文档介绍：介质的极化强度P与电场强度E的关系......)3(0)2(0)1(0+??+?+=EEEEEEPχεχεχεχ(1),χ(2),χ(3)……一阶,二阶,三阶……极化率dielectric susceptibility, E?E为E和E的直积22022202)(??=????NLPEEμ非线性介质中的Maxwell方程缓变包络近似(SVEA,Slow varying envelope approximation)zPEE0002εω?=??+??.).ee(EEeamxxmtxmtxmtiti++?=+++ωωωγω1和ω2的两个光电场中,质量为m的电子运动的方程非线性项逐次叠代法解此方程]}.)(*)(e*)()(e)(e)(e[|)(||)({|4.].)(e)(e[421)(2121)(21222221222122221122221122)1(DEDEmaeamxtitititititi++++++=++=?+ωωωωωωωωωωωωωωωωωω0,2ω1,2ω2,ω1+ω2和ω1-ω2的五个新的频率分量??????ΔΔ=2sin2)(22)2(02kLEckniLEωωχω二次谐波二次谐波SHGSHG倍频效率倍频效率2233002)2(]2/)2/sin([)(2][)()2(IIΔΔ≈=ωεωχωωη()()ωωωωnnkk==2;22相位匹配条件三阶非线性效应:三阶非线性极化强度:非线性折射率:n=n0+n2I非线性吸收系数:α= α0+ α2I自聚焦现象n2>0光学双稳原理光学双稳原理实现双稳的两个条件:1、非线性2、反馈这两个条件在光学中很容易满足T(IT)ITIIbaT1132T2Τ(ΙΤ)ITba132v1v2PΙΤIIlkjlkjijkliNLEEEP∑=,,)3(0)3()(χε光学双稳器件Bistable Optical Devices?非线性光学介质---non-linear?反馈feed back---Ring cavity or Fabry-Perot etalon两类非线性光学双稳元件:色散型元件(Dispersive elements): 折射率n是光强的函数。吸收型元件(Absorptive non-linear elements): 吸收系数α为光强的函数。non-linearEI, IIET, IT100 %100 %lε(0)TTRRIIITnon-linearn =n0+n2Iα= α0+ α2I环形腔环形腔如图在环形腔内放入非线性介质,设环形腔长为L,介质两侧反射镜的光反射率为R,两侧反射镜的的距离为l′,入射光和透射光强度分别为II和IT,又设样品的厚度l 很薄,吸收很小。()()()()()()()()()()()ikllLiklikllLiklikllliklikllliklTIIIeREReEREEeTeeETEETEkInncIkkkInnnIE+?+?+?+?+?+?+??=====+=+=+='21'2121''2''2111202020000000';;;;ααααω非线性介质外波矢为::则:非线性介质内波矢介质折射率:入射光强度:入射电场强度:non-linearEI, IIET, IT100 %100 %lΕ1(0)TTLl'()()()()()()()()()()()()()()()()()ikllLiklikllliklITIikllLiklikllliklikllLiklIikllliklikllLiklikllliklikllLiklTnnTTTnikllLiklnTTikllLiklikllliklikllLiklikllliklTTeEEETeETeTEeTEEEEEEeeRETeETE+?+?+?+?+?+?+?+?+?+?+?+?+?+?+?+?+?+?∞=?+?+?+?+?+?+?+?+?+?+??=?=?=?=?==????????=∴===∑'2''2'2''2'2''2'21''2'21111'21'2''2'21''222Re1Re1Re1Re10Re1ReRe00αααααααααααααα()()()() ()()ikllLiklikllliklTIeREEEeTEETE+?+?+?+?==='2121''2110000αα()()()kllLkeRIIeReTEEIITeEElllITlllITITikllLiklikllliklIT+?=+??????????=?+==?=??????+?+?+?+?'2sinRe4Re1)1(cosRe21Re1222222222'2''2βββαααααααα其中:---忽略吸收的影响---忽略吸收的影响() ()( )()() ( )()()TITTTITTTTlllITI