Optical Resonators With Whispering-Gallery applications(6)

ApplicationofWGRsinhigh eldhighfrequencyelectronmagneticresonancemeasurementswasdiscussedin[98].F.MechanicalSensors

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

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

WGM谐振腔综述

20IEEEJOURNALOFSELECTEDTOPICSINQUANTUMELECTRONICS,VOL.12,NO.1,JANUARY/FEBRUARY2006

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].

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