会计学Nonlinearopticsisn’tsomethingyouseeeveryday.NonlineareffectsinatomsNonlinearopticsandanharmonicoscillatorsMaxwell'sEquationsinaMediumSolvingthewaveequationinthepresenceoflinearinducedpolarizationMaxwell'sEquationsinaNonlinearMediumSum-anddifference-frequencygenerationComplicatednonlinear-opticaleffectscanoccur.InducedpolarizationfornonlinearopticaleffectsSolvingthewaveequationinnonlinearopticsThenon-depletionassumptionWe’llwritethepulseE-fieldasaproductofanenvelopeandcomplexexponential:Esig(z,t)=Esig(z,t)exp[i(wsigt–ksigz)]We'llassumethatthenewpulseenvelopewon’tchangetoorapidly.ThisistheSlowlyVaryingEnvelopeApproximation(SVEA).Ifdisthelengthscaleforvariationoftheenvelope,SVEAsays:d>>lsigWe’lldothesameintime:Iftisthetimescaleforvariationoftheenvelope,SVEAsays:t>>TsigwhereTsigisoneopticalperiod,2p/wsig.Andwe’lldothesameforthepolarization:Psig(z,t)=Psig(z,t)exp[i(wsigt–ksigz)]Iftisthetimescaleforvariationoftheenvelope,SVEAsays:t>>TsigwhereTsigisoneopticalperiod,2p/wsig.Computingthederivatives:Now,becauseksig=wsig/c,thelasttwobracketedtermscancel.Andwecancancelthecomplexexponentials,leaving:IncludingdispersionintheSVEATransformingtoamovingco-ordinatesystemIntegratingtheSVEAWechoosewsigtobethesumoftheinputw’s:Phase-matchingPhase-matching(continued)SinusoidaldependenceofSHGintensityonlengthPhase-matching=Conservationlawsforphotonsinnonlinearoptics感谢您的观看(guānkàn)。