Optical Resonators With Whispering-Gallery applications(12)

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

WGM谐振腔综述

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.

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