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Label free optical sensor by designing a high-Q photonic crystal ring slot structure

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OpticsCommunications335(2015)73–77

ContentslistsavailableatScienceDirect

OpticsCommunications

journalhomepage:http://wendang.chazidian.com/locate/optcom

Label-freeopticalsensorbydesigningahigh-Qphotoniccrystalring–slotstructure

LijunHuanga,b,HuipingTiana,n,JianZhoua,QiLiua,PanZhanga,YuefengJia

StateKeyLaboratoryofInformationPhotonicsandOpticalCommunications,SchoolofInformationandCommunicationEngineering,BeijingUniversityofPostsandTelecommunications,Beijing100876,Chinab

DepartmentofPhysicsandInformationEngineering,HuaihuaUniversity,Huaihua,Hunan418008,China

a

articleinfo

Articlehistory:

Received24June2014Receivedinrevisedform20August2014

Accepted5September2014

Availableonline18September2014Keywords:

OpticalsensingandsensorsRing–slotstructureCoupledresonatorsResonators

Photoniccrystals

abstract

Weproposealabel-freerefractiveindex(RI)sensorbasedonahigh-Qphotoniccrystal(PhC)ring–slotresonator.Theproposeddeviceconsistsofaring–slotcavity,inwhichlightiscoupledinputandoutputbyusingaPhClinedefectwaveguide(W1).Byusingtwodimensional?nite-differencetime-domain(2D–FDTD)simulation,weshowthataQ-factorashighas107isachievedwhenthewidth(w)ofring–slotequalsto0.20aandtheradiusofcenterairholeinnerring–slotequalsto0.34a.Eventhoughtherefractiveindex(RI)equalsto1.330(watersurroundings)attelecomwavelengthrange,Qof$11477.3canalsobeachievedwhenthewidthofring–slotequalsto0.28a.TheRIsensitivity(S)equalsto160nm/RIU(refractiveindexunit)andthedetectlimit(DL)of8.75Â10À5RIUisobtained.Thesesuggestthatthedesignisapromisingcandidateforlabel-freebiosensinginmedicaldiagnosis,lifescienceandenvironmentalmonitoring.

&2014ElsevierB.V.Allrightsreserved.

1.Introduction

Highqualityfactor(Q-factor)micro-cavities[1–3],duetothenarrowresonancelinewidthandlongphotonstoragetime,areprominentcandidatesforsensorswithenhanceddetectionsensi-tivity[4–10]andaccuratedetectionlimitation[10].Severalmicro-cavitiessuchasmicro-ringcavities[4,11–20],micro-toroids[21],?berbragggrating/Fabry–Perot(FBG/FP)cavity[22],photoniccrystals[5,6,9,23–39]hadbeenextensivelystudiedinthepastfewdecades.AhighQmicro-ringcavityisrecentdemandedforanumberofapplications[10],suchaslabel-freeRIsensor,becausehighQoftheresonatorcandecreasetheimpactofnoiseonthedetectionoftheresonancewavelength.Vosetal.[14]proposedalabel-freebiosensorbasedonmicro-ringcavitiesinSilicon-on-Insulator(SOI),andtheyusedtheavidin/biotinhighaf?nitycoupletodemonstrategoodrepeatabilityanddetectionofproteincon-centrationsdownto10ng/ml,andthissensorhasaQfactorof20,000.Carlosetal.[15]representedanintegratedbiochemicalsensorbasedonaslot-waveguidemicro-ringresonatorwhichpossessesQfactorof1800andSof212nm/RIU.Claesetal.[16]demonstratedaslot-waveguide-basedringresonatorinSOIwiththeSof298nm/RIU,andHsiaoetal.[18]presentedSof250nm/RIUinaslotphotoniccrystalring-resonatorforRIsensing,

n

Correspondingauthor.

E-mailaddresses:hptian@http://wendang.chazidian.com(H.Tian),jyf@http://wendang.chazidian.com(Y.Ji).

whereastheQfactorsarelimitedto1200in[16]and800in[18],andLingetal.[17]demonstratedaQfactorof105inpolymermicro-ringresonatorwhichachievesanacousticsensitivityaround36.3mV/kPawith240μWoperatingpower.InordertominimizethesmallestdetectablewavelengthshiftΔλminandenhancethedetectablesensitivity,highQcavitiesandalownoisedetectionsystemarerequired.AhighQfactorresultsinnarrowspectralpeaks:Q¼λ0/ΔλFWHM,whereλ0andΔλFWHMrepresenttheresonancewavelengthandfull-widthathalf-maximum(FWHM)oftheresonancepeak,respectively.ThereareanumberofparametersthatdeterminetheQfactorofcavity,suchas,reducedopticallossesenhancetheQfactor,andmadeopticalmodemorelocalizedbetweenthering–slotwaveguideandtheinput/outputwaveguidesreducestheresonancecavitylosses.Thelastbutnottheleast,smallerradiicanincreasebendlossesbutdecreasescatteringlossesduetoreducedroundtriplength.

Inthispaper,inordertoobtainhighQfactorsensor,alabel-freeRIsensorbasedonPhCring–slotcavityisproposed.Theproposeddeviceconsistsofaphotoniccrystalring–slot(PhCRS)structure,whichisdesignedbyremovingsixairholesinthecenterofstruc-tureandetchingthering–slotcavity,inwhichlightiscoupledinputandoutputbyusingaPhClinedefectwaveguide(W1).WithFDTDsimulation,weadjustthering–slotwidthwandtheradiusoftheredairholer1tooptimizetheQfactorandsensitivityS,andweshowthattheQfactorashighas107isachievedwhenthewidth(w)ofring–http://wendang.chazidian.comparedwithRefs.[14–18],theQfactorisenhancedbyabouttwoordersofmagnitude.Eventhough

http://wendang.chazidian.com/10.1016/j.optcom.2014.09.014

0030-4018/&2014ElsevierB.V.Allrights

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reserved.

74L.Huangetal./OpticsCommunications335(2015)73–77

waterabsorptionattelecomwavelengthrangeisconsidered,aQfactorof$11477.3canalsobeobtainedwhenthewidthofring–slotequalsto0.28a,andthiswidth,consideringthefabricationprogresslater,canalsomaketheslotregiontobecompletely?lledwiththeglucosesolution[15,16].Inordertoquantitativelyanalyzesensitiv-itySoftheproposedsensordevice,wechangetherefractiveindexasRI¼1.0,1.30,1.330,1.345and1.377,respectively.TheRIsensitivitySof160nm/RIUiscalculated.Inaddition,theDLof8.75Â10À5RIUisobtained.Thisisofextremeimportantintheoryforlabel-freeRIsensortoapplysurfacebiomoleculedetection.

2.Structuredesignofphotoniccrystalring–slotcavityTheschematicviewofthePhCRSstructuredesignisshowninFig.1,whichisbasedonatriangularlattice,hole-arrayPhC.Thatisbecausethehole-arraybasedPhCisusuallyselectivelyremovedthematerialunderneaththecavitytoformasimilarfree-standingmembranewhichcanbeeasiertorestricttheverticalleakageintothesubstratethanthepillar-arraybasedPhCcavity[34].Inaddition,atriangularlatticePhCcancreateawiderphotonicbandgap(PBG)thanthesquarelatticePhC.Therefore,thestructuredesigninthispaperisbasedonthetriangularlattice,hole-arraybasedPhCinFig.1(a).Inthedesign,triangularlatticeairholesarearrangedinsilicon(nsi¼3.48),inwhichsixairholesareremovedandetchedthering–slotinthecenterofstructure.WesimulatethePhCRSstructurebyusingtheopensourceFDTDsoftwareMeepwhichfurtherdividesspaceintoadiscretegridandthe?eldsareevolvedintimeusingdiscretetimesteps[40].Asaresult,thegridandthetimestepsaremade?nerand?ner,thisbecomesacloserandcloserapproximationforthetruecontinuousequations.Inthesimulationprocess,TheTEGaussian-pulsesourcewiththecenterfrequency(ω¼0.25(2πc/a))isusedandrunforseveraliterations.Theresolutionissetto20(thatis,withagridspacingofa/20,wherearepresentsthelatticeconstant)andthetimestepof0.025a/cisemployed.Allthesimulationsarecarriedoutwiththesamemeshsizeandtimestepforfuturecomparableresults.Sincetheboundaryconditionsatthespatialedgesofthecomputationaldomainmustbecarefullyconsidered,one-spatialunitthickperfectlymatchedlayer(PML)whichsurroundsthesimulatedareaabsorbsthe?eldsleavingthesimulatedregiontoimplementre?ections.Lightsourceisplacedattheheadoftheinputlinedefectwaveguideandmonitorisplacedattheendoftheoutputlinedefectwaveguide.Bydividingtheoutputpowerdetectedwiththemonitorbytheinputpowerofthesource,weobtainthetransmittancespectra.

AsseeninFig.1,thelatticeconstantaequalsto378nmandtheairholesradiusris0.34a(128.5nm).Basedonthisstructure,thetransmissionspectrainthePhCRSstructureisshowninFig.2(a),

andtheresultsdisplayobviouslyseveraldifferentresonantmodesatnormalizedfrequenciesof0.2239(2πc/a),0.2493(2πc/a),0.304(2πc/a),0.313(2πc/a),whichcorrespondtoresonantwavelengthsof1688.25nm,1516.25nm,1243.42nm,1207.67nm,respectively.Inordertoquantitativelywellanalysisthepropertiesofsensingstructure,wechoosetheresonantfrequencyof0.2493(2πc/a)toobservetheshiftofresonantwavelengthwhenrefractiveindexnearthering–slotareaandthering–slotcavitystructurearemodi?ed.Fig.2(b)showsthesteady-stateelectric?eldpro?leinthePhCRSstructureinthex–yplane,inwhichtheoptical?eldishorizontallycon?nedinthein-planedirection.However,wecanalso?ndthatthecon?neoflightneedtobestrengthenedandtheTE-likepolarizedlightneedfurthercoupledintotheringwave-guidein-plandirection.

3.Simulationresultsanddiscussion

3.1.ThesimulationanalysisofQfactorandsensitivitySinPhCRSstructure

TheQfactorofacavityisdeterminedbytheenergylosspercycleversustheenergystored.Theenergylossmainlyincludesre?ectionlossandtheabsorptionlossofcavitymaterial.There-fore,toimprovetheQfactorofthePhCRSstructuredesign,weshoulddecreasetheenergyloss.WiththePhCRSstructure,theQfactorcanbeexpressedasfollows:[2,3]

11¼þ1

closs

ð1Þ

WhereQcrepresentsthelifetime,thatis,thetimeoflightcandecayfromthecavityintothewaveguide,andQlossreferstothematerialabsorptionandopticalradiationfromthecavityintothesurroundingair.Eq.(1)givesanimportanthintthatsuppressingradiationlosscanenhancetheQfactor.Therefore,weadjustthecavitystructureandmakethattheelectric?eldpro?leofcavityedgesshouldnotbeabruptbutgentlesothattheenergylosspercycleversustheenergystoredislower.Herethestrategytoalterthering–slotwidthwandtheradiusoftheredairholer1makescon?nementgentlerandobtainshighQfactor.Whenwechangethering–slotwidthandtheradiusofredairholenearthecavityedge,theBraggre?ectioneffectinmultipledirectionscanbemodi?ed.Becausethephasesofpartialrefectionatthecavityedgesaremodi?ed,theresultantphase-mismatchweakensthemagnitudeofBraggre?ection.Tocompensateforthereductionofthere?ection,lightisconsideredtopenetratemoreinsidethemirrorandbere?ectedperfectly.Thismeansthattheelectric?eldpro?leatthecavityedgesbecomesgentler.Withtheappropriatealteration,thepro?leisconsideredtobeclosetotheidealcon?nementexpressedbytheGaussianfunction[http://wendang.chazidian.coming

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this

Fig.1.Thephotoniccrystalring–slot(PhCRS)structuredesignusinga2Dphotonic-crystal.(a)Schematicofthebasecavitystructurewithtriangularlatticeofairholes,wherea¼378nm,r¼0.34a,W1¼√3a.(b)Designedcavitystructurecreatedbyalteringthering–slotwidthwandtheradiusr1.

L.Huangetal./OpticsCommunications335(2015)73–7775

Fig.2.(a)ThetransmissionspectraoftheinitialPhCRSstructuredesign,andobservingtheshiftoftheresonantfrequencyof0.2493(2πc/a)surroundedbybluedashed.(b)ThelightdistributionthroughPhCRSstructureinthex–y

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plane.

Fig.3.(a)TheQfactorsandresonancefrequenciesasafunctionofring–slotwidthwinthePhCRSstructure.(b)TheQfactorsandresonancefrequenciesasafunctionofradiusoftheredairholer1whenw¼0.20a

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.

strategy,ring–slotwidthwandradiusoftheredairholer1is

modi?edinFig.1(b),andthevariationtendencyofQfactorand

resonancefrequenciesasafunctionofring–slotwidthwand

radiusoftheredairholer1isshowninFig.3(a)and(b),

respectively.Thereisanunambiguousvariationtendencyin

Fig.3(a),theQfactorgetpromotedwiththeincrementofring–

slotwidthwhenring–slotwidthislessthan0.2a;however,theQ

factorisdeclinedquicklywhenthering–slotwidthismorethan

0.2a.Whereastheresonancefrequenciesisincreasedmonoto-

nouslywhenring–slotisbroaden.Becausetheopticalmodeis

morelocalizedwiththeincreaseofring–slotwidthwhenthe

widthofring–slotislessthan0.2a,andthephotonlifetimecanbe

enhancedandthehigherQfactorcanbeachieved,whereasit

turnstothecontrarytendencywhenthewidthofring–slotis

morethan0.2a.Withthewidthofring–slotincreased,thehigh-

dielectricmaterialisdecreasedandthelow-dielectricmaterialis

increasedinthecavityregion,asaresult,theresonancefrequen-

ciesispushedtohigherfrequency.Similarly,withtheincreaseof

theredairholer1,thereisamaximumoftheQ(1.0Â107)factor

forr1¼0.34a,w¼0.2aandresonancefrequenciesispushedcon-

tinuallyhigherfrequencyinFig.3(http://wendang.chazidian.comparedwiththeothers

situation,thatisbecausetheleakageoflightbecomessmallerand

thelifetimeofphotonsismoreenhancedinthecavityregionfor

r1¼0.34a,w¼0.2a.

Therearetwoimportantroutestoenhancethedetection

sensitivityofsensor:onewayistomaximizetheQfactorofthe

resonator,whichwillreducetheimpactofnoiseonthedetermi-

nationoftheresonancefrequency[10],andwealreadyobtainthe

highestQfactorinabovediscussion.Theotheroneistomaximize

theaverageresonancewavelengthshiftperrefractiveindexunitFig.4.Simulatedsensitivityagainstvariedtheradiusofredairholer1from0.1ato0.50a.Eachlinerepresentsindividualofring–slotwidthwfrom0.15ato0.35a.byincreasinglightandmatterinteractionthatgetattachedtothewaveguidesurface[41].Basedonthesecondscheme,tomakethePhCRSstructurevalidforsensing,wefurtheraltertheradiusofredairholer1andadjustthering–slotwidthwtooptimizethesensitivityofthePhCRSstructuredesign.Thecalculatedsensitivityforring–slotwidthwandtheradiusofredairholer1modi?edasafunctionofrefractiveindexchangeΔnisshowninFig.4.There-fore,inordertointuitivelyanalyzesensitivity,thesensitivityS

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of

76L.Huangetal./OpticsCommunications335(2015)73–77

sensorisgivenbyS¼

Δλð2Þ

InFig.4,sixsensitivitycurvesofring–slotstructureforr1from0.1ato0.50aareplotted,andeachcurverepresentsdifferentring–slotwidthwfrom0.15ato0.35a.Withincreasingr1,wecanseeanevidenttrendthatthesensitivityraisesandreachesitsmaximumaroundr1¼0.30a–0.34a,whereasitfallsrapidlywhenther1comestoabout0.5a.Thestrongestdependenceisobtainedwithring–slotwidthw¼0.28a,andthehighestsensitivityreaches160nm/RIUwithr1¼0.34a.However,forotherring–slotwidthw,theenhancementofsensitivitybecomeslesssigni?cant.Becausetheoverlapbetweenopticalmodeandthedetectingtargetisenhancedgraduallyandcausestheenhanceofsensitivitywhentheairholer1isincreasedfrom0.1ato0.34a,whereastheoverlapisweakenpromptlywhentheairholer1isincreasedfromthe0.34ato0.50a.Similarly,theoverlapbetweenopticalmodeandthedetectingtargetisenhanced?rstlyandweakenthenwiththering–slotwidthwwidenfrom0.15ato0.35a.3.2.TheoptimalresultsofQfactorandsensitivitySinPhCRSstructure

BasedonthediscussionbetweenQfactorandsensitivity,theQfactorreachesitsmaximumwhenr1¼0.34a,w¼0.20a,whereassensitivitypossessestheoptimalSof160nm/RIUwithr1¼0.34a,w¼http://wendang.chazidian.comparedtotwokindsofcircumstancesandconsideringthefurtherfabricationprogress,wechoosetheparametersofthisstructureforr1¼0.34a(128.5nm),w¼0.28a(106nm),respectively,

andthiswidthcanmakethering–slotregioncompletely?lledwithglucosesolution[15,16].ByapplyingtheFDTDmethod,thesimula-tionoflightpropagationpro?leinthex–yplanefortheoptimalring–slotstructureisshowninFig.5.AsseeninFig.5,thereisasigni?cantamountoflightampli?cationwithintheresonantcavity.Inviewoftheevanescent?eldatthesidewallsofthecavity,wecanobservethatmostofthesideholesofring–slotcavityhaveastrongeroptical?eld.Thiscausesthecavitytobeverysensitivetorefractiveindexchangesduetothephotonlifetimeenhancedandthelargedegreeoflight-matterinteraction.

InordertoquantitativelyanalyzetheRIsensitivityofthesensorstructure,weobservetheshiftofresonantpeakwhentherefractiveindexisaltered.ThetransmissionspectraofTE-likepolarizedlight-wavewithdifferentRI(RI¼1.0,1.30,1.330,1.345,1.377)parametersasafunctionofwavelengthareshowninFig.6andinsetshowstheampli?edimageoftheblacktransmissionpeak.FromthesimulationresultsshowninFig.6,wecanobserveaclearshiftoftheresonantwavelengthtohighervaluesforanincreasedbackgroundrefractiveindex:λ1.0¼1554.08nm(Q1.0¼13,060),λ1.30¼1602.04nm(Q1.30¼11438.5),λ1.330¼1606.83nm(Q1.330¼11477.3),λ1.345¼1609.25nm(Qair¼10937.6),λ1.377¼1614.36nm(Q1.377¼11133.5).Basedontheelectromagneticenergyandthevariationprinciple[42],

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the

Fig.5.Theelectric?elddistributioninthex–yplanefortheoptimalring–slotstructure

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design.

Fig.7.Theblacksquaresindicatetheshiftvaluesofresonantwavelengthfordifferentrefractiveindexvariationandtheredsolidlineislinearly?twhenairholesandring–slotequalto0.34aand0.28a,respectively.

Fig.6.ThetransmissionspectraofTE-likepolarizedlight-wavewithdifferentRIparameters(RI¼1.0,1.30,1.330,1.345,1.377).Insetshowstheampli?edimageoftheblacktransmission

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peak.

L.Huangetal./OpticsCommunications335(2015)73–7777

low-frequencymodesconcentratetheirenergyinthehigh-εregionsandthehigh-frequencymodeshavealargerfractionoftheirenergyinthelow-εregions.Therefore,thepropertiesoftransmissionarechangedinthering–slotstructurewhentherefractiveindexofairholesandring–slotisaltered,andtheresonantpeakispushedlowerfrequency(longerwavelength)whentherefractiveindexisincreasedinthering–slotstructure.Theblacksquaresindicatetheshiftvaluesofresonantwavelengthfordifferentrefractiveindexalterationandtheredsolidlineislinearly?tinFig.7whenairholes(r1)andthewidth(w)ofring–slotequalto0.34aand0.28a,respectively.BasedthesedataandEq.(2),wecancalculatesensitivitySof160nm/RIU.AsseenfromtheFigs.6and7,theresonantpeakislinearlyshiftedlongerwavelengthwiththeincreaseofrefractiveindex.ThisvariationtrendisanalogoustothatoftransmissionpeakshiftoftheFabry–Perotcavitywhenitscavitylengthchanges.Withthislinearrelationship,itispotentialtocalculatethechangeofrefractiveindexbytheshiftresonantpeakinglucosesolutionbasedondetectionofresonantwavelengthshift[10,15,16].Takingwaterabsorptionintoconsiderationattelecomwavelengthrange,theQfactorandthesensitivityareequalto11477.3(Q1.330)and160nm/RIU,respectively.Inaddition,Inordertoanalyzequantitativelythedetectionlimit(DL)ofsensors,thedetectionlimit(DL)oftheproposedsensorstructureiscalculatedbythesensitivity(S)andtheresolution(R).Inpractice,theresolution(R)representsaminimalresolvablewavelengthshifttoaline-widthanddependsontheexperimentalnoiselevel,andone-tenthofline-widthcaneasilyberesolvedintheRef.[31].Therefore,wehereassumeRgivingby[10,31]R¼

λ0ð3Þ

Whereλ0representstheresonantwavelength,therefore,wecancalculateaminimaldetectablechangeDLasfollows[10]:DL¼R=S¼λ0=10QS

ð4Þ

Therefore,thenumericalsimulationsshowthatthedetectableminimumchangesinrefractiveindexisabout8.75Â10Àhttp://wendang.chazidian.comparedwiththetechniqueslikesurfaceplasmonresonance(SPR)sensor[43,44],thisproposedsensorstructurebasedPhCpossessesabigadvantageduetotheextremelysmalldetectionvolumeandcanbeintegratedtoon-chipsensingapplications.4.Conclusion

WehavepresentedaSiphotoniccrystalring–slotstructureforlabel-freebiosensingandnumericallyoptimizedtheparametersofthering–slotcavity.ByFDTDsimulation,weshowedthattheQfactorashighas107isachievedwhenthewidth(w)ofring–slotequalsto0.20a.Tomaketheslotregioninthefurtherfabricationprogresstobecompletely?lledwithglucosesolution,weincreasedthering–slotwidthandconsideredwaterabsorptionattelecomwavelengthrange,andaQfactorof$11477.3canalsobeachievedwhenthewidthofring–slotequalsto0.28a.Simulta-neouslytheproposedsensorpossessessensitivity(S)of160nm/RIUandaminimaldetectlimit(DL)isobtainedasgoodas8.75Â10À5RIU.ThesesimulationresultsshowthattheproposedsensorstructurecanobtainhighQfactorandwellapplytoRIsensingfordetectingthesurfacebiomolecule.Acknowledgments

ThisresearchwassupportedbyNSFC(No.61372038),National973Program(No.2012CB315705),National863Program(No.

2011AA010306)andFundofStateKeyLaboratoryofInformationPhotonicsandOpticalCommunications(BeijingUniversityofPostsandTelecommunications),P.R.China.

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