2Opticalsusceptibilityproperties15

Fundamentalconceptsinnonlinearoptics:1.NonlinearOptics,2.thesecond-ordernonlinearopticaleffects3.thethird-ordernonlinearopticaleffects4.theparametricinteraction:secondharmonicgeneration(SHG)Fundamentalconcepts:(continue)thirdharmonicgeneration(THG)sumfrequency(SF)differencefrequency(DF)opticalparametricamplification(OPA)opticalparametricoscillation(OPO)fourwavemixingself-focusingdegenerationfourwavemixing(DFWM)Fundamentalconcepts:(continue)5.thenon-parametricinteraction:saturationabsorption(SA)two(twin)photonabsorption(TPA)stimulatedRamanscattering(SRS)stimulatedBrillouinscattering(SBS)opticalKerreffect(OKE)phasematchingopticalphaseconjugation(OPC)Chapter1Nonlinearopticalsusceptibility-Polarizationinducedbylaser-matterinteraction非线性光学的宏观描述不同介质中非线性光学效应共性：都可以进行统一的宏观描述特殊性：非线性极化产生的微观过程和机制不同§1Macroscopictheoryfornonlinearopticalsusceptibility1.NonlinearelectricpolarizationDBJDHBE0ttEJHBPED00极化Polarization①无极分子（Nonpolarmolecule）在无外场作用下整个分子无电矩。正负电荷中心重合。例如，CO2H2N2O2He②有极分子（Polarmolecule）在无外场作用下存在固有电矩。正负电荷中心不重合。例如，H2OHclCOSO2因无序排列对外不呈现电性。电子云的正电中心有极分子无极分子0rqp电介质的极化：0E位移极化取向极化0E①无极分子位移极化Displacementpolarization主要是电子发生位移②有极分子取向极化Orientationpolarization由于热运动这种取向只能是部分的，遵守统计规律。线性条件下：0P=000EEEEEPPPP)3(0)2(0:LNLLIngeneralaE1)2()3()1()2(whereistheintensityofaverageCoulombfieldofthelightatom,itsvalueisaboutaEcmV/108)1()2()3()(nisasecond-ordertensor,ithas9matrixelements.isathird-ordertensor,ithas27matrixelements.isafourth-ordertensor,ithas81matrixelements.)1(3nisa(n+1)-ordertensor,ithasmatrixelements.1.1Responsefunctionofmediumtoopticalfield1)线性响应函数因果性原理:t时刻介质感应的线性极化强度P(t)不仅和t时刻的光电场E(t)有关，而且和t时刻前所有光电场有关。时间不变原理：τ时刻的光场对t时刻极化强度的影响与τ+T0时刻同样的光场对t+T0时刻极化强度的影响相同。也就是说介质响应函数只和时间间隔有关。t时刻介质感应的极化强度为dP(t),dP(t)=ε0R(t-τ)∙E(τ)dτR(t-τ)称为介质的线性电极化强度响应函数,二阶张量因果原理知t时刻以后的光电场对P(t)不会产生贡献，即tt时，R(t-t)=0,00()()()()()PtRtEdREtdtttttt－－因为电场E(t)是实函数，响应函数R(τ)必须是实函数才能保证P(t)也是实函数。真实性条件。将E(t)时间函数通过傅里叶积分展开成各种频率光场E(w)的叠加，进行变量代换，可以化成00()()()ttdtttPRE0()()()tttdtttPRE－(2)(2)1212120()(,):()()PtddREtEttttttt－－2)非线性响应函数二阶非线性极化强度P(2)(t)(2)12(,)Rtt是三阶张量，介质的二阶极化响应函数t()itEEed（）t()itPPed（）(1)00()[()]()PtdRtdEwttw－－则有：(1)()()iRedwtwtt令可得：(1)(1)0P()()()Ewww()()1212012n()(,,)()()()nnnnPtdddREtEtEtttttttttt－－－n阶非线性极化强度P(2)(t)()12(,)nnRttt是n+1阶张量，介质的n阶极化响应函数同样从时域转到频域，利用Fourier变换得二阶极化(,)(,)ittedErEr(,)(,)ittedPrPr1122()(2)(2)12121212[(),,](,)iddRewtwt(2)1212(2)1212[(),,]()[,,]d又若组成光波的频率分量不连续，则积分用求和代替。(2)(2)012121212P()[,,]()()()ddEEwww(3)(3)0123123123123P()(,,,)()()()()dddEEEw类似方法可得三阶极化强度表达式Intheinteractionbetweenlaserbeamwiththefrequencyandmedium,thepolarizationisnotrelatedtothelightfieldwiththefrequencyonly.Therefore,thelaserfieldshouldbeexpandedinfrequency,thatis,ww)(nP),(),(rErE2.Nonlinearsusceptibilityanditsproperties)(n(1))(nTheopticalfieldisarealquantity,anditscomplexfrequencycomponentsmustobey:),(),(*wwrErESimilarlywehave,),(),(rPrP),(),(*wwrPrP2.Nonlinearsusceptibilityanditsproperties(continued)(1))(n2.Nonlinearsusceptibilityanditsproperties(continued)(1)Undertheconditionconsideringonlythefrequencydispersion(notspatialdispersion),weobtain),()(),()1(0)1(wwwrErPThereisonlyonefieldforfirst-orderpolarization.Thereforecanbeanygivenfield.),(wrE)(n2.Nonlinearsusceptibilityanditsproperties(continued)(1)Undertheconditionthattherearetwomonochromaticfields,),,()()(:),,(),(212121)2(210)2(wwwEEddrPi.e.,)()(),,(),(2121)2(0)2(wkjijkiEErP)(n2.Nonlinearsusceptibilityanditsproperties(continued)(1)Thereforetheintensityofthen-ordernonlinearpolarizationappearsintheformnnntkjjklnnlkjinidddrErErErPw...),...,,(),()...,(),(),...,,(),(212121...21)(...,,,0)(where)(n2.Nonlinearsusceptibilityanditsproperties(continued)(1)where),()(wrPniisthei-thcomponentofthen-ordernonlinearpolarization.)(...ntijklisthetensorelementofthe(n+1)-ordertensor.)(n)...,(),,(21wwrErEkjarecomponentsoftheopticalfieldswiththefrequenciesrespectively....,21ww...),,(21is-function.2.Nonlinearsusceptibilityanditsproperties(continued)(1)Infact,thelightfieldislaserfieldwhichhasverynarrowspectralwidth.Soaboveequationscanbesimplified.Usingthemethodwhichhasbeenusedbymanyresearchers,actuallightfieldcanbeexpandedtoaseriesofmonochromaticfields,i.e.,itiicceEtrEi..)()2/1(),(ww2.Nonlinearsusceptibilityanditsproperties(continued)(1)whereistheamplitudeofthemono-chromaticfieldwiththefrequency,)(iEwiwand.)(*)(iiEEwwSimilarly,itiiccePtrPi..)()2/1(),(ww*()()iiPPww2.NonlinearsusceptibilityanditspropertiesForthelinearpolarization,wecanwrite(1)0()()()www(1)PχEThereisonlyonefieldforlinearpolarization.ThereforeE(w)canbeanygivenfield.)(n(1)(1)0(1)(1)0()(;)(,),(,1,2,3)()=(;)(,)()iijjjiijjPErijrjwPE，对重复脚标求和IntheCartesiancoo