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1、Coupled-ModeTheoryHERMA”A.HAUSANDWEIPINGHUANG,MEMBER,IEEEInvitedPaperTheprincipalfeaturesofcoupledmodetheoryarereviewed,andfiberopticsinrecentyearsaredescribed.Wethencon-inparticularasappliedtopassivestructures,suchascoupledsiderlosslesscouplingoftwomodesintime.
2、Twocoupledresonatorsandcoupledwaveguides.Theformerareexamplesofresonancecircuits,ortwocoupledmicrowaveoropticalcouplingofmodesintime,thelatterareexamplesofcouplingofmodesinspace.Activestructuresareconsideredbrieflyinsofarresonators,arethephysicalexamples.Energyc
3、onservationastheyobeyconservationlawsintermsofpositiveandnegativerequiresthattheeigenfrequenciesbereal.Thestart-upofaenergies.Thecomplicationscausedbynonorthogonalityoftheparametricoscillatorisanotherexample.Thenwelookatmodeenergies,orpowers,arebroughtup.Thesewe
4、rethetopictheformalderivationofcoupledmodetheoryandconsiderofrecentpublications.themoregeneralcasewhenthemodesarenotenergy-Thecouplingofmodesformalismhasintuitiveappealinthatthecouplingequationsintheirsimplestformcanbewrittendownbyorthogonalandtheenergiesarenotn
5、ecessarilypositive.inspection.When‘%nepoints”as,forinstance,crosstalkareatAmoredetailedaccountofthenonorthogonalcoupledissue,thenmoreformalderivationsarerequired.Theonepresentedmodetheorydevelopedinthelastfiveyearsforopticalhereisbasedonavariationalprinciple.wav
6、eguidesisgiven.Whenoneresonatorstoresnegativeenergy,theotherpositiveenergy,thefrequenciesappearinI.INTRODUCTIONcomplex-conjugatepairs.Aresonatorcontaininganactivemedium,thelattertreatedinalinearizedapproximation,isInthispaperwereviewtheprincipalfeaturesofcoupled
7、anexample.modetheory.TheliteratureonthesubjectisvastanditThisstudyisfollowedupbyshowinghowthecoupledwouldbedifficulttodojusticetoallaspectsofcoupledmodeformalismcanbederivedfromavariationalprinciplemodetheory.Whenthefirstauthor,H.A.Haus,wasaskedforthefrequencies
8、ofthesystem.Ifatrialsolutionistocontributethisinvitedpaper,heacceptedonthegroundsintroducedfortheelectricfieldinalosslesselectromagneticthataspectsofcoupledmodetheory