Fast and slow light enhancement using cascaded microring resonators with the sagnac reflector

Fast and slow light enhancement using cascaded microringDuy-Tien Lea, Manh-Cuong Nguyenb, Trung-Thanh Lec,∗ a Posts and Telecommunications Institute of Technology PTIT and Finance-Bankin

Fast and slow light enhancement using cascaded microring

Duy-Tien Lea, Manh-Cuong Nguyenb, Trung-Thanh Lec,∗

a Posts and Telecommunications Institute of Technology (PTIT) and Finance-Banking University, Hanoi, Viet Nam

b Le Quy Don Technical University, Hanoi, Viet Nam

c International School (IS-VNU), Vietnam National University (VNU), Hanoi, Viet Nam

Article history:

Received 3 September 2015

Received in revised form 31 October 2016

Accepted 7 November 2016

Keywords:

Microring resonator

Fast light

Slow light

Silicon waveguides

FDTD

Transfer matrix method

Multimode interference (MMI)

Microresonators

AcascadedmicroringresonatorbasedonsiliconwaveguideswithanMMI(Multimode Interference)basedSagnacreflectorisproposedinthisstudy.Bycontrollingthecoupling coefficientswiththeusedoftheMMIbasedSagnacreflector,thedoubleofbothpulse delayandadvancementfortheslowandfastlightcanbeachieved.Thenewstructurecan producethefastandslowlightphenomenonononechipwithadoubleofthetimedelay andpulseadvancement.ByusingtheSagnacreflector,thedeviceisverycompact.Transfer matrixmethodandFDTD(FiniteDifferenceTimeDomain)simulationareusedtoobtainthe characteristicsofthedevice.Thetransmission,phase,groupdelayandpulsepropagation areanalyzedindetail.OurFDTDsimulationsshowagoodagreementwiththeanalytical theory

©2016ElsevierGmbH.Allrightsreserved

1 Introduction

Inrecentyears,opticalmicroringresonatorshavebeenofgreatinterestforapplicationsinopticalcommunicationssuchas opticaldelaylines,opticalswitches,modulators,filters,dispersioncompensatorsetc.[1,2].Micro-ringresonatorstructures consistsofanumberofsinglemicro-ringresonatorscascadedinseriesorinparallelcanbeusedforhigherorderfilterswith extendedfreespectralratios[3]orswitching[4],modulatingapplications[5],fastandslowlight[6]

Analysisofthegroupdelayandtransmissioncharacteristicsofcascadedmicroringresonatorsusedforopticalfiltersand dispersioncompensatorshavebeenstudied[7–9].However,thesestructureshavepositivegroupdelayandmainlydesigned forpulsedelayapplications.Slowandfastlightgenerationareemergingasaveryattractiveresearchtopic.Varioustechniques havebeendevelopedtorealizefastlightandslowlightinatomicvaporsandsolid-statematerials[10].Oneapplicationamong thesetechniquesistocontrolthegroupvelocityvgoflightpulsestomakethempropagateeitherveryslow(vg<c)orvery fast(vg>corvgisnegative),wherecisthevelocityoflight

Inthisstudy,weproposeanewcascadedmicroringstructurebasedonsiliconwaveguideswithaSagnacloopreflector TheSagnacloopreflectorhasbeenappliedtomanyapplicationstructuressuchasfilteringandfastlightstructures[11,12]

Bycontrollingthecouplingcoefficientsofthecouplerusedinmicroringresonatorsintheproposedstructure,negativeand positivegroupdelaycanbeobtained.Thismeansthatthelightvelocitycanbecontrolledandthereforethefastandslow

∗ Corresponding author.

E-mail addresses: thanh.le@vnu.edu.vn, thanhvn au@yahoo.com (T.-T Le).

http://dx.doi.org/10.1016/j.ijleo.2016.11.038

0030-4026/© 2016 Elsevier GmbH All rights reserved.

Fig 2.Transmission, phase and group delay characteristics of the single microring resonator.

lightcanbeinducedbythestructure[13–15].Here,weuseaSagnacloopreflectorbasedonan1×2MMI(Multimode Interferencecoupler)attheendofthestructuretoenhancethefastandslowlight.TheuseofanMMIbasedreflectorforthe reflectiontodoublethepulsedelayandpulseadvancement.Itisshownthatthegroupdelay,timedelayandadvancement aredoubledcomparedtothecasewithoutusingtheMMISagnacloopreflector.Weusesiliconmicroringresonatorsbecause

ofhighqualityoffabricationbyusingCMOScompatibleprocessanddevicecompactnesswithahighindexcontrastsystem

2 Design

ThestructureconsistingofN-singlemicroringresonatorscascadedinserieswithaSagnacloopreflectorisproposedin Fig.1(a)

Fig 3. Input and output pulses at the single microring resonator.

2.1 Singlemicroringresonator

ForasinglemicroringresonatorasshowninFig.1(b),theoutputfieldcanberelatedtotheinputfieldbytheexpression [16]

H1=E2

E1 = 1−˛1exp



j1



1−˛11exp

whereE1,E2arethefieldamplitudeattheinputandoutput;1 and1=

1−|1|2arethetransmissionandcoupling coefficientsofthecoupler;˛1 isthelossfactorintheringwaveguideand1=2

NeffLR1istheaccumulatedphaseshift overtheringwaveguide.Neff istheeffectiverefractiveindexofthewaveguide,isthewavelengthandLR1=2R1isthe circumferenceoftheringwaveguide

Theeffectivephaseshiftofthemicroringresonatorcanbedefinedby

single=arg

2

E1



=artan



˛12sin (ω)



1+˛1 

−(1+2)˛1cos (ω)



(2)

Thenormalizedgroupdelayisgivenbyn=−dsingle

dω Theabsolutegroupdelayisd=Tn,whereTistheunitdelayofthe signalpropagatingoverthemicroringwaveguide.Theresonanceisoccurredatthephase1=2m,wheremisaninteger

Atresonance,1>˛1theringresonatorandwaveguideisunder-coupledandleadingtopulseadvancementorfastlight; when1<˛1,theyareover-coupledandleadingtopulsedelayorslowlight;thecriticalcouplingoccurswhen1=˛1 The transmission, phase and group delay of the single microring resonator at the transmission coefficients 1= 0.9975,0.9966and0.99respectivelyareshowninFig.2.Theparametersaresetasfollows:thelossfactorofthewaveguide

˛1=1dB/cm,thelengthofthemicroringwaveguideLR1=300␮m.Thesimulationshowsthatthepositiveandnegative groupdelaycanbeachievedbyadjustingthecouplingcoefficientofthecoupler.Itisassumedthatasiliconwaveguidewith

aheightof220nmandwidthof400nmandrefractiveindexNeff =2.25

Wenowinvestigatethepulsepropagationoverthesingleringresonator.ItisassumedthattheinputpulseisGaussian andcanbeexpressedas[17]

Fig 4.Transmission characteristics of the cascaded microring resonators (a)  =  1 = 0.99 and (b)  =  1 = 0.9975.

where0istheresonancewavelengthofthesinglemicroringresonator,THW=Tb/2isthebithalfwidthat1/e2intensityand

Tbisthebitperiod.FromthesimulationsofFig.2,theresonancewavelengthis0=1.54817␮m.Theinputandcorresponding outputpulseswiththetransmissioncoefficients1=0.9975, 0.9966and0.99areshowninFig.3,wheretheinputpulse widthTp=50ps[18].Thesimulationsshowthatpulsedelayof20pscanbeobtainedwhen1=0.99andwhen1=0.9975 thepulseadvancementof12psisobtained

2.2 Cascadedmicroringresonators

Asidecoupledintegratedspacedsequenceofresonators(SCISSOR)orcascadedmicroringresonatorwithouttheSagnac reflectorhasbeenfirstlyproposedbyHeebnerandBoyd[19].ItwasshownthatbyusingSCISSORstructure,fastandslow

Fig 5.Input and output pulses at the cascaded microring resonator structure.

lightcanbeobtained.Here,weconsideraSCISSORasshowninFig.1withaSagnacloopreflector.Forsimplicity,weassume thatNringresonatorsareidentical.Asaresult,thetransferfunctionoftheSCISSORcanbewrittenby

HSCISSOR=H1H2 HN=(E2

E1)

N

=



−˛exp

j

1−˛exp

j

(4)

Here=1and˛=˛1isthelossfactorintheringwaveguideand=2

NeffLR Thetransmission,phaseandgroupdelayofthecascadedmicroringresonatorforN=1,2,3areshowninFigs.4and5.It

isassumedthatthetransmissioncoefficientofthecoupleris1=0.99and0.9975.Thesimulationresultsshowthatslow andfastlightareinducedbyadjustingthecouplingcoefficients.Inaddition,thepulsedelayandpulseadvancementare increasedbyNtimescomparedwiththesinglemicroringresonator

2.3 CascadedmicroringresonatorswiththeSagnacreflector

Fig.1showsthecascadedmicroringresonatorwiththeSagnacreflector.Inthisstudy,weusean1×2MMIcouplerin theSagnacreflector.Asaresult,thetransferfunctionoftheproposedstructureinFig.1canbeexpressedby

H=(2j˛sss)



−˛exp

j

1−˛exp

j

2N

(5)

wheresands=

1−|s|2arethetransmissionandcouplingcoefficientsofthecoupleroftheSagnacreflectorand˛sis thelossfactorintheringwaveguideoftheSagnacreflector

Fig.6(a)and(b)showsthetransmission,phase,groupdelayandoutputpulsespropagatingoverthestructurewithand withoutSagnacreflector.ItisassumedthatthestructureconsistingofNidenticalmicroringresonators(N=1and2)with thetransmissioncoefficientof1=0.99.ByusingtheSagnacreflector,weobtainthepulsedelaysof43psand83psfor

N=1and2respectively,comparedwith20psand40pswithoutusingtheSagnacreflector

When1=0.9975,theundercoupledconditionoccurs.Therefore,thefastlightcanbeinducedbyusingtheproposed structure.Fig.7(a)and(b)showsthetransmissioncharacteristicsandoutputpulsespropagatingoverthestructurewithand withoutSagnacreflector.Itisshownthatpulseadvancementsof25psand50psareachievedwhentheSagnacreflectoris used(comparedwith12psand24pswithouttheSagnacreflector)

Bycontrollingthecouplingcoefficientsofringresonators,thefastandslowlightcanbeachieved.Thepulsedelayand advancementcanbeincreasedbyNtimesifNidenticalringresonatorsareused.Fig.8showsthetimedelayandadvancement

ofthepulsepropagatingthroughourprosedstructure.WecanseethatbyusingtheSagnacreflector,thepulsedelayand advancementcanbedoubledcomparedwiththeconventionalSCISSORstructure

Toverifytheaccuracyofthetransfermatrixanalysis,wecomparetheresultsobtainedwiththeFDTD.ForourFDTD simulations,theradiusofthemicroringresonatoristobeR=5␮m,thewaveguidewidthisWa=400nm,thegapbetween themicroringwaveguideandthestraightwaveguideischosentobeg=160nminorderforthepowertransmissioncoupling (||2)tobe||2=0.9asshowninFig.10(a).Herewetakeintoaccountthewavelengthdispersionofthesiliconwaveguide usingtheexpressionNeff(␭)=4.7020−1.6667for=1.5−1.6␮m(Fig.10(b))

AGaussianlightpulseof15fspulsewidthislaunchedfromtheinputtoinvestigatethetransmissioncharacteristicsof thedevice.Thegridsize x= y=0.02nmand z=0.05arechoseninoursimulations.AsshowninFig.11(a)witha numberofthemicroringresonatorN=1andFig.12(a)withN=2,thetransmissionscalculatedbytheFDTDarequitesimilar

Fig 6.Transmission characteristics of the cascaded microring resonators (a)  =  = 0.99 and (b) output pulses.

Fig 7. Transmission characteristics of the cascaded microring resonators (a)  =  1 = 0.9975 and (b) output pulses.

Fig 8.Time delay and advancement with and without the Sagnac reflector.

Fig 9.Directional coupler used for microring resonator.

Fig 10. FDTD simulations (a) transmission coefficient at different gap and (b) wavelength dispersion of the silicon waveguide with a width of 400 nm (the inset shows the field at  = 1.55␮m).

tothetransmissioncalculatedbytheanalyticaltheory.Figs.11(b)and12(b)showtheFDTDfielddistributionsatonand off-resonances

Thesimulationresultsforthedeviationofthetransmissioncoefficient 2dependingonthewaveguidewidthvariation

WaareshowninFig.13.Duetothemanufacturingtolerances,thevariationinwaveguidewidthoccursandleadingtoa newwaveguidewidthexpressedbyW=Wa± Wa.Addingtothechangeofthetransmissioncoefficient,thedeviation

ofthewaveguidewidthalsoleadstothechangeineffectiveindex.Forapositive Wa,theeffectiveindexisincreased.For anygapandradius,apositive Waleadstoadecreaseinthetransmissioncoefficient.For Wa=+10nm,thetransmission coefficientisdecreasedby0.044forg=120nmand0.037forg=130nmatthesamewidthWa=450nmandradiusR=10␮m Whilethiscoefficientisdecreasedonlyby0.012iftheringradiusR=5␮m.Asaresult,thetransmissioncoefficientofthe couplerisquitestableforasmallerringradiusandlargergap.Forawidthvariationwithin±20nm,adeviationofthe

Fig 11.FDTD simulation of the proposed structure with one ring resonator and Sagnac reflector.

Fig 12.FDTD simulation of the proposed structure with two ring resonators and Sagnac reflector.

Fig 13. Change of the transmission coefficient and the deviation from the calculated value at Wa = 450 nm as the effect of the width variation.

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