Research Article Low-Loss Polymer-Based Ring...

Research ArticleLow-Loss Polymer-Based Ring Resonator for ResonantIntegrated Optical Gyroscopes

Guang Qian123 Jie Tang123 Xiao-Yang Zhang234 Ruo-Zhou Li234

Yu Lu234 and Tong Zhang1234

1 School of Instrument Science and Engineering Southeast University Nanjing 210096 China2 Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology Ministry of Education Nanjing 210096 China3 Suzhou Key Laboratory of Metal Nano-Optoelectronic Technology Suzhou Research Institute of Southeast UniversitySuzhou 215123 China

4 School of Electronic Science and Engineering Southeast University Nanjing 210096 China

Correspondence should be addressed to Tong Zhang tzhangseueducn

Received 28 February 2014 Revised 25 April 2014 Accepted 28 April 2014 Published 22 May 2014

Academic Editor Qin Chen

Copyright copy 2014 Guang Qian et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Waveguide ring resonator is the sensing element of resonant integrated optical gyroscope (RIOG) This paper reports a polymer-based ring resonator with a low propagation loss of about 0476 dBcm for RIOG The geometrical parameters of the waveguideand the coupler of the resonator were optimally designed We also discussed the optical properties and gyroscope performance ofthe polymer resonator which shows a high quality factor of about 105 The polymer-based RIOG exhibits a limited sensitivity of lessthan 20 degh for the low and medium resolution navigation systems

1 Introduction

Resonant integrated optical gyroscope (RIOG) is a highperformance rotation sensor based on the Sagnac effect inwhich an optical waveguide ring resonator is utilized asthe sensing element [1ndash3] Due to the excellent advantagesof compactness stability reliability and ease of fabricationRIOGs have attracted much attention in the field of inertialnavigation [4ndash6] Meanwhile the less complex and cheapergyroscopes suited for mass production are urgently requiredespecially in the low andmedium resolution fields such as carnavigation and robotics

Optical polymeric materials permit the mass productionof low-cost integrated optical devices and circuits on a planarsubstrate [7 8] Polymer-based optical waveguide is the basiclight transmission medium for integrated optical device Thepolymer-based integrated optical devices have been widelyused in many laboratories worldwide and some achievedcommercialization [9 10] Especially the polymer-basedoptical ring resonators have become the focus of research dueto their good optical characteristics [11] and have been widely

used in integrated optical devices such as modulators [12ndash14] filters [15 16] sensors [17] and optical communicationsystems [18] However these applied polymer ring resonatorsare not suitable for the sensing elements of RIOGs due to thecharacteristics of small diameter and high propagation lossThe polymer-based resonator used in RIOG requires a muchlarger diameter and a lower propagation loss because theperformance of gyroscope mainly depends on the enclosedarea and the propagation loss of the waveguide resonator[3 19]

In this paper we reported a polymer-based resonatorwitha big diameter and a low propagation loss for constructingthe polymer-based RIOGWe optimally designed the couplerand analyzed the optical properties and corresponding RIOGperformance of the polymer-based resonator

2 Materials and Methods

Figure 1(a) shows the scheme of the polymer ring resonatorfor RIOG It consists of a buswaveguide and a ringwaveguideFor RIOG the ring resonator is the rotation sensing element

Hindawi Publishing CorporationJournal of NanomaterialsVolume 2014 Article ID 146510 6 pageshttpdxdoiorg1011552014146510

2 Journal of Nanomaterials

CW

Out

Out

CCW

Coupler

In

In

D

k

(a)

Si

h

w

1

2

(b)

Figure 1 (a) Configuration of the polymer-based ring resonator for RIOG (b) Cross section view of the geometry of the polymer waveguide

1

0

(a) (b)

Pow

er (d

Bm)

Length (mm)75 100 125 150

minus328

minus326

minus324

minus322

Propagation loss = 0476dBcm

(c)

Figure 2 Simulation result (a) and measurement photograph (b) of optical field distribution of the polymer waveguide with parameters119908 = 5120583m and ℎ = 5 120583m (c) Propagation loss measurement of the polymer waveguide

in which two beams with equal power launch into the twoinput ports of the bus waveguide respectivelyThe input lightis split into two beams by the coupler One beam couples intothe ring resonator with coupling ratio 119896 while the other beamtransmits through the coupler directly For polymer-basedRIOG a resonant frequency difference between the clockwise(CW) beam and the counterclockwise (CCW) beam in thering resonator shown in Figure 1(a)will arise correspondinglywhen there is a rotationThe resonant frequency difference isproportional to the rotation ratio

Figure 1(b) shows the configuration of the polymerwaveguide from the cross section A polymer stripe with awidth of 119908 and a thickness of ℎ is buried in polymer 1 Therefractive index of polymer 1 and polymer 2 is 145 and 146respectivelyThe refractive index contrast of the cladding andthe buried core is 001 The parameters were designed aimingat having an optimal coupling ratio 119896 and a low propagationloss

3 Results and Discussion

In this section we researched the light propagation in thepolymer waveguide the influence of the gap between the busand the ring waveguide on coupling ratio and the opticalproperties of the polymer ring resonator and its correspond-ing gyroscope performance

31 Coupler Design For the view of coupler in the ringresonator shown in Figure 1(a) the buried core of thewaveguide needs a small width and a small thickness [20]The obtained optimal thickness (ℎ) and width (119908) of thepolymer waveguide shown in Figure 1(b) are all equal to5 120583m Figure 2(a) shows the simulation result of optical fielddistribution of the utilized polymer waveguide at an incidentwavelength of 1550 nm The calculated effective refractiveindex of the polymer waveguide is 1454 Figure 2(b) showsthe measurement result of optical field distribution in the

Journal of Nanomaterials 3

1 2 3 400

05

10

Cou

plin

g ra

tiok

Gap (120583m)

D = 10mmD = 20mmD = 30mm

Figure 3 Influences of the minimum gap and the resonator diam-eter on coupling ratio 119896 The inset shows the power transmission inthe bus and ring polymer waveguides with 119863 = 10mm and gap =2 120583m

polymer waveguide Figure 2(c) shows the propagation lossmeasurement of the polymer waveguide by the traditionalcut-back method The measured propagation loss is about0476 dBcmat an incidentwavelength of 1550 nmThe resultsshow that this polymer waveguide has a good performancefor light propagation

To construct a polymer-based ring resonator the rela-tionship between the minimum gap of busring waveguideand the coupling ratio 119896 of the coupler is studied Couplingratio 119896 is the significant parameter of the coupler whichrepresents the fraction of power coupled into the ringresonator from the input port of the bus waveguide [21] Themain factor of coupling ratio 119896 is the geometrical dimensionof the minimum gap between the bus and ring waveguideFigure 3 shows the influences of the minimum gap and thediameter of resonator on the coupling ratio 119896with parameters119908 = 5120583m and ℎ = 5 120583m at an incident wavelength of1550 nm

From the calculated results we can see that the couplingratio 119896 is highly dependent on the diameter 119863 and theminimum gap of the busring waveguide With an increasingminimumgap the value of coupling ratio 119896 decreases becausethe bigger gap reduces the power coupling between the busand ring waveguide In addition the coupling ratio 119896 canbe improved by increasing the diameter of the polymerresonator which is mainly because of the increase of thecoupling length between the bus and ring waveguide Theinset of Figure 3 shows the power transmission in the bus andring polymer waveguides with parameters 119863 = 10mm andgap = 2 120583m at wavelength of 1550 nm The correspondingcalculated result of coupling ratio 119896 is about 032 shown inFigure 3

00

05

10

Tran

smiss

ion

Frequency (GHz)

D = 10mmD = 20mmD = 30mm

4 8 12 16

Figure 4 Transmission spectra of the polymer ring resonator withdifferent diameter of 10mm 20mm and 30mm at 119896 = 032

32 Optical Properties of the Polymer Resonator For thepolymer-based ring resonator the propagation loss couplingratio and circumference of the resonator are crucial parame-ters to determine its performanceThe transmission functionof a ring resonator is given by [6 22]

119879 =

10038161003816100381610038161003816100381610038161003816

119864out119864in

10038161003816100381610038161003816100381610038161003816

2

=

(1 minus 119896) + 1205742minus 2120574radic1 minus 119896 cos (120573119871)

1 + 1205742(1 minus 119896) minus 2120574radic1 minus 119896 cos (120573119871)

(1)

where 120574 = exp(minus120572119871) 119896 is the coupling ratio 120573 is theoptical propagation constant and 119871 is the circumferenceof the polymer resonator 120572 is the propagation loss of thepolymer waveguide which mainly contains material lossbending loss and scatter loss The material loss is power lossabsorbed inside the material due to the absorption and theimperfections in the bulk waveguide material [20] Bendingloss is power leakage that occurred in the curved part ofwaveguide and primarily determined by the bend radius [23]Scatter loss is caused by physical surface roughness especiallyon the side walls of waveguide produced typically during itsfabrication [24]

Equation (1) indicates that the propagation loss of thepolymer waveguide significantly influences the transmissionproperty of the ring resonator The calculated bending lossof the proposed polymer resonator with bend radius 5mmis about 001 dBcm This value is so small that it can beneglected The measured propagation loss of the polymerwaveguide is 0476 dBcm Figure 4 shows the transmissionspectra of the polymer ring resonatorwith different diametersat 119896 = 032 When the propagation loss 120572 and the couplingratio 119896 are fixed the transmission spectrum is determinedby the circumference of the polymer ring resonator FromFigure 4 we can see that the free spectral range (FSR) andthe resonant depth of the ring resonator all decrease with theincrease of the diameter of ring resonator For a givenmaterial


Table 1 Performance parameters of the polymer resonator with D = 10mm and gap = 2 120583m

Parameters Loss (dBcm) Coupling ratio FSR (GHz) FWHM (GHz) 119876 (105) FinesseValue 0476 032 656 107 18 613

00

05

10

Tran

smiss

ion

Frequency (GHz)

k = 012k = 032

k = 067

k = kr

4 8 12 16

Figure 5 Transmission spectra of the polymer ring resonator with119863 = 10mm and coupling ratio 119896 of 067 032 012 and 119896

119903

(ie a fixed loss factor) the output signal decreases dra-matically with an increasing diameter 119863 shown in Figure 4This is mainly because the long propagation length of thelarge diameter resonator results in large power attenua-tion

For RIOG a large resonant depth is beneficial for rotationsignal detection The resonant depth of the ring resonatoris also related to the coupling ratio 119896 Figure 5 shows theinfluence of coupling ratio 119896 on the resonance of polymer ringresonator

The minimum gap dimension of the busring waveguidecorresponding to the coupling ration 119896 of 067 032 and 012is 1 120583m 2 120583m and 3 120583m respectively The resonant depthreaches the largest value at the critical coupling point (119896 =

119896119903

= 1 minus 1205742) Figure 5 indicates that the coupling ratio

119896 of the ring resonator influences not only the resonantdepth but also the full width at the half maximum of thefrequency (FWHM)The three ring resonators have the samefree spectral range because of the same diameter

For polymer ring resonator with 119863 = 10mm and gap =

2 120583m the free spectral range (FSR) FWHM and qualityfactor (119876) are 656GHz 107GHz and 18 times 105 respectivelyThe detailed performance parameters are shown in Table 1

33 Gyroscope Performance The sensitivity of a resonantintegrated optical gyroscope is typically limited by the shot

noise at the two photodetectors included in the readoutsystem It can be estimated by the following formula [25]

120575Ω cong

120582119871

4119860

sdot

radic2 sdot 12057511989112

SNR=

120582

119863

sdot

radic2 sdot 12057511989112

SNR (2)

12057511989112

=

2119888

120587119899119871

sinminus11 minus 120574radic1 minus 119896

radic2 [1 + (1 minus 119896) 1205742]

(3)

SNR = radic

120578119905119875in2ℎ119891

119879max minus 119879min

radic119879max (4)

where119863 is the diameter of the polymer-based ring resonator120582 is the sensor operating wavelength and 120575119891

12is the FWHM

119879max is maximum value of 119879 when cos(120573119871) = minus1 119879min is theminimum value of 119879 when cos(120573119871) = 1 SNR is the signal tonoise ratio of the detective systemwhich is related to quantumefficiency 120578 integral time of photodetector 119905 Planck constantℎ frequency of light 119891 and input power of light 119875in

Equation (2)ndash(4) shows that the value of limited sensi-tivity 120575Ω is negatively related to the closed area of the ringresonator The results indicate that a large closed area canlead to an improvement of sensitivity of resonant opticalgyroscope The limited sensitivity can be also improved byreducing the 120575119891

12which is determined by the propagation

loss 120572 the circumference of the polymer resonator 119871 and thecoupling ratio 119896 In addition (2) indicates that the gyroscopersquossensitivity can be also improved by increasing the signal tonoise ratio of the detective system The input power of lightis proportional to the signal to noise ratio of the detectivesystem Therefore improvement of the input power of lightis an effective way to achieve a higher sensitivity when thestructure of resonant optical gyroscope is fixed

Figure 6 shows the relationships between the couplerratio 119896 and the sensitivity of the polymer-based gyroscopeat different diameter 119863 of ring resonator It can be observedthat the sensitivity of polymer-based resonant integratedoptical gyroscope increases with the increase of diameter119863 of the polymer resonator when coupling ratio 119896 is aconstant Furthermore there is an optimal value of couplingratio 119896 for the limited sensitivity of gyroscope The optimallimited sensitivity of the polymer-based gyroscope with 119863 =

10mm resonator is less than 20 degh For RIOG with 119863 =

30mm the optimal limited sensitivity is about 5 degh Thegyroscope with this sensitivity can be widely used in theinertial navigation field

4 Conclusions

A polymer-based ring resonator is proposed for constructingresonant integrated optical gyroscopeWeoptimally designed


0

20

40

60

80

100

Sens

itivi

ty (d

egh

)

Coupling ratio k00 02 04 06 08 10

D = 10mmD = 20mmD = 30mm

Figure 6 The sensitivity of polymer-based RIOG versus thecoupling ratio for various resonator diameters

and fabricated the polymer waveguide with good measure-ment results The measured propagation loss of the polymerwaveguide at 1550 nm is about 0476 dBcm The analysisabout coupler shows that the value of coupling ratio ismainly determined by the gap of the busring waveguideand the diameter of ring resonator The optical propertiesand gyroscope performance of the polymer ring resonatorare discussed which shows a potential shot noise limitedsensitivity less than 20 degh The polymer-based integratedoptical gyroscopes permitted mass production will be apromising candidate of the new generation gyroscopes on achip

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by NSFC under Grant no 61307066Doctoral Fund of Ministry of Education of China underGrant nos 20110092110016 and 20130092120024 NaturalScience Foundation of Jiangsu Province under Grant noBK20130630 the National Basic Research Program of China(973 Program) underGrant no 2011CB302004 and the Foun-dation of Key Laboratory of Micro-Inertial Instrument andAdvanced Navigation Technology Ministry of EducationChina under Grant no 201204

References

[1] K Suzuki K Takiguchi and K Hotate ldquoMonolithically inte-grated resonator microoptic gyro on silica planar lightwave

circuitrdquo Journal of Lightwave Technology vol 18 no 1 pp 66ndash722000

[2] T Zhang G Qian Y Y Wang et al ldquoIntegrated opticalgyroscope using active Long-range surface plasmon-polaritonwaveguide resonatorrdquo Scientific Reports vol 4 article 38552014

[3] X-Y Zhang C-L Ji T Zhang and Y-P Cui ldquoAnalysis of ringresonator of integrated optical waveguide gyroscoperdquo in 3rdInternational Symposium on Advanced Optical ManufacturingandTesting Technologies AdvancedOpticalManufacturing Tech-nologies vol 6722 of Proceedings of SPIE p 94 July 2007

[4] C Ciminelli F DellrsquoOlio C E Campanella and M NArmenise ldquoPhotonic technologies for angular velocity sensingrdquoAdvances in Optics and Photonics vol 2 no 3 pp 370ndash4042010

[5] M A Guillen-Torres E Cretu N A F Jaeger and L Chrostow-ski ldquoRing resonator optical gyroscopesmdashparameter optimiza-tion and robustness analysisrdquo Journal of Lightwave Technologyvol 30 no 12 Article ID 6157591 pp 1802ndash1817 2012

[6] F Zhang and J W Lit ldquoDirect-coupling single-mode fiber ringresonatorrdquo Journal of the Optical Society of America A vol 5 no8 pp 1347ndash1355 1988

[7] L Eldada and LW Shacklette ldquoAdvances in polymer integratedopticsrdquo IEEE Journal on Selected Topics in Quantum Electronicsvol 6 no 1 pp 54ndash68 2000

[8] J-G Chen T Zhang J-S Zhu et al ldquoLow-loss planar opticalwaveguides fabricated from polycarbonaterdquo Polymer Engineer-ing and Science vol 49 no 10 pp 2015ndash2019 2009

[9] H Ma A K Jen and L R Dalton ldquoPolymer-based opti-cal waveguides materials processing and devicesrdquo AdvancedMaterials vol 14 no 19 pp 1339ndash1365 2002

[10] D-M Zhang C Chen X Sun et al ldquoOptical propertiesof Er(DBM)3Phen-doped polymer and fabrication of ridgewaveguiderdquo Optics Communications vol 278 no 1 pp 90ndash932007

[11] X-Y Zhang T Zhang and J-G Chen ldquoThermooptical poly-mer ring resonator integrated with tunable directional couplerrdquoin 2008 International Conference on Optical Instruments andTechnologyMicroelectronic andOptoelectronicDevices and Inte-gration vol 7158 of Proceedings of SPIE p 71580X November2008

[12] B Bortnik Y Hung H Tazawa et al ldquoElectrooptic polymerring resonator modulation up to 165GHzrdquo IEEE Journal onSelected Topics in Quantum Electronics vol 13 no 1 pp 104ndash110 2007

[13] X-Y Zhang T Zhang X-J Xue et al ldquoTunable optical ringresonator integrated with asymmetric machzehnder interfer-ometerrdquo Journal of Lightwave Technology vol 28 no 17 pp2512ndash2520 2010

[14] M Gould T Baehr-Jones R Ding et al ldquoSilicon-polymerhybrid slot waveguide ring-resonator modulatorrdquo OpticsExpress vol 19 no 5 pp 3952ndash3961 2011

[15] S Yamagata Y Yanagase andY Kokubun ldquoWide-range tunablemicroring resonator filter by thermo-optic effect in polymerwaveguiderdquo Japanese Journal of Applied Physics 1 Regular Papersand Short Notes and Review Papers vol 43 no 8 supplementpp 5766ndash5770 2004

[16] P Rabiei W H Steier C Zhang and L R Dalton ldquoPolymermicro-ring filters and modulatorsrdquo Journal of Lightwave Tech-nology vol 20 no 11 pp 1968ndash1975 2002


[17] J Ren L-H Wang X-Y Han et al ldquoOrganic silicone sol-gelpolymer as a noncovalent carrier of receptor proteins for label-free optical biosensor applicationrdquo ACS Applied Materials ampInterfaces vol 5 no 2 pp 386ndash394 2012

[18] A Chen H Sun A Pyayt L R Dalton J Luo and A K-Y Jen ldquoMicroring resonators made in poled and unpoledchromophore-containing polymers for optical communicationand sensorsrdquo IEEE Journal on Selected Topics in QuantumElectronics vol 14 no 5 pp 1281ndash1288 2008

[19] D M Shupe ldquoFiber resonator gyroscope sensitivity and ther-mal nonreciprocityrdquo Applied Optics vol 20 no 2 pp 286ndash2891981

[20] B Seo S Kim H Fetterman W Steier D Jin and R DinuldquoDesign of ring resonators using electro-optic polymer waveg-uidesrdquo Journal of Physical Chemistry C vol 112 no 21 pp 7953ndash7958 2008

[21] H Hsiao and K A Winick ldquoPlanar glass waveguide ringresonators with gainrdquo Optics Express vol 15 no 26 pp 17783ndash17797 2007

[22] A Yariv ldquoUniversal relations for coupling of optical powerbetween microresonators and dielectric waveguidesrdquo Electron-ics Letters vol 36 no 4 pp 321ndash322 2000

[23] Y A Vlasov and S J McNab ldquoLosses in single-mode silicon-on-insulator strip waveguides and bendsrdquo Optics Express vol12 no 8 pp 1622ndash1631 2004

[24] C Chao and L J Guo ldquoReduction of surface scattering lossin polymer microrings using thermal-reflow techniquerdquo IEEEPhotonics Technology Letters vol 16 no 6 pp 1498ndash1500 2004

[25] W Li T Zhang X-Y Zhang S-Q Zhu and D-X YangldquoTheoretical analysis of long-range surface plasmon-polaritonwaveguide gyroscoperdquoNanoscience andNanotechnology Lettersvol 5 no 2 pp 126ndash129 2013

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


CW

Out

Out

CCW

Coupler

In

In

D

k

(a)

Si

h

w

1

2

(b)

Figure 1 (a) Configuration of the polymer-based ring resonator for RIOG (b) Cross section view of the geometry of the polymer waveguide

1

0

(a) (b)

Pow

er (d

Bm)

Length (mm)75 100 125 150

minus328

minus326

minus324

minus322

Propagation loss = 0476dBcm

(c)

Figure 2 Simulation result (a) and measurement photograph (b) of optical field distribution of the polymer waveguide with parameters119908 = 5120583m and ℎ = 5 120583m (c) Propagation loss measurement of the polymer waveguide

in which two beams with equal power launch into the twoinput ports of the bus waveguide respectivelyThe input lightis split into two beams by the coupler One beam couples intothe ring resonator with coupling ratio 119896 while the other beamtransmits through the coupler directly For polymer-basedRIOG a resonant frequency difference between the clockwise(CW) beam and the counterclockwise (CCW) beam in thering resonator shown in Figure 1(a)will arise correspondinglywhen there is a rotationThe resonant frequency difference isproportional to the rotation ratio

Figure 1(b) shows the configuration of the polymerwaveguide from the cross section A polymer stripe with awidth of 119908 and a thickness of ℎ is buried in polymer 1 Therefractive index of polymer 1 and polymer 2 is 145 and 146respectivelyThe refractive index contrast of the cladding andthe buried core is 001 The parameters were designed aimingat having an optimal coupling ratio 119896 and a low propagationloss

3 Results and Discussion

In this section we researched the light propagation in thepolymer waveguide the influence of the gap between the busand the ring waveguide on coupling ratio and the opticalproperties of the polymer ring resonator and its correspond-ing gyroscope performance

31 Coupler Design For the view of coupler in the ringresonator shown in Figure 1(a) the buried core of thewaveguide needs a small width and a small thickness [20]The obtained optimal thickness (ℎ) and width (119908) of thepolymer waveguide shown in Figure 1(b) are all equal to5 120583m Figure 2(a) shows the simulation result of optical fielddistribution of the utilized polymer waveguide at an incidentwavelength of 1550 nm The calculated effective refractiveindex of the polymer waveguide is 1454 Figure 2(b) showsthe measurement result of optical field distribution in the


1 2 3 400

05

10

Cou

plin

g ra

tiok

Gap (120583m)

D = 10mmD = 20mmD = 30mm





00

05

10

Tran

smiss

ion

Frequency (GHz)

D = 10mmD = 20mmD = 30mm

4 8 12 16



119879 =

10038161003816100381610038161003816100381610038161003816

119864out119864in

10038161003816100381610038161003816100381610038161003816

2

=



(1)






00

05

10

Tran

smiss

ion

Frequency (GHz)

k = 012k = 032

k = 067

k = kr

4 8 12 16


119903




119896119903







120575Ω cong

120582119871

4119860

sdot

radic2 sdot 12057511989112

SNR=

120582

119863

sdot

radic2 sdot 12057511989112

SNR (2)

12057511989112

=

2119888

120587119899119871


radic2 [1 + (1 minus 119896) 1205742]

(3)

SNR = radic

120578119905119875in2ℎ119891


radic119879max (4)


12is the FWHM








4 Conclusions



0

20

40

60

80

100

Sens

itivi

ty (d

egh

)


D = 10mmD = 20mmD = 30mm





Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




1 2 3 400

05

10

Cou

plin

g ra

tiok

Gap (120583m)

D = 10mmD = 20mmD = 30mm





00

05

10

Tran

smiss

ion

Frequency (GHz)

D = 10mmD = 20mmD = 30mm

4 8 12 16



119879 =

10038161003816100381610038161003816100381610038161003816

119864out119864in

10038161003816100381610038161003816100381610038161003816

2

=



(1)






00

05

10

Tran

smiss

ion

Frequency (GHz)

k = 012k = 032

k = 067

k = kr

4 8 12 16


119903




119896119903







120575Ω cong

120582119871

4119860

sdot

radic2 sdot 12057511989112

SNR=

120582

119863

sdot

radic2 sdot 12057511989112

SNR (2)

12057511989112

=

2119888

120587119899119871


radic2 [1 + (1 minus 119896) 1205742]

(3)

SNR = radic

120578119905119875in2ℎ119891


radic119879max (4)


12is the FWHM








4 Conclusions



0

20

40

60

80

100

Sens

itivi

ty (d

egh

)


D = 10mmD = 20mmD = 30mm





Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






00

05

10

Tran

smiss

ion

Frequency (GHz)

k = 012k = 032

k = 067

k = kr

4 8 12 16


119903




119896119903







120575Ω cong

120582119871

4119860

sdot

radic2 sdot 12057511989112

SNR=

120582

119863

sdot

radic2 sdot 12057511989112

SNR (2)

12057511989112

=

2119888

120587119899119871


radic2 [1 + (1 minus 119896) 1205742]

(3)

SNR = radic

120578119905119875in2ℎ119891


radic119879max (4)


12is the FWHM








4 Conclusions



0

20

40

60

80

100

Sens

itivi

ty (d

egh

)


D = 10mmD = 20mmD = 30mm





Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

20

40

60

80

100

Sens

itivi

ty (d

egh

)


D = 10mmD = 20mmD = 30mm





Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Research Article Low-Loss Polymer-Based Ring...

Documents

Transcript of Research Article Low-Loss Polymer-Based Ring...