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.