler, P. Gunter, D.W. Pohl, Laser induced dynamic

gratings, Opti. Sci. 50 (1986) 17.

[2] A.E. Siegman, Appl. Phys. Lett. 3 (1977) 21.

[3] R. Trebino, A.E. Siegman, Appl. Phys. B 28 (1982) 250.

[4] I.A. Avrutsky, M. Fay, J.M. Xu, Photon. Tech. Lett. 10

(1998) 839.

[5] J. Bao, X. Zhang, K. Chen, W. Zhou, Optic. Commun. 188

(2001) 31.

Triple overwritten Bragg gratings based multiwavelength distributed feedback dye laser

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