Optical Resonators With Whispering-Gallery applications

WGM谐振腔综述

OpticalResonatorsWithWhispering-Gallery

Modes—PartII:Applications

VladimirS.IlchenkoandAndreyB.Matsko

(InvitedPaper)

Abstract—Wereviewphotonicapplicationsofdielectricwhispering-gallerymode(WGM)resonators—tracingthegrowthofthetechnologyfromexperimentswithlevitatingdropletsofaerosolstoultrahigh-Qsolidstatecrystallineandintegratedon-chipmicroresonators.

IndexTerms—Four-wavemixing(FWM),high-orderoptical lters,lasers,laserresonators,monolithicopticaltotalinternalre ectionresonators,morphologydependentresonances,nonlin-earoptics,optical lters,opticalresonators,parametricoptics,Q-factor,solidstatelasers,spectroscopy,tunable lters,wavemix-ing,whispering-gallerymode(WGM)resonators.

I.INTRODUCTION

I

NTHISpaper,weaddressapplicationsofopendielectricres-onatorsandleavethedetaileddescriptionsoftheirpropertiestotextbooks[1],[2]andreviews[3]–[8].Thebasicpropertiesofresonatorsthatareimportanttotheirpracticalapplicationsarealsosummarizedinthepreviouspaperofthisissue[9].

Antalkingabout“photonicapplications,”weuseabroadmeaningofphotonics,whichincludeslinear,nonlinear,andquantumoptics,opticalengineering,andotherrelatedbranchesofscienceandtechnology.Specialattentionisgiventomi-crowavephotonics,wheredielectricresonatorsareusedtopro-cessmicrowavesignalsbyopticalmeans.

Wediscusstheresonatorsthataremadeoftransparentopti-caldielectricsandhavemonolithicringresonatordesign(wedonotconsidermacroscopic berringresonatorsbasedondirectionalcouplers).Theopticalmodesinsuchresonators;e.g.,morphology-dependentresonancesorwhisperinggallerymodes(WGMs),canbeunderstoodasclosedcircularbeamssupportedbytotalinternalre ectionsfromboundariesoftheresonators.

Modernopendielectricopticalresonatorshavecylindrical,spherical,spheroidal/toroidal,ring,andothershapesandtopolo-gieswithvariouscon ningprinciples.Forthesakeofuni ca-tion,weusethroughoutthisreviewthetermswhisperinggalleryresonators(WGRs)andwhisperinggallerymodestodescribethoseresonatorsandtheirmodes.

Itisusefultonotethat,strictlyspeaking,thetermWGMcannotbeappliedtoquasi-one-dimensionalobjectssuchasmi-

crorings.Insuchcases,thecurvatureoftheresonatordoesnotplayasigni cantroleintheformationofthespatialmodestruc-tures,andtheseobjectscouldsimplybedescribedasloopsmadeoutofanopticalwaveguide.

OriginalWGMsdonothavealotincommonwithsuchawaveguidepropagation.OriginallystudiedassoundwavespropagatingveryclosetothecylindricalwallofthegalleryinSt.Paul’scathedral,London[10],theWGMs(LordRayleighs’sterm)werefoundtobepartiallycon nedduetothesuppressionofthewavediffractionbythesoundre ectionfromthecurveddomewalls.Theeffectivevolumesand elddistributionsofthosemodesdependontheradiusofthe“resonator”[11].

Toavoidthisdiscrepancy,inourreview,werede neanopticalWGRasamonolithicringresonatorbasedontotalinternalre ectionoflight.

II.DEVICESWITHPASSIVEWGMRESONATORS

UniquespectralpropertiesofWGMs,includingnarrowlinewidth,tunability,andhighstabilityunderenvironmentalconditions,makeWGRsattractivefornumerouspracticalappli-cations.Inthissection,wereviewapplicationsofpassiveWGRsfor ltering,frequencystabilization,andsensing.

Photonic ltersbasedonopticalWGRsarecurrentlyamongthemostdevelopeddevicesthatinvolveWGMs.Foropticaltelecommunicationpurposes,themaintaskofthe ltersistoselectchannelsinwavelengthdivisionmultiplexing(WDM)schemes.Inthisdomain,wherechannelspacingisusuallynolessthan10GHz,planarringresonatorswithWGMandsimilardeviceswithQ<1×105areadequate.

Ultra-high-QWGRswithMHzrangeresonancebandwidthsofferauniqueopportunityforcreationofphotonicmicrowave ltersinwhichopticaldomainselectionisusedforseparatingtheRFchannelsimprintedassidebandsonastableopticalcar-rier.ImportantapplicationsofWGRsoccurinmetrologyforopticalandmicrowavefrequencystabilization,wherealongphotonstoragetimehelpstosuppressphaseandfrequencyde-viationofoscillators.

High-QandlongrecirculationoflightincompactWGRsofferinterestingnewcapabilitiesinspectroscopyandsensing,wherethechangeinQorresonancefrequencyofWGMscanserveasameasureofabsorptioninthesurroundingmedium,orinasmall(downtosinglemolecule)quantityofdepositedsubstanceonaresonatorsurface.Theresonatorcanalsobeusedformeasurementofchangeinambientparameters,suchastemperature,pressure,motion,etc.

ManuscriptreceivedApril10,2005;revisedOctober31,2005.ThisworkwassupportedinpartbytheNationalAeronauticsandSpaceAdministrationandinpartbyDefenseAdvancedResearchProjectsAgency(DARPA).

TheauthorsarewiththeJetPropulsionLaboratory,CaliforniaInstituteofTechnology,Pasadena,CA91109-8099USA(e-mail:vladimir@jpl.nasa.gov;andery.matsko@jpl.nasa.gov).

DigitalObjectIdenti er10.1109/JSTQE.2005.862943

1077-260X/$20.00©2006IEEE

WGM谐振腔综述

A.OpticalandPhotonicSingleResonatorFilters

Thesimplestresonator-based lterincludesaWGRandanopticalcoupler;e.g.,aprismcoupler.TransmissionofamonochromaticelectromagneticwaveoffrequencyωbyanopticalWGRinasingleprismcon gurationmaybecharacterizedbythecoef cient

T=

γc γ i(ω ω0)

γγ+i(ω ω(1)c+0)

whereTdescribestheamplitudetransmission,γ,γc,andω0aretheabsorptionandcouplinglinewidth,andresonancefrequencyofamodeoftheresonator,respectively[weassumethat|ω ω0|ismuchlessthanthecavityfreespectralrange(FSR)].Thepowertransmission|T|2throughtheresonatorisLorentzian.Conditionγ=γccorrespondstocriticalcouplingoftheresonator[12],[13].

The lterdescribedby(1)isastop-band lterbecauseitischaracterizedbytheabsorptionresonance.AWGRwithtwoinputandoutputcouplersischaracterizedbyatransmissionres-onance.Thisisanexampleofapassband lter.Thetransmissionandre ectioncoef cientsthroughtheresonatorare

T=

γc

γω ω,R=i(ω ω0)i(ω ω(2)c+i(0)γc+0)

whereTandRdescribetheamplitudetransmission(lightgoesintoonecouplerandexitstheothercoupler)andre ection(lightgoesandexitsthesamecoupler),respectively,andγc γisassumedforsimplicity.

Singlering-shapedWGR-based lterswerestudiedin[14]–[19],seealso[8],[20]forareview.Anall-opticalpassivefour-portsystemincludingafusedsilicamicrosphereandtwota-pered berswasusedasachanneladding–droppingdevice[21].The lterresponseofsingle-ringresonatorswithintegratedsemiconductoropticalampli ersbasedonGaInAsP–InPispre-sentedin[22].Achanneldropping lterbasedonadielectricmi-crosphereintegratedtoasiliconphotodiodewasstudiedin[23].Twodielectricwaveguidesthatareevanescentlycoupledtoafewmicronsizedsquareorrectangularregionofincreasedrefractiveindexcanserveasaverycompactintegratedopticalmicroresonator,similartoaringWGR.Applicationsofthedevicefor lteringarediscussedin[24].

Unfortunately,theLorentzianlineshapeofthe lterfunctionassociatedwithasinglemicroresonatorrepresentsalimitationforitsapplicationinmanysystemsthatrequirelargesidemoderejection,inadditiontoanarrowbandpassandalargetuningrange.

B.High-OrderFilters

Cascadedresonators,suchascoupledoptical berresonators,arewidelyusedasopticalandphotonic lters[25],[26].WGRsoffernewpossibilitiesformultipole lteringbecauseoftheirsmallsize,lowlosses,andintegrabilityintoopticalnetworks.Multipole ltersbasedoncascadedintegratedmicroringresonatorsfabricatedwithsilicahavebeendemonstratedincompactandrobustpackages.The ltershave10–100GHzbandwidthsandcorrespondingopticalQsontheorderof105–104[15],[27]–[31],andare,infact,commerciallyavailable.These ltersprovidepassbandswith attopsandsharpskirts,suitableforhighperformanceapplications,especiallyinopticalWDM.Asecond-orderoptical lterwithaMHzbandwidthwasrealizedwithtwocoupledhigh-Q(108)microsphereresonators,oneofwhichwastunable.ThetunableWGRwasmadeofgermanateglass[32].

Atunablethree-resonator ltermadeofLiNbO3WGRswasdemonstratedin[33].The lterhasthefollowingdistinctivefeatures/advantagesoverotherWGM lters:1)agiletunabilityaccompaniedbyahigh-order lterfunction;2)narrowlinewidth(≤20MHz);and3)low ber-to- berloss.Acombinationofthethreefeaturesmakesthis lterauniquedeviceforawiderangeofapplicationsinoptics.Sincethemicrowavesignalsinphotonicsystemsaresidebandsofanopticalcarrier,these lters,inprinciple,canbeusedatanymicrowavefrequency,providingthesamecharacteristicsthroughouttheband,from1to100GHzandhigher.

Multiresonator ltershavesigni cantlymoresparsespec-tracomparedwithastandaloneWGMresonator.ThisfeatureisduetothesocalledVerniereffect[34],andissimilartothefeatureobservedincoupled ber-ringresonators[25],[26]whicharenotedforararespectrum.Anef cient nesseofsuchmultiresonatorsystems,introducedasaratiooffrequencydif-ferencebetweenthetransmissionbandsofthe lterdividedoverthefrequencywidthofaband,isverylarge;e.g.,theFSRofthe lterreportedin[33]exceedsoneterahertz.Polymerdoublemicroring lterswiththermoopticaswellaselectrooptictuningweredemonstratedandreportedin[35].

Itwasnotedthatoneofseveraladvantagesofusingcou-pledmicroringsfor lteringisthepossibilityofahightuningenhancementfactorMgivenby

M=

1

1 a(3)2/a1

wherea1anda2aretheradiiofthetworings.Thetuningrangeofthedoublemicroring lterisMtimesthetuningrangeofasinglering[36].SinceMcanbeverylargeindouble-WGRstructures,thefasterbutmuchsmallerelectro-opticeffectcanbeusedfortuning.Itisimportanttonotethatthethederivationoftheparameterisvalidfortheresonatorswithsucharadiusratio,andthatMstayslessthanthe nesseoftheresonators.EachringresonatorhasasetoftransmissionspectraandthewavelengthperioddeterminedbyitsFSRfFSR.Thetworingshaveslightlydifferentradii(oreffectiveindices).Therefore,thetwosetsoftransmissionpeakcombshavesmalldifferentpeakspacing.Wavelengthtuningisachievedbyaligningthepeaksinthetwosetsofcombswiththeadjustmentofindexinoneorbothringresonators.The ltertransmissiondiscreetlyjumpsfromtransmissionatwavelengthf0tof0+fFSR,withMtimeslessvoltageappliedtooneoftheringscomparedwithvoltagenecessarytocontinuouslyshiftthespectrumoftheringbyfFSR.AtuningenhancementfactorofM=40inadouble-ring lterwasachievedatwavelengthsnear1.55µm[35].Thetuningrateforthethermoopticdeviceis120GHz/mW,andfortheelectroopticdeviceis120GHz/12V.Atunablelaserwithaside-modesuppressionratiogreaterthan30dBwasdemonstratedusingthis lteranderbium-doped berampli ergain.Thermaltuningover35nmwasachieved[35].

WGM谐振腔综述

ILCHENKOANDMATSKO:OPTICALRESONATORSWITHWGMs—PARTII:APPLICATIONS17

Oneofapparentapplicationsoftheoptical ltersisinopticaldelaylines.OpticaldelaydevicesbasedonchainsofcoupledWGRshavebeenstudiedin[37],[38].ItwasshownthattheQ-factorofthecoupling-splitmodesforasystemofNidenticalcoupledresonatorsisgreaterthanthatofasingleresonatorinthechainbyafactorofN,andevenmoreinthecaseofoptimumcoupling[39].Stoppinglightallopticallywithachainofinteractingtunableopticalresonatorswasdiscussedin[40].Anotherconceptofcoupledresonatoropticalwaveguideswasdevelopedin[41],[42].Inparticular,suchwaveguidescanberealizedinchainsofcoupledWGRs[44].Anumericalsimu-lationoflightpropagationinmicrocylindercoupledresonatorwaveguideswasreportedin[43].ThesimulationsshowthatlightpropagatesslowerintheWGMchainsformedbycouplingofthemodeshavingbiggerazimuthalnumbers.Thelightprop-agationbyWGMsofthesameazimuthalnumberhavethesamespeedregardlessofthesizeandthematerialoftheresonators.Generally,WGRtunable ltersallowshiftingthespectrumoftheresonators;however,theydonotprovidelinewidthtuningcapabilities.Cascadedresonatorswereproposedtobeusedforreal-timeshapingoftheirmodalstructures[45],[46].Akeyfeatureoftheapproachisthatitpointstoasimpletuningofthefrequencyandthewidthofthe ltertransmissionwindow,resultinginthetuningofthegroupdelayofopticalsignals—ahighlydesirablefeatureforsignalprocessingapplications.Thetransmissionspectralwindowofthe ltercouldbecuri-ouslynarrow.Theoretically,inthecaseofresonatorswithoutab-sorption,thewidthofthewindowcanbearbitrarilynarrow[45];however,inreality,theminimumwidthoftheresonanceisde-terminedbythematerialabsorption.Thephysicalprincipleofthe lteroperationthatresultsinthenarrowspectralwindowhasbeenrecognizedin[15],[25],[26].Theexistenceofthewindowhasalsobeendemonstratedexperimentally[47].C.TunableFilters

Tunabilityisahighlydesirablepropertyofanyapplicationofresonators.ThoughWGRsaresolidstatedevicesandtheirtun-abilityisnotreadilyconceivable,tunabilitycan,infact,achievedbyseveralmethods.MechanicaltrimmingofWGMswithap-pliedstrain[48]–[50]andtemperaturetuning[51],[52]havebeenpreviouslyused.Thoughthemechanicalaswellastem-peraturetuningrangesarerelativelylarge;e.g.,ontheorderofafewtoseveraltensofnanometersforthermaltuning,thesemethodsarenotveryconvenientformanyapplicationsbecauseofsmalltuningspeedsandlowtuningaccuracy.Thetuningaccuracyisespeciallyimportantforhigh-Qresonatorswithnar-row lterbandwidth.Anall-opticaltunable lterdesignbasedon“discontinuity-assistedringresonators”thatdoesnothavethepreviouslymentioneddisadvantageshasalsobeenproposedtheoretically[53],but,toourknowledge,noexperimentalim-plementationofthecon gurationhasbeenreported.

AtechniqueforWGMresonancetuningwasdemonstratedusingmicroringresonatorswithaphotosensitivecoating.Inthatstudy,glassmicroringsweredippedinapolymercoatingmaterialandwereexposedtoUVlight.ThismethodproducedresonatorswithrelativelysmallQ(about800)becauseofthe

polymer-inducedabsorption;yetitstillallowedlargetunabilityoftheopticalresonanceofthemicroring,enoughforwavelengthselectiveapplications[47].

Amethodforthetrimmingofpolymeropticalmicrores-onatorswasproposedin[54].Themethodisbasedonphoto-bleachingCLD-1chromophores.Amaximumwavelengthshiftof8.73nmwasobservedat1.55µm.Theresonatorshada3dBbandwidthof0.12nm,anFSRof1.11nm,anintrinsicQvalueof～2×104,anda nesseof～10.

Anotherapproachfortrimmingthefrequencyofmicrores-onatorsexploitsthephotosensitivityofthegermanatesilicaglass.WhenexposedtoUVlight,thismaterialundergoesasmallpermanentchangeinstructurethataltersitsindexofre-fraction.InthecaseofaWGR,thespatiallyuniformchangeintheindexofrefractionresultsinauniformtranslationoftheresonantfrequencies.Suchatunableresonator,aswellasasecond-orderoptical lterbasedontwocoupledresonators,oneofwhichwastunable,wasexperimentallyrealizedforopticalhigh-Q(108)WGMs[32],[55],[56].

Recently,fabricationofopticalWGMresonatorswithlithiumniobate[57]hasledtothedemonstrationofahigh-Qmicrowave lterwithalinewidthofabout10MHzandfastelectrooptictuningwithatuningrangeinexcessof10GHz[58].ThebesttunabilityforaLiNbO3singleresonator lterwas±20GHzbyapplyingdcvoltageof±50Vtoanelectrodeplacedovertheresonator.

ThefrequencyshiftoftheTEandTMmodesinaWGRmaybefoundfromthetheoryoftheelectroopticeffect[59].FortheLiNbO3WGR lterdiscussedin[58],we nd

ωTE

=ωn2

0e2

r33EZ,

ωTωn2

M

=0o2

r13EZ

(4)

whereω0=2π×2×1014Hzisthecarrierfrequencyofthelaser;r33=31pm/Vandr13=10pm/Varetheelectroopticconstants;ne=2.28andno=2.2aretherefractiveindicesofLiNbO3;andEZistheamplitudeoftheelectric eldappliedalongthecavityaxis.TMmodeswereusedintheexperimentreportedin[58]becausetheyhavelargerqualityfactorsthantheTEmodes.Ifthequalityfactorisnotveryimportant,itisbettertousetheTEmodes,becausetheirelectroopticshiftsarethreetimesaslargeasthoseofTMmodesforthesamevaluesoftheappliedvoltage.

Theoretically, ωTEand ωTMdonotdependontheres-onatorproperties,andarerelatedtothefundamentallimita-tionsofopticalresonator-basedhighspeedelectroopticmod-ulators[60].Forexample,thedomainreversalinacongruentLiNbO3crystaloccursatEZ 20kV/mm,whichcorrespondstoarelativeWGRfrequencyshiftof ωTE/ω0 1.6×10 3and ωTM 5×10 4,whichiswellabovetheobservedshifts.Lithiumniobate ltersareconvenient;however,theirlinewidthisrestrictedbyafewMHzbecauseoftheresidualabsorptionofthematerial.CrystallineWGRscouldpossessmanyordersofmagnitudenarrowerlines.Forinstance,opti-cal lterswithbandwidthsofabout10kHzusingCaF2WGMresonatorswasdemonstratedin[61].TheCaF2resonatorshavestableultrahighQ-factorscomparedwithfusedsilicaresonators,whereQdegradeswithtime.LimitedtuningoftheCaF2 lters

WGM谐振腔综述

18IEEEJOURNALOFSELECTEDTOPICSINQUANTUMELECTRONICS,VOL.12,NO.1,JANUARY/FEBRUARY2006

canberealizedwithtemperature.Theinsertionlossofthe lterwasatthe5dBlevel.

Tocharacterizetheabsolutetunabilityofanopticalresonator-basedphotonic lter,itisusefultointroducetheratiooftheresonatorFSRandlineartunabilityrangegivenbythehostma-terial.Tuningthe ltersdoesnotchangetheFSRinthe rstapproximation,butonlyshiftsthecomboftheopticalmodes,makingitoverlapwithitselfforeachfrequencyshiftpropor-tionaltotheFSR.Hence,the ltercanbetunedatanyprescribedsinglefrequencyifthelineartunabilityexceedstheFSR.Thelackofselectivityinasingle-resonator ltercanbecompen-satedwiththeapplicationofcoupled-resonator lters.Ifeachresonatorinthe ltercanbetunedbyitsFSR,thewhole l-tercanbetunedatanyfrequency,whereasthespectrumofthemultiresonator ltercanbeveryrareduetotheVerniereffect.Somephotonicapplicationscallfornarrowband lterssimul-taneouslypassingboththecarrierandsidebands.Forexample,thisisimportantforthegenerationofspectrallypuremicrowavesignalsinoptoelectronicoscillators[62],wherebeatingoftheopticalsidebandsandthecarrieronafastphotodiodegeneratesmicrowaves.Tunabilityofthemicrowavefrequencyoftheos-cillatorrequiresthatthefrequencydifferencebetweenthe lterpassbandschangecontrollably.Thispropertyislackinginex-istingtunable lters,wheretheentire lterspectrumshiftsasawholeasthetuningvoltageisapplied.Acriticalcomponentofanovelminiature lterwithelectro-opticallyrecon gurablespectrumwasrecentlyreported.The lterisbasedonaWGRfabricatedfromacommerciallyavailablelithiumniobatewaferhavingaspeciallyengineereddomainstructure[63].D.WGMFiltersinOptoelectronicOscillatorsandLasersforStabilization

1)WGMFiltersforOEO:Generationofspectrallypuresig-nalsat1to100GHzisrequiredincommunications,radar,andnavigation.Theadventofhighthroughputopticalcommunica-tionlinkspointstotheprospectsfornetworksoperatingatdataratesashighas160Gb/sandconsistingofmultiplesofchannelsseparatedbyafewGHz.Schemesforrealizingthistypeofcapa-bilityrelyonsourcescapableofprovidinghighfrequency,lowphasenoisesignals,withoutwhicherror-freehighdataratesys-temswouldnotbepossible.Similarly,highperformanceradarsystemsrequirelowphasenoiseoscillatorstoallowdetectionoffeeblesignalsfromadensebackgroundclutter.

Theoptoelectronicoscillator(OEO)isadevicethatproducesspectrallypuresignalsatmanytensofgigaltertgbasedonpho-tonictechniques,andthusovercomessomeoftheinherentlim-itationsoftheconventionalelectronicdevices[62],[64]–[69].TheOEOisagenericarchitectureconsistingofalaserasthesourceoflightenergy.Thelaserradiationpropagatesthroughamodulatorandanopticalenergystorageelement,suchasanoptical ber,beforeitisconvertedtotheelectricalenergywithafastphotodiode.TheRFelectricalsignalattheoutputofthephotodiodeisampli edand ltered,andthenfedbackintothemodulator,closingtheloop.Ifthetotalgainexceedslinearlosesoftheloop,thesystemoscillatesatthefrequencydeterminedbythe lter.TheuseofopticalstorageelementsallowsfortherealizationofextremelyhighQsandthusspectrallypuresignalsinopti-caloscillators,sincethenoiseperformanceofanoscillatorisdeterminedbytheenergystoragetime,orqualityfactorQ.Inparticular,along berdelayleadstorealizationofmicrosec-ondstoragetimes,correspondingtoQsofaboutamillionata10GHzoscillationfrequency.Thisisahighvaluecomparedtoconventionaldielectricmicrowavecavitiesusedinoscilla-tors[70],[71].The berdelaylinealsoprovidesforwidebandfrequencyoperationunhinderedbytheusualdegradationoftheoscillatorQwithincreasingfrequency.Thus,spectrallypuresignalsatfrequenciesashighas43GHz,limitedonlybythemodulatoranddetectorbandwidth,havebeendemonstrated.InagenericOEO[62],thelong berdelaylinesupportsmanymicrowavemodesimposedonanopticalwave.Anarrowbandelectrical ltershouldbeinsertedintotheelectronicseg-mentoftheOEOfeedbacklooptoachieveastablesinglemodeoperation.Thecenterfrequencyofthis lterdeterminestheop-erationalfrequencyoftheOEO.Whilethisapproachyieldsthedesiredspectrallypurehighfrequencysignals,thephysicalsizeoftheOEOisratherbulkybecauseofthekilometersof berdelayneeded.Moreover,thelong berdelayisverysensitivetothesurroundingenvironmentsotheOEOdoesnotproduceanoutputwithhighlongtermfrequencyaccuracyandstability.TheOEOistypicallyphaselockedtoastablereferenceforlongtermstability.

ThepropertiesoftheOEOwithahigh-QWGRinplaceoftheelectronic lter,aswellasthe berdelay,wasstudiedin[72].Itwasshownthatthemethodallowsonetochoosevirtuallyanarbitraryfrequencyofoscillationbytuningtheresonator.

2)WGMFiltersfortheLaserStabilization:InadditiontothestabilizationoftheOEO,WGRscanbeusedforlaserstabi-lization.Opticalfeedbackfromahigh-Qmicrosphereresonatorwasusedtonarrowthespectrumofaminiaturehigh-coherentdiodelaser,andanearlyhalf-pitchgradient-indexlensservedasacouplingelement[73].Aswasestimatedfromthevariationinfrequency-tuningrange(chirp-reductionfactor),thefastlinewidthofthelaserwasreducedbymorethanthreeordersofmagnitude.

Amodi cationofexternalopticalfeedbackthatincludesaWGRwasusedtonarrowthelineofadiodelaser[74].AWGMofahigh-Qmicrospherewasexcitedbymeansoffrustratedtotalinternalre ection,whilethefeedbackforopticallockingofthelaserwasprovidedbyintracavityRayleighbackscattering.Abeatnoteofthetwolaserdiodesopticallylockedtoapairoforthogonallypolarizedmodesofthesamemicroresonatorhadtheindicated 6aspectralwidthof20kHz,andthestabilityof2×10overaveragingtimesof10s.AtheoreticalmodelforthelaserstabilizationwithaWGRwaspresentedin[75].

Finally,insteadoflockingalasertoaWGM,theoppositewasrealizedin[76].AWGMofafused-silicamicrospherewaslockedtoafrequency-scanninglaser.Theresonancefrequencywasmodulatedbyaxialcompressionofthemicrosphere,andphase-sensitivedetectionofthe ber-coupledopticalthroughputwasusedforlocking.SuchasystemisparticularlyusefulinWGR-basedchemicalsensors,whichthefollowingsectionisdevotedto.

WGM谐振腔综述

ILCHENKOANDMATSKO:OPTICALRESONATORSWITHWGMs—PARTII:APPLICATIONS19

E.SpectroscopyandAnalysisofChemicalandBiologicalAgents

StartingfromliquidWGRsusedforresonator-enhancedspec-troscopy(see[77]forreview),solidstateWGRswereutilizetoenhancetheinteractionbetweenlightandatoms/molecules.Oneofthe rstexperimentsonthesubjectwasrealizedintheframeofcavity-QED[78].Theradiativecouplingoffreeatomstotheexternalevanescent eldofaWGMwasdetected.Thecouplingmanifesteditselfasanarrowabsorptionlineobservedintheres-onatortransmissionspectrum.Itwasproventhattheevanescent eldofthehigh-Q(5×107)andsmallmodevolume(10 8cm3)fusedsilicamicrosphereenablesvelocity-selectivein-teractionsbetweenasinglephotonintheWGMandasingleatominthesurroundingatomicvapor.Anultrasensitivespec-trometerbasedonastretchedsilicamicrospherewasproposedin[50],[79].

ThenextstageinthesensordevelopmentwasrelatedtoWGR-basedbiosensors[80]–[82].Opticalbiosensorsaretypi-callytransducersthatdetectthepresenceofmoleculesatasur-face.Theyhaveseveraldesirablefeatures,particularlyforthedetectionofbiologicalmolecules,thatinclude:1)highsensi-tivity(lessthannanomoles);2)non-destructivitytothesample;3)highselectivity;and4)applicabilitytovarioussubstances.Thetransductionprocessesinopticalbiosensorsgenerallytakeplaceonasurfaceandcanbetailoredtosensealmostanykindofmolecule,chemicalandprebiotic,aswellasbiological.WGRsensorsbelongtotheevanescentwavesensors,whichareamongthemostsensitiveclassofbiosensors[83],[84].Anevanescentwaveproducedbythetotalre ectionoflightwithinthewaveguideinteractswithanalytesonthewaveguidesurfaceintheevanescent eldsensors.Theevanescentwaveprotrudesabovethewaveguidesurfaceby～100nm(theactualdistancedependsontherelativeindexofrefractionofthewaveguideandthesamplemedium),andsamplesonlytheanalyteonthesur-face.Surfacetreatmentssuchasantibodiesoroligonucleotidestrandscanprovidespeci cityfortheanalyte;thesensorthendetectsonlythoseboundtothesurface.Transductionmech-anismsforboundanalyteinclude uorescence,masschangeintheevanescentregion[85],andchangeintheindexofre-fraction[86].Typicalsensitivityofevanescentwavebiosensorsbasedon beropticsensorsorplanarwaveguidesensorsisintherangeofnano-molestopico-moles.

ThebasicdetectionschemethatutilizesWGRsisthatbindingofmoleculestothemicroresonatorsurfaceinducesanopticalchangeproportionaltothequantityofboundmolecules.TheparadigmforthisprocessisachangeinthecavityQasthesurfaceboundmoleculesaffectthephotonstoragetime,eitherthroughincreasedscatteringorabsorption.Ineffect,theanalytespoilstheQ,andtheresultingchangecanbemeasured.

AnyproteinwilladheretoglasssurfaceofagenericWGR,andhence re-polishedspheresareentirelynonspeci c.Twoconditionsmustbemetforchemicalmodi cationofthemicro-spheresurface: rst,theglassmustbecoatedwithacompoundthatwillminimizenonspeci cbinding.Second,anantibodyorotherproteinwithsensitivitytoaparticularligandmustbelinkedtothesphereinsuchawaythatboththeprotein’sfunctionality

andthesphere’sQarepreserved.Athin lmofamaterialwiththicknesssmallerthantheWGM’sevanescent eldwillnotsig-ni cantlyaltertheQofthemicro-resonator;thus,athicknessof～10–100nmcanbeappliedtothemicrospherewhileretainingitshigh-Q.

Apossibilityofenhancementofthedetectionsensitivityofevanescent-waveopticalbiosensorswasdiscussedin[87]–[92].ItwasshownthattheresonantcouplingofpowerintotheWGRallowsforef cientuseofthelongphotonlifetimesofthehigh-QWGMstoincreasetheinteractionofthelightandtheparticlesunderthestudy.Thisenhancementresultsinstronger uores-cenceandinchangesoftheresonatorparameters.

Aspectroscopictechniqueforhigh-sensitivity,label-freeDNAquanti cationwasdevelopedin[93].ItwasdemonstratedthataWGMexcitedinamicron-sizedsilicaspherecanbeusedtodetectandmeasurenucleicacids.Thesurfaceofthesilicasphereistobechemicallymodi edwitholigonucleotides.A rst-orderperturbationtheorywasdevelopedforWGMsinadielectricmicrosphere[94],[95].Thetheorywereappliedtothreesensorapplicationsofthemicrospheretoprobethemediuminwhichthesphereisimmersed:arefractive-indexdetector,anadsorptionsensor,andarefractive-indexpro lesensor.

BiosensorsbasedontheshiftofWGMsinmicrospheresac-companyingproteinadsorptionweredescribedbyuseofaper-turbationtheoryin[94].Forrandomspatialadsorption,theorypredictsthattheshiftshouldbeinverselyproportionaltomicro-sphereradiusa,andproportionaltoproteinsurfacedensityandexcesspolarizability.

Hybridzincoxide/silicamicrodisklaserswereutilizedtosensevolatileorganiccompounds,suchastolueneandnitroben-zene[96].Nonspeci cadsorptionoftheseorganicmoleculesontotheWGRsurfacecausesanincreaseinthediskrefractiveindex,ultimatelyresultinginaredshiftoftheobservedlasingwavelengths.

ImprovementofphotonicWGMsensorsusingthefano-resonantlineshapewasproposedin[97].Polystyrenemicror-ingresonatorswerefabricatedbythenanoimprintingtechnique,andtheopticalspectraweremeasuredinglucosesolutionsofdifferentconcentrations.Theshiftinresonantwavelengthandvariationofthenormalizedtransmittedintensitywerelinearlyrelatedtotheconcentrationoftheglucosesolution.

ApplicationofWGRsinhigh eldhighfrequencyelectronmagneticresonancemeasurementswasdiscussedin[98].F.MechanicalSensors

High-QWGMsresultinincreaseinsensitivityofvariousmechanicalexperiments.Forinstance,WGMscouldbeusedforthemeasurementofstraininoptical bers[48].Atwo-resonatorsensorofsmalldisplacementsthatutilizeshigh-QandmechanicaltunabilityofnormalmodesincoupledopticalWGRswasproposedin[99].

Anaccelerometerutilizinghigh-QWGRswaspresentedin[100].Inducedconsoledisplacementsweremonitoredthroughchangesintheresonancecharacteristicsofasphericalopti-calcavitycoupledtothe exure.Instantaneousmeasurement

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sensitivityofbetterthan1mgat250Hzbandwidth,andanoise oorof100µg,wereachieved.

Theideaofusageofpassiveandactiveopticalringinter-ferometersfordetectionofrotationwasdevelopedandim-plementedacoupleofdecadesago[101]–[103].AminiatureintegratedWGMopticalsensorforgyroscopesystemswasre-centlyproposed[104].Itwaspredictedthatthesensormaypossesshighenoughsensitivityevenonamillimetersizescale.ApassiveWGMgyroscopewasdiscussedin[105].ThebasicdifferenceofthegyroscopecomparedwiththeexistingringresonatorgyroscopesisintheusageofcrystallineWGRin-steadoftheusualringresonator.TheWGR-basedgyroscopeisexpectedtohavemuchlessbackscatteringandpolariza-tionrotationnoisescomparedwithconventional ber-basedgyroscopes.

G.FundamentalPhysicsWithPassiveWGMs

WGRsofferinterestingpossibilitiesfrombothclassicalaswellasquantumpointsofview.HighQ-factorsaswellassmallmodevolumesofWGMsresultinamultitudeofinterestingandimportantphenomena.Inthissection,wediscussthosephenomenarelatedto“passive”WGMs,whichdonotleadtogenerationoflight,leavingfundamentalpropertiesofWGMlasersandotheractivedevicestoasubsequentsection.

1)Chaos:OneofthefundamentalproblemsisrelatedtoWGMsinanasymmetricWGR.Itwasshownthatdeparturefromanaxialsymmetryresultsintheoccurrenceofchaoticbe-havioroflightintheresonator.Thishasbeenpredictedtogiverisetoauniversal,frequency-independentbroadeningoftheWGRs,andtohighlyanisotropicemission[106]–[110].Aso-lutionoftheproblemwhichcon rmsthesepredictions,butalsorevealsfrequency-dependenteffectscharacteristicofquantumchaos,waspresentedin[111].ItwasshownthatforsmallWGRdeformations,thelifetimeiscontrolledbyevanescentleakage,theopticalanalogofquantumtunneling[112].Theproblemofthedirectionalemissionfromegg-shapedasymmetricresonantcavitieswasdiscussedintheoreticaltermsin[115].

Thelifetimeoflightcon nedinaWGRcanbesigni -cantlyshortenedbyaprocessknownas“chaos-assistedtun-neling”[113].Surprisingly,evenforlargedeformations,someresonanceswerefoundtohavelongerlifetimesthanpredictedbytheraychaosmodelduetothephenomenonof“dynamicallocalization”[114].

Modesofpartially-stableWGRswerediscussedin[116]us-ingatheory,whereinexponentiallysuppressedtunnelingin-teractionbetweenregularandchaoticmodeswasconsideredasaperturbation.Itwasshownthatchaos-assistedtunnelingcanleadtosplittingofregularWGMsinasymmetricopticalresonances.Atheoryofin uenceofthechaos-assistedtunnel-ingonlifetimesandemissionpatternsoftheopticalmodesingenericmicroresonatorswasdevelopedin[117]usingapproachpresentedin[118].

The rstexperimentonchaos-assistedtunnelinginatwo-dimensionalannularbilliardwasreportedin[119].Highlydi-rectionalemissionfromWGMswasdemonstratedindeformednonaxisymmetricfused-silica“microspheres”[120].2)“PhotonicAtoms”:Anotherfundamentalareaofappli-cationofWGRsisbasedontheabilityoftheresonatorstomimicatomicproperties.ItwasshownthatWGMscanbethoughtofasclassicalanalogyofatomicorbitals[121].ItwaspointedoutthatWGMmodenumberscorrespondtoangular,radial,andtheazimuthalquantumnumbers,respectively,thesameasintheatomicphysics.Suchanapproachresultedinintro-ducingtheterm“photonicatoms”withrespecttoWGMres-onators[122],[123].“Photonicmolecules,”basedoncoupledWGRs,wasstudiedin[124],[125].

3)CavityQED:Thereisgreatactivityinboththeoreticalandexperimentalinvestigationsofcavityquantumelectrody-namics[126]–[130]effectsinWGRs.Forinstance,spontaneousemissionprocessesmaybeeitherenhancedorinhibitedinacav-ityduetoamodi cationofthedensityofelectromagneticstatescomparedwiththedensityinafreespace[131],[132].Thiseffectwasstudiedtheoretically[133]–[135]aswellasexperi-mentally[136],[137]inWGRs.

Methodsforcontrolofatomicquantumstateinatomscou-pledtosingle-modeandmultimodecavitiesandmicrosphereswerediscussedin[138].Thosemethodsincludeexcitation,de-caycontrol,location-dependentcontrolofinterferenceofdecaychannels,anddecoherencecontrolby“conditionallyinterferingparallelevolutions.”

Propertiesofatomicinteractionwiththe eldofahigh-Qcavitywasstudiedin[139]using“pseudomode”theory.ItwasshownthatthetheorycanbederivedbyapplyingtheFanodiag-onalizationmethodtoasysteminwhichtheatomictransitionsarecoupledtoadiscretesetofcavity“quasimodes.”Thecavitymodesdecayintoacontinuumsetofexternal“quasimodes.”Itwasshownthateach“pseudomode”canbeidenti edwithadis-crete“quasimode,”whichcontainsstructuretotheactualreser-voir.

PonderomotiveinteractionofanatomandaWGMwasdis-cussedin[143],[140],[141],seealso[142],[144],forreview.Inparticular,itwasshownthattheexternal eldsofopticalWGMsmaybeusedtocon neatomsinstableorbitsaroundadielectricmicrosphere[143].Theboundstatestructureanddynamicsfortheatomtrapwereinvestigatedin[140].Thedynamicsofthecenter-of-massofanultracoldexcitedatomicoscillatorinthevicinityofadielectricmicrospherewasstudiedin[141].

Theponderomotiveinteractionofanatomandphotonscon nedinaWGM,canbeusedforquantumnondemolitionmeasurements.Itwasshown[145]–[147]thatthedipoleforceexperiencedbyanatominanoff-resonantspatiallyinhomo-geneouslight eldisquantizedbythediscretenatureofthephoton.Similarschemestoperformquantumnondemolitiondetectionofopticalphotonsbyobservingthede ectionofabeamofatoms yingclosetoanopendielectricresonatorwereproposedinthestudies.

Theponderomotiveinteractionofanelectron,insteadofanatom,andphotonsinaWGM,wasproposedforaquantumnon-demolitionmeasurementofphotonnumber(thephotonnumberisde nedastheenergystoredinthemodedividedby¯hω0,whereω0isthefrequencyofthemode).Thetechniqueisbasedontheeffectofquadraticscatteringofelectronstravelingalongtheresonatorwithavelocityclosetothephasevelocityofthe

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waveintheresonator[148].Themeasurementideareliesonthefactthatanelectrontravelingalongabaredielectricwaveguide(orsurfaceofaWGR),atavelocitynearthephasevelocity,ac-quiresatransversemomentumproportionaltothephotonenergyofthelightinthewaveguide.Itwasnotedthatthismomentumcanbemeasured[149].Thescatteringeffectwasanalyzedwithconsiderationforthewaveguide(andWGM)dispersion,radia-tionfriction,andthespuriousCherenkovradiation.

Aradiativecouplingofananoparticle/atomwithaWGMwasstudiedin[78],[150];seealso[130],[152]forareview.Thepossibilityofstrongcouplingbetweenaphotoncon nedinaWGMandanatomwasanalyzedin[153]–[155].TheresonantinteractionofanatomwithdipolarJ=0 J=1angular-momentumtransitionwiththequantized eldindielec-tricspheresandspheroidswasstudiedin[153].ThepossibilityoftheapplicationofamicrodiskWGRforthedetectionofasingletrappedatomwasstudiedin[156].

Ameasurementsofcavity-QEDeffectsfortheradiativecou-plingofatomsinadilutevaportotheexternalevanescent eldofaWGMwasreportedin[78].ExperimentsonthecouplingofasinglenanoemitterandWGMswerediscussedin[150],[151].AcompositesystemconsistingofaGaAsquantumwellstruc-tureplacedintheevanescent eldofafusedsilicamicrosphere,andevanescentcouplingbetweenexcitonsinthequantumwellandWGMsofthecompositesystem,wasdemonstratedin[157].AcompositesystemconsistingofCdSeZnSnanocrystalsandafused-silicamicrospherewasdemonstratedin[158].TheQ-factorsofthesystemwereoftheorderof108,providingamodelforinvestigatingcavityQEDandmicrolasersatthelevelofsinglequantumdots.

Opticalpropertiesofcon nedphotonstatesinanextremelysmallsphericalWGRswithsizesof2λ<R<10λ(dubbed“photonicdots”)resonantlyexcitedbyphotonsemittedfromsemiconductornanocrystals(thequantumdots)werestudiedin[159],[160]withparticularfocusonQEDpropertiesofWGRscontainingCdSequantumdotsandquantumrods.BothglassandpolymerWGRswerecharacterizedbyspatiallyandtemporallyresolvedmicrophotoluminescence.

III.WGRSWITHACTIVEMODES

SmallvolumesandhighQ-factorsofWGMsresultinen-hancementofnonlinearopticalprocesses.Duetothisenhance-ment,WGRbasednonlinearopticdevicespossessuniquechar-acteristics.Forexample,usageofWGMsallowstherealizationoflasersandwave-mixingdeviceswithmicroWattthresholds.NarrowlinewidthofWGMsresultinnarrowspectralcharacter-isticsofthelasers.Inthissection,wereviewresultsofrecentstudiesinthe eld.

A.Continuous-Wave(CW)WGMLasers

MiniaturelasersareamongthemostobviousapplicationsofWGRs.Thehighqualityfactoroftheresonatorsleadstothereducedthresholdofthelasing.The rstWGMlaserswerereal-izedinsolidmaterials[161]–[163].However,probablybecauseofthelackofinput-outputtechniquesforWGMs,theworkwasdiscontinuedatthatpoint.ThenextdevelopmentoftheWGM-basedlaserswasinliquidaerosolsandindividualliquiddroplets[164]–[169].Finally,duringthelastdecade,thelasersbasedonsolesolidstateWGRswererediscovered,demon-stratedexperimentally,andintensivelystudied.Inthissection,wereviewrecentresultswithWGRCWlasers,leavingWGRRamanlasersforSectionIII-B.

1)LasinginCapillaries:TheWGRlasercanberealizedinacylindricalresonator.Thesimplestresonatorofthiskindisacap-illary.Thegainmediumcouldresideinsidethecapillary,whereWGMsarelocalized.Forinstance,laseremissionfromWGMsinahighlyrefractivedye-dopedsolvent owinginanormallyilluminatedsilicacapillary berwasdemonstratedin[170].ThecylindricalWGMlaserdiffersfromthesphericaldropletlaser[164]inthatithasaninternalrefractiveindexdiscontinu-ity.Thelightpenetratesintotheactivemediumiftherefractiveindexofthemediumishigherthantheoneofthecapillarymaterials;e.g.,nolaserpeaksareobservedwhentherefractiveindexofthesolventislessthanthatofsilica[170].AnexampleofmicroringlasingusingCdSenanocrystalquantumdotsincor-poratedintomicrocapillarytubeswasdemonstratedin[171].Thelasinginacapillarybasedontheevanescent eldcou-plingwiththegainmediumisalsopossible.Thelayeredmicro-cavitywasrealizedin[172],[173]by owingdye-dopedethanolthroughathinwallfusedsilicacapillarytubewhoserefractiveindexwaslargerthanthatoftheliquid.Thelasingspectrumshowedastrongmodeselection,andnearlyevensinglecon-structiveinterferencepeaks,duetotheinterferentialcouplingofWGMsattheinnerboundary.Variousmodeorders,whicharenotallowedintherayopticspicture,weremadetooscillateduetotheevanescentpropagationofWGMsattheouterboundary.Theestimatedcavityqualityfactorswerehigherthan106.Thelasingcharacteristicsofresonancemodesinathindye-dopeddielectricringcavitymadeontheinnerwallofacylindricalcapillarywerealsostudiedin[174].

AWGMlaserwithpulsedopticalpumpingfabricatedbysurroundingasmallsectionofaglasscapillarywithasolutionofRhodamine6G,andbycouplingthepumplightintothecapillarywall,wasdemonstratedin[175].Thelasingthresholdpumpenergywas100nJ/pulseatapumppulsedurationof6ns.2)LasinginDopedWGRs:AnotherwaytocreateaWGRlaseristheuseofsolidsdopedwithactiveelements;e.g.,rareearthionsasaWGRhostmaterial.

AWGMlaserbasedonneodymium-dopedsilicamicro-sphereswitha200nWthresholdwasrealized[176]withmicrospheresofradiusa～25–50µm,formedbyheat-fusingthetipofalengthofdopedsilica ber.Neodymiumionsprovideafavorablefour-levellasersystemthatcanbepumpedonthe4I9/2 4F5/2transitionat～810nmwithadiodelaser.Thelasertransition4F3/2 4I11/2inthe1.06–1.09µmrangeconnectsalonglivedupperleveltoalowerlevelthatisdepletedbystrongphononrelaxationsothatpopulationinversioniseasilyachieved.Similarexperimentswithaneodymium-dopedsilicamicrospherelaseroperatingat2Kandabsorbing200nWpumppowerwerereportedin[177].CWlaseroscillationonboththe4F3/2→4I11/2and4F3/2→4I13/2transitionsofNd3+ionsin uorideglassWGRswasalsoachieved[178].FabricationofNd-dopedtelluriteglassWGRsandobservations

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oflaseroscillationcorrespondingtotheopticaltransition4

F3/2→4I11/2at1.06µmwasreportedin[179].

AWGMlaserutilizingamicrospheremadeofhighlydopederbium:ytterbiumphosphateglasswasusedtogeneratelightat1.5µm[180].Laserthresholdpumppowerof60µWand ber-coupledoutputpowerashighas3µWwithsingle-modeoperationwereobtained.Abispherelasersystemconsistingoftwomicrospheresattachedtoasingle bertaperwasalsodemonstrated.

AnEr3+-dopedtelluriteglassL-bandWGRlaserwasdemon-stratedanddiscussedin[181].Themicrospheresweremadebya“spinmethod.”Fibertaperswereutilizedtocouple975nmpumpintothesphereandcouplegeneratedlight(1.56–1.61µm)outofthesphere.Theerbiumionconcentrationofthetelluriteglasswas1.7×1020ions/cm3.

Agreenroomtemperatureup-conversionlaserwasdemon-stratedina120µmdiametermicrosphereofEr3+dopedZBLAN[182],[183].Lasingoccurredaround540nmwitha801nmdiodelaserpump.Thelasingthresholdwas30µWofabsorbedpumppower.

Experimentalresultsontherealizationandspectralcharac-terizationofEr:ZBLANmicrosphericallasersat1.56µmwerepresentedin[184],[185].Thelasingwasobtainedwiththeexternal1.48µmpumping.Multimodeoperationandalaserthresholdaslowas600µWwereobserved.

Greenlasinghaving4mWthresholdwasdemonstratedinanerbium-ion-doped uoro-zirconateglassWGR[186].Peri-odicnarrowpeaksoftheemissionspectracorrespondingtotheWGRswereobserved.

Anerbium-dopedmicrolaseronsilicon,operatingatwave-lengthof1.5µmandcharacterizedwithpumpthresholdaslowas4.5µW,wasdemonstratedin[187].The40-µmdi-ametertoroidallaserWGRwasmadeusingacombinationoferbiumionimplantation,photolithography,wetanddryetch-ing,andlaserannealing,usingathermallygrownSiO2 lmonaSisubstrateasastartingmaterial.Singlemodelasingwasobserved.

Anothererbium-dopedhigh-QsilicatoroidalWGRmicro-laser(25–80µmindiameter)wasdemonstratedin[188].TheWGRwascoupledwithataperedoptical ber.Erbiumioncon-centrationswereintherange0.009–0.09at.%.Thresholdpumppowerwasaslowas4.5µW.

ATm3+-dopedtelluriteglassWGRlaserwasdiscussedin[189].Thelaser,pumpedat800nmwithataperedopti-cal ber,oscillatesinboththeSbandandthe1.9-µmband.Thepeakat1.5µm(S-band)correspondstoemissionofthe3

H4→3F4transition,whilethepeakat1.9µmcorrespondstothe3F4→3H6transition.

Numericalanalysisofamicrodisklaser,takingintoaccountfullgainsaturationeffectandthevectorcharacterofthe eld,waspresentedin[190].TheauthorssuggestedthatNd:YAGmicrodisklasersaretheexcellentcandidatesforalightsourceforoptical bercommunicationsoperatingat1.064and1.3µm.Atheoreticalstudyofthein uenceofdeformationofaWGRonlasingpropertieswasreportedin[191].

3)LasinginCoatedWGRs:Insteadofusingdopedmateri-als,apassiveWGRcanbecoatedwithgainmedium.Forex-ample,erbium-dopedsolgel lmswereappliedtothesurfaceofsilicamicrospherestocreatelow-thresholdWGRlasers[192].Lasingactioninanultra-high-QsphericalWGRcoatedwithgainmediumwasreportedin[193].

LasinginasquarecavitywithroundcornerscoatedwithpolymethylmethacrylateandwithRhodamine6Gmolecules,wasstudiedin[194].Athingainlayerwascoatedonlyontheouterboundaryofcavity.Thethicknessofthegainlayervariedfromonemicrometertoseveralmicrometers.

Ultravioletmicrodisklasersonsiliconsubstratewithalayerofzincoxidegainmediumgrownontopofthesilicamicrodisksweredemonstratedin[195].LasingoccursintheWGRsatroomtemperature.ThehybridZnO–SiO2WGRwasopticallypumpedbythethirdharmonics(355nm)ofamode-lockedNd:YAGlaserwith～10Hzrepetitionrateand20pspulsewidth.Amicroscopeobjectivelensisusedforfocusingpumplightontheresonatoraswellasforcollectingtheultravioletemissionat～390nm.AWGM-enhancedinelasticemissionfromamonolayerofA488 uorophoresonthesurfaceofa9.8µmWGR(polystyrenebeadtrappedinanopticaltrap)wasobservedandreported[196].ItwaspointedoutthatitwaslikelythattheWGM-enhancedemissionisduetoA488lasing,withalasingthresholdbetween0.29and0.87W·cm 2.

4)WGMLasersWithSemiconductorGainMedia:WGM-basedlaserscanbecreatedwithsemiconductorquantumdotscoupledtotheWGMs.Oneofthemostimportantproblemshereisfabricationofasinglequantumdotmicrolaser.SuchamicrolasermadebycapturingthelightemittedfromasingleInAs–GaAsquantumdotintheWGMofaglassmicrospherewasproposedtheoreticallyin[197].Amasterequationmodelofasinglequantumdotmicrospherelaserwasdescribedin[198].Theoperationofasinglequantum-dot-microspherelaserandasemiconductormicrospherebistableelementwastheoreticallystudiedin[199].

Aquantumdot-microcavitysystemconsistingofCdTenanocrystalsattachedtoamelamineformaldehydelatexmi-crospherewasrealizedexperimentally[200].Thehighopticaltransparency,andthermalandmechanicalstabilityofmelamineformaldehyde,makeitinterestingasapotentialcandidateinop-ticalapplications.Therefractiveindexofmelamineformalde-hydeinthevisibleregion(n=1.68)isgreaterthanthatofsilica(n=1.47)orotherglassmaterials(n≈1.5).Photolumines-cencespectraofthemicrospherescoveredbyathinshellofCdTenanocrystalswerestudiedinordertoexaminetheemis-sionintensityasafunctionofexcitationpower.

Ultralow-threshold(thepumpwaslessthan2µW)CWlasingwasachievedatroomtemperatureinafused-silicamicrospherethatwascoatedwithHgTequantumdots(colloidalnanoparticles)[201].

WGRscansigni cantlyimproveoperationofsemiconductorquantumwelllasers.Amicrolaserdesignbasedonthehigh-re ectivityWGMsaroundtheedgeofathinsemiconductormicrodiskwasdescribed,andinitialexperimentalresultswerepresentedin[202].ItwasshownthatopticallypumpedInGaAsquantumwellsprovidesuf cientgainwhencooledwithliq-uidnitrogentoobtainsingle-modelasingat1.3and1.5µmwavelengthswiththresholdpumppowersbelow100µW.

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ArealizationofanInGaAs–InGaAsProomtemperaturequantumwelldisklaser1.6µmindiameterand0.18µminthickness,operatingat1.542µmandusing0.85µmopticalpumping,wasreportedin[204].Methodsfordirectionalcou-plingoflightoutputfromandtoWGRmicrodisklasersweredescribedin[203].

Anopticallypumped,pulsedGaNmicrodisklaseroperatingatroomtemperaturewascreated[205].WGMsofthediskhadlinewidthasnarrowas0.1nm.WGRswithdiameterscoveringtherange25750µmweretested.Opticalpumpingwasperformedperpendiculartothediskplanebythethirdharmonic(355nm)orthefourthharmonic(266nm)ofaQ-switchedNd:YAGlaser.Theoutputlightemissionfromthesestructureswascollectedbyare ectingobjectivelocated80 fromthesurfacenormal,Quantum-cascadeWGMdisklasersemittingat9.5-and11.5-µmwavelengthswerereportedin[206].Takingadvantageofthehigh-qualityresonator(Q～200),thethresholdcurrentdensityofdisklasersemittingat9.5µmwasreducedtobelowthevalueofthecorrespondingridgewaveguidegeometry.

A“microgear”lasercomposedofamicrodiskandarota-tionallysymmetricBragggratingwasdescribedin[207].AGaInAsP-InPdevicewithmicronsizewasfabricated,andtheroomtemperatureCWoperationwasobtainedby17-µWpump-ing.

AnopticallypumpedmicrodiscGaN-basedlaserwasdemon-stratedin[208].TheopticallypumpedWGRshaddistinctmodesatexcitationpowersrangingfromabout8to16W·cm 2.Qualityfactorsforthemicrodiskswereoftheorderof4600.Theobservedlasingthresholdwas12.1W·cm 2.B.ResonatorModi edScattering

Thereareatleastthreescatteringprocessesplayingsigni -cantrolesinWGRs.TheyareBrillouin,Rayleigh,andRamanscattering.

1)BrillouinScattering:StimulatedBrillouinScattering(SBS)wasdemonstratedinliquiddroplets[209]–[218],thoughnoSBSinhigh-QsolidWGRswasregisteredbecauseofselec-tionrules[215].

2)RayleighScattering:Rayleighscatteringleadstothelim-itationoftheQ-factorofWGMsaswellastotheinter-modecoupling.Thescatteringislargelysuppressedinhigh-QWGRsbecauseofrestrictionsimposedonscatteringanglesbycavitycon nement,soveryhigh-QWGMsarefeasible[219].Thescattering,ontheotherhand,couplesinitiallydegeneratecoun-terpropagatingmodesintheWGRsandcreatestheintracavityfeedbackmechanisminstrumentalforthelaserfrequencylock-ingapplication[74].Rayleighscatteringmediatedintracavitybackscatteringreaches100%,aswasshowntheoretically[219]anddemonstratedexperimentally[220].Inthefrequencydo-main,intracavitybackscatteringisobservedasthesplittingofinitiallydegenerateWGMresonancesandtheoccurrenceofcharacteristicmodedoublets[221],[222].In uenceofRayleighscatteringonQ-factorsofhighrefractiveindexcontrastWGRsfabricatedfromsilicon-on-insulatorwaferswasstudiedusinganexternalsilica bertaperwaveguide[223],[224].

3)RamanScattering:Substantialopticalpowerenhance-mentwithinahigh- nesseopticalcavityhasrecentlyyieldedCWRamanlaserswithlowthresholdandlargetunability(see,e.g.,[225],[226]).Suchpropertiesmakecavity-enhancedCWRamanlasersattractiveforhighresolutionspectroscopy,remotesensing,atomicphysics,andtelecommunications.Reducingthecavitysizemayfurtherimprovetheperformanceofthelasers.Opendielectricsphericalmicrocavitiesarepromisingforthosepurposes.

AnenhancementofstimulatedRamanscattering(SRS)isoneoftheeffectsdemonstratedinsphericalmicrocavities.LowthresholdSRSwasobservedwithpulsed[213],[227]–[233]andCW[234],[235]opticalpumpinginmicrometer-sizeliquiddroplets.Theoreticaldescriptionoftheprocesswaspresentedin[236]–[239].

SRSwasinvestigatedinaliquidparahydrogendropletchar-acterizedwithWGMhavingQ-factorexceeding109[240].TheSRSwasregisterednotonlyforvibrationaltransitionbutalsoforrotationaltransitionasinthegas-phaseH2system,leadingtomultiorderSRSsidebandscoveringthewholevisiblespectralrange.

SRSinultrahigh-Qsurfacetension-inducedsphericalandchip-basedtoroidmicrocavitiesisconsideredboththeoreti-callyandexperimentallyin[241].ThesefusedsilicaWGRsexhibitsmallmodevolume(typically103µm3)andpossesswhispering-gallerytypemodeswithlongphotonstoragetimes(intherangeof100ns),signi cantlyreducingthethresholdforstimulatednonlinearopticalphenomena.

ThestudiesofRamangaininisolatedhigh-QWGRsareimportanttounderstandcavityQEDpropertiesofRamanlasing.Previously,microcavityQEDenhancementofRamangainhasbeeninferredastheresultofmeasurementsofadependenceoftheSRSthresholdonthesizeandmaterialofthemicrodroplets,anditscomparisonwiththevaluesofSRSthresholdreportedforliquidcore bershavingequivalentinteractionlengthandcorecomposition[234],[235].Thisenhancementhasbeenlinkedtothecavitymodi cationofthepropertiesofausuallaser.AtheoryoftheRamangainmodi cationthatexplainstheexperimentalresultswasdeveloped[242],[243].Recentexperimentswithsilicamicrosphereshavenotshownanysigni cantchangeinSRSgainwhichmightbeattributedtoquantumeffects[241],[244].Thisissuewasaddressedin[245],whereitwasshownthatnocavityQED-associatedRamangainenhancementexists,unlikethecavityenhancementofthespontaneousemission.C.SwitchesandModulators

1)WGMSwitches:WGRscanbeusedasef cientandcompactopticalswitchesandmodulators.NonlinearopticalswitchesbasedonWGMsareprimarilyconsideredinrelationwiththeirapplicationstoall-opticalcomputing.ApossibilityofsuchswitchingandapplicationsofWGRtocreateaquantummechanicalcomputerwas rstrecognizedin[246].

ThemajorityofstudiesofopticalswitchesthatutilizeWGMsaretheoretical.ItwasshowntheoreticallythatWGRmicrodisklasersarestableandswitchreliably[247],andhencearesuitableasswitchingelementsinall-opticalnetworks.

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Anintegratedall-opticalswitchbasedonahigh-Qnonlin-earcylindricalmicrocavityresonatorwasproposed[248].TheswitchconsistsoftwoplanarwaveguidescoupledtoaWGR.Itwasarguedthatduetothehigh-Qfactorandthesmalldi-mensions,fastswitchingatlowpowerisfeasibleforthedevicesbasedonpresentlyavailablenonlinearpolymersastheactivematerial.

Ageneralelectrodynamicaltheoryofahigh-Qopticalmicro-sphereresonatorinanexternalalternatingmagnetic eldwasreportedin[249].ItwasshownthatthatsuchasystemcanchangeapolarizationstateoftheWGMphotonscon nedinthesphereduetotheFaradayeffect.Thispropertywasproposedforuseinall-opticalswitchesandlogicaldevices.

Numericalevaluationofanopticalresponseofaprism-couplednonlinearmicrospherewasdiscussedin[250].Thenumericalresultshaveshownthatthecontroland/orthesig-nallightscaninducetheopticalswitching-likevariationinthelightre ectance.ThiseffectwasinterpretedbythevariationinthedielectricconstantofthesphereduetoitsKerrnonlinearity.CoupledWGRspossessdifferentandfrequentlymoread-vancedpropertiescomparedtoasingleWGR.Sequencesofop-ticalmicroresonatorscanbeusedtoconstructintegratedstruc-turesthatdisplayslowgroupvelocityoflight,ultrahighorlowdispersionofcontrollablesign,enhancedself-phasemodulation,andnonlinearopticalswitching[251].

Itwaspointedoutthatthereshouldbeareductioninswitchingthresholdfornonlinearopticaldevicesincorporating berringresonators[252],[253].ThecirculatingpowerinsuchWGRsismuchlargerthantheincidentpower,andthephaseofthetransmittedlightvariesrapidlywiththesingle-passphaseshift.Itwasshownthatthecombinedactionoftheseeffectsleadstoa nesse-squaredreductionintheswitchingthreshold[252],allowingforphotonicswitchingdevicesthatoperateatmilli-wattpowerlevelsinordinaryoptical bers.AsetofcoupleddifferentialequationsthatdescribeKerrnonlinearopticalpulsepropagationandopticalswitchinginsystemscoupledbyafewmicroresonatorswasderivedin[254].Gap-solitonswitchinginasystemcomposedoftwochannelwaveguidescoupledbymicroresonatorswasstudiedin[255].

Anumericaldemonstrationofthefeasibilityofconstructinganall-optical“AND”gatebyusingamicroresonatorstructurewithKerrnonlinearitywaspresentedin[256].Itwasshownthatthegatecanbemuchsmallerthansimilar“AND”gatesbasedonBragggratings,andhaslowerpowerrequirements.

Thereareafewexperimentalstudiesofall-opticalswitchesthatutilizeWGMs.Forinstance,laser-inducedmodi cationofcavityQ’swasachievedinamicrodropletcontainingasat-urableabsorber[257].Theelastic-scatteringspectrafromsuchdropletsforhigherincidentintensitiesshowthatcavityQ’sareincreasedwhentheabsorptionisbleached.Thelasingspectrafromadropletcontainingasaturableabsorberandlaserdyeweremodi edwhenanintensebleaching eldwasinjectedintothedropletcavityafterthepump eldhadinitiatedthelasing.All-opticalnonlinearswitchingincompactGaAs–AlGaAsmicroringresonatorsatthe1.55-µmwavelengthwasdemon-stratedin[258].Switchingwasaccomplishedinthepump–probecon gurationinwhichthepump–probesignalswere

tunedtodifferentresonancewavelengthsofthemicroring.Re-fractiveindexchangeinthemicroringduetofreecarriersgen-eratedbytwophotonabsorptionwasusedtoswitchtheprobebeaminandoutofresonance.

Anall-opticalswitchingtechniqueutilizingasilicamicro-sphereopticalresonatorcoatedbyaconjugatedpolymerwasdevelopedin[51].A250-µm-diametersilicamicrospherewascoatedbydippingintoatoluenesolutionofthepolymer.WGMresonantfrequencyshiftsaslargeas3.2GHzwereobservedwhen405nmpumplightwithapowerdensityontheorderof10W/cm2wasincidentonthemicrosphere.Thetimeconstantoftheobservedfrequencyshiftswasapproximately0.165s,lead-ingustoattributethefrequencyshifttothermo-opticeffects.SuchasystemiscapableofswitchingtheWGMresonantfre-quencyhaving2MHzlinewidthatspeedsontheorderof100ms.Finally,opticalmemoryelementsweredevelopedusingWGMdevices.Amemoryelementconstructedbyinterconnect-ingWGMmicroscopiclaserswasdemonstratedin[259].Thedeviceswitcheswithin20pswith5.5-fJopticalswitchingen-ergy.Ontheotherhand,itwasshowntheoreticallyanddemon-stratedexperimentallythatarandomdistributionofsphericalmicroparticlesmaybeusedasaspectralholeburningmem-ory[122],[123].

2)WGMModulators:Microwavecellularphonesystemsandpersonaldataassistantnetworksrequiredevicescapableofreceiving,transforming,andprocessingsignalsinmillime-terwavelengthdomain[260].Electroopticmodulatorsbasedonelectromagneticwaveinteractioninnonlinearopticalcavitieswithhigh-QWGMswillplayanenablingrolefortheseandsimilarapplications.

Anapproachtocreatecouplingbetweenlightandami-crowave eldinaWGRwasrecentlyproposed[80],[81].Inthatstudy,anef cientresonantinteractionofseveralopticalWGMsandamicrowavemodewasachievedbyengineeringtheshapeofamicrowaveresonatorcoupledtoamicrotoroidalopticalcavity.Basedonthisinteraction,anewkindofelectro-opticmodulator,aswellasphotonicmicrowavereceiver,wassuggestedandrealized[261]–[268].D.OptoelectronicElectronicOscillator

Besidesthesourcesofcoherentopticalradiation;i.e.,lasers,opticalWGRscanbeusedinsourcesofcoherentmicrowaveradiation.Anoptoelectronicoscillator(OEO)isanexampleofsuchasource.AnOEOproducesmicrowavesignalsusingpho-tonictechniques[62],[64]–[69].ThemodulatorisoneofthemainsourcesofpowerconsumptionintheOEObecauseofthelargepowerrequiredtodrivetheconventionalmodulators.BothbroadbandMach–Zehndermodulatorsandfreespacemi-crowavecavity-assistednarrow-bandmodulatorstypicallyre-quireonetoafewWattsofmicrowavepowertoachieveasig-ni cantmodulation.ThismeansthateitherthephotocurrentintheOEOsystemshouldbeampli edsigni cantly,orapowerfullasershouldbeusedasthesourceofthedrivepowerfortheOEO.AnOEObasedonaWGMresonantmodulatorwasrecentlyproposedandfabricated[269].Thedeviceischaracterizedbylowthresholdandlowpowerconsumption.Thedisadvantages

WGM谐振腔综述

ILCHENKOANDMATSKO:OPTICALRESONATORSWITHWGMs—PARTII:APPLICATIONS25

ofthedevicearelowsaturationandlowoutputpower,andapossibilityoftransformingthenoiseofthelight eldintothemicrowavesignal.Ingeneral,resonantandconventionalOEOshavenonoverlappingcharacteristicsandarebothuseful,dependingontheapplication.E.PulsePropagationandGeneration

Itisconvenienttodistinguishbetweentworegimesofopti-calpulsepropagationinaWGR:1)thepulsedurationexceedstheinverseoftheFSRofthecavity;and2)thepulsedura-tionisshorterthantheinversecavityFSR.Studiespresentedin[270]–[273]areprimarilyfocusedonthe rstregime.Specif-ically,thetransientbehavioroflightintensityinsideadielectricsphereexcitedbyalightpulsewasdiscussedin[270],[271].Longopticalpulseswereusedforpumpingofpolymermicro-lasers[272].Linearandnonlinearopticalpropertiesofwaveg-uidecoupledWGRshasalsobeenstudiedtheoretically[273].Thesecondcase,propagationofshortpulsesinWGRs,wasalsoexamined[274]–[276],[278],andageneraltheoreticalanalysisofthepropagationwaspresentedin[274].Timeresolvedmea-surementsofpicosecondopticalpulsespropagatingindielectricspheres[275]andsubpicosecondterahertzpulsepropagationinadielectriccylinder[276],[277]wererecentlyreported,andmicrocavityinternal eldscreatedbypicosecondpulseswasdiscussedtheoretically[278].Thebehaviorofultrashortlightpulsescoupledintotheresonantmodesofsphericalmicrocav-itieswasexploredin[279].Anoninvasivepulse-trackingtech-niquewasexploitedtoobservethetime-resolvedmotionofanultrashortlightpulsewithinanintegratedopticalmicrores-onator[280].

Theminimumpulsewidth,aswellastheperiodoftheop-ticalpulsetraingeneratedbyasystemthatinvolvesahigh-Qcavity,isdeterminedbytheresonatordispersion.Dependingonthedielectrichostmaterialandthegeometricsize,aWGRmaypossesseitherapositive,negative,orzerogroupvelocitydispersion(GVD)[281].ThisdispersionisimportantwhenthepulsedurationisshorterthantheinversecavityFSR.ResonatorspossessingapositivegroupvelocitydispersionmaybeusedforGVDcompensationinoptical berlinks.NegativeGVDcav-itieswithKerrnonlinearity(e.g.,fusedsilicacavities)sustainnonlinearSchrodingersolitonpropagation,andmaybeusedforpulseshapingandsolitonshorteninginconventionalmode-lockedlasers(see,e.g.,[282]–[284]).ZeroGVDcavitiesmaybeusedashigh- nesseetalonstostabilizeactivelymode-lockedlasers(asin[285]).IntegratedopticalWGMall-pass lterscanalsobeusedfortunabledispersioncompensationintheopticaltransmissionlineifthepulsedurationexceedstheinverseoftheFSRoftheresonator[251],[286].

Smallresonators,likeWGRs,areimportantforthestablegenerationofopticalpulseswithhighrepetitionrates.Thisiscon rmedbytheexperimentswithplanar,notWGM,smallres-onators.Forexample,2-pspulsesata16.3-GHzrepetitionratewereobtainedfora2.5-mm-longactivelymode-lockedmono-lithiclaser[287];420GHzsubharmonicsynchronousmodelockingwasrealizedinalasercavityoftotallengthofap-proximately174µm[288].Asigni cantsupermodenoisesup-

pressionwasdemonstratedbyinsertingasmallhigh- nesseFabry–Perotresonatortothecavityofanactivelymode-lockedlaser[285],[289].

ItwasproposedtouseWGRstogenerateshortopticalpulses[281],[290].Theideaofthislaserisbasedontworecentlyreal-izedWGMdevices:theelectroopticmodulator,andtheerbium-dopedmicrosphereglasslaser[80],[180],[183],[186],[192].Itisalsoknownthatanelectroopticmodulatorplacedinanopticalresonatorcangenerateafrequencycomb[291]–[294],andthattheoutputofsuchadeviceissimilartothatofamode-lockedlaser.However,unlikethemode-lockedlaser,thepulsedurationisnotlimitedbythebandwidthofthelasergainbecausethesystemispassive.Thepulsewidthde-creaseswiththemodulationindexincrease,andwiththeoverallcavitydispersiondecrease.ThemodulationindexmaybeverylargeinaWGMmodulator,whichmaysigni cantlyimprovetheperformanceofthesystem[281].F.WaveMixingandOscillations

WGRswereusedinopticalparametricaswellashyperpara-metricwavemixingprocesses.

1)Hyper-ParametricOscillator:Hyperparametricopticaloscillation[295],alsoknownin beropticsasmodulationinsta-bility[296],isbasedonfour-wavemixing(FWM)amongtwopump,signal,andidlerphotons,andresultsinthegrowthofthesignalandidleropticalsidebandsfromvacuum uctuationsattheexpenseofthepumpingwave.Thehyperparametricoscil-lationsaredifferentfromtheparametricones.Theparametricoscillations1)arebasedonχ(2)nonlinearitycouplingthreephotons,and2)havephasematchingconditionsinvolvingfarseparatedopticalfrequenciesthatcanonlybesatis edinbire-fringentmaterialsintheforwarddirection.Inthecontrast,thehyperparametricoscillations1)arebasedonχ(3)nonlinearitycouplingfourphotons,and2)havephasematchingconditionsinvolvingnearly-degenerateopticalfrequenciesthatcanbesat-is edinmostofthematerials,bothintheforwardandbackwarddirections.

Recently,thestudyofhyperparametricoscillationshadanewstageconnectedwiththedevelopmentofWGM,aswellasphotoniccrystalmicroresonatortechnology[297],[8].Theos-cillationsoccurringincavities,orcavity-likesystems lledwithtransparentsolids,wereanalyzedtheoretically;e.g.,inisotropicphotoniccrystals[298],andwereobservedexperimentallyincrystallineWGMresonators[299],[300].Itwassuggested,inparticular,thatthenarrow-bandbeat-notesignalbetweentheop-ticalpumpandthegeneratedsidebandsemergingfromahigh-QWGMresonatorcouldbeusedasasecondaryfrequencyrefer-ence[300],[301].

ThephasestabilityofthefrequencyreferencesignalincreaseswithincreaseoftheQ-factoroftheresonatormodesforthesamegivenvalueofthepumppower.Thereexistsamaximumofthephasestability(minimumofthephasediffusion)ofthebeat-notesignalthatdoesnotdependeitheronthepumppowerorQ-factorofthemodes.KeepinginmindthatWGMsQ-factorcanexceed1010(afewtensofkilohertzresonancelinewidth)[61],itwasfoundthattheAllandeviationfactoroftheoscillations

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26IEEEJOURNALOFSELECTEDTOPICSINQUANTUMELECTRONICS,VOL.12,NO.1,JANUARY/FEBRUARY2006

issmallerthan10 12s 1/2forsub-milliwattopticalpumping.Thepumpthresholdcouldreachmicrowattlevelsforreasonableexperimentalparameters.

2)ParametricProcesses:Opticalparametricoscillators(OPO)havebeenextensivelystudiedsincethediscoveryoflasers[302]–[304].PropertiesofOPOarewellunderstoodbynow[305],[311],[312],[295],[59].TheCW-OPOisconsideredticalapplications.Filters,modulators,lasers,andotherwhisper-inggallerymodedeviceshavemultipleadvantagesovertheir“ordinary”counterparts.

ACKNOWLEDGMENT

A.MatskoacknowledgesilluminatingdiscussionswithJ.DickandL.Maleki.

anidealdevicethatcangenerateabroadrangeofwavelengths.Ef cientfrequencydoublingatλ=1.55µmandλ=1.319µmwasrealized[57]usingthesameWGRmadeofpe-riodicallypoledLiNbO3(PPLN)[306].TheWGRwasdoublyresonant,bothatfundamentalandsecondharmonicfrequen-cies.ThefollowupstudiesoftheparametricprocessesinPPLNWGRsareimportantbecauseithasbeenpredictedthatanop-ticalparametricoscillatorbasedontheresonatormighthaveapowerthresholdbelowamicrowatt[307]—ordersofmagnitudelessthanthatofthestate-of-the-artOPOs,typicallyat0.5themilliwattlevel[308].

Itwasshowntheoretically[309]thatanondegeneratemul-tifrequencyparametricoscillatorhasdifferentpropertiescom-paredwiththeusualthree-waveparametricoscillator.AschemeforaresonantCWmonolithicmicrowave-opticalparametricos-cillatorbasedonhigh-QWGMsexcitedinanonlineardielectriccavitywassuggested.Suchanoscillatormayhaveanextremelylowthresholdandstableoperation,andmaybeusedinspec-troscopyandmetrology.Theoscillatormimicsdevicesbasedonresonantχ(3)nonlinearity(hyperparametricprocess)andcanbeutilizedforef cientfour-wavemixingandopticalcombgeneration.

G.FundamentalPhysicsWithActiveWGMs

WGRscanbeusedforgenerationofnonclassicalstatesoflight.Forinstance,thepossibilitywasshownforthegenerationofheraldedsinglephotonsandofsub-Poissonianlaserlightintheelectricallypumpedsinglequantumdotmicrospherelaser[198].

Thereduceddensitymatrixmethodwasusedtocalculatethequantum-statisticalpropertiesoftheradiationofaquantumdotlaseroperatingontheWGMofadielectricmicrosphere[310].Itwasshownthatundertheconditionsofstrongcouplingbetweenthequantumdotandanelectromagnetic eld,theradiationofsuchalasercanbeinanonclassical(sub-Poissonian)state.Thelaserschemewascharacterizedbyanextremelylowlas-ingthresholdandasmallnumberofsaturationphotons;conse-quently,lasingispossiblewithclosetozeropopulationinversionoftheworkinglevels.

IV.CONCLUSION

Inthisreview,wehavecoveredrecentdevelopmentsintheapplicationsofwhisperinggallerymoderesonatorsinopticsandphotonics.Wehavetriedtomentionalltheactivitiesinthe eld,thoughweadmitthatsomeoftherecentadvancescouldhaveescapedourattentionbecausetheareagrowsveryfast,andeachmonthbringsnewstudiesrelatedtothesubject.

Thoughwhisperinggallerymodesareinterestingphysicalob-jectsbythemselves,weforeseethefastestgrowthintheirprac-

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1998.

VladimirS.Ilchenko,receivedtheM.S.andPh.D.degreesfromMoscowStateUniversity,Russia,in1983and1986,respectively.

HehasbeenaSeniorMemberoftheTechnicalStaffattheNASAJetPropulsionLaboratory(JPL),CaliforniaInstituteTechnology,Pasadena,CA,since1998.HejoinedtheTimeandFrequencyGroupatJPL(currentlyQuantumSciencesandTechnologyGroup)aftera12yeartenureasResearchAssociateandAssociateProfessorinthePhysicsDepartment,MoscowStateUniversitywhere,withcolleagues,he

pioneeredtheexperimentaldemonstrationofultrahigh-Qopticalwhispering-gallerymicroresonators(microspheres).Hiscurrentresearchinterestsarefo-cusedonthedevelopmentandapplicationsofcrystallineopticalmicroresonatorswithkilohertzlinewidthsforhighspectralpurityopticalandmicrowaveoscil-lators,photonic lters,modulators,andsensors.Since2001,hehasbeenChiefScientistofOEwaves,Inc.,Pasadena,CA.

Dr.IlchenkoisamemberoftheOpticalSocietyofAmerica,

SPIE.AndreyB.MatskoreceivedtheM.S.andPh.D.de-greesfromMoscowStateUniversity,Russia,in1994and1996,respectively.

HehasbeenaSeniorMemberofTechnicalStaffwiththeQuantumSciencesandTechnologyGroupattheJetPropulsionLaboratory(JPL),CaliforniaInstituteTechnology,Pasadena,CA,since2001.Hereceivedpost-doctoraltrainingattheDepartmentofPhysics,TexasA&MUniversity(1997–2001),wherehewasawardedtheRobertA.WelchFoundationPostdoctoralFellowship.Hiscurrentresearchinter-estsinclude,butarenotrestrictedto,applicationsofwhispering-gallerymoderesonatorsinquantumandnonlinearopticsandphotonics;coherenceeffectsinresonantmedia;andquantumtheoryofmeasurements.

Dr.MatskoisamemberoftheOpticalSocietyofAmerica.HereceivedJPL’sLewAllenAwardforexcellencein2005.

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