1、1v5.0 预备知识v5.1 热透镜腔和基模动态稳定腔2v基模高斯光束的基本性质v光学传输矩阵vABCD法则v谐振腔的本征方程和稳定性条件v稳定腔与基模高斯光束vG参数等价腔v非稳腔32222( )( )020( , )( )( )1( )krrikz R zzAA r zee zz zfzfR zffzzarctgf422( )rwze522220( )1zzf6( )zfR zffz722( , )( )2 ( )2 ( )kr r zkz zR zkrR zkzzarctgf总相移：总相移：几何相移：几何相移：径向相移：径向相移：附加相移：附加相移：820f9 00limz zz1021
2、1( )( )( )iq zR zz0qif211Re( )1Im( )R zqzq110101rrA BC D 离轴距离光线与轴线距离Rr符符号号规规则则：，出出射射点点位位于于轴轴线线上上方方，向向轴轴线线上上方方出出射射，出出射射点点位位于于轴轴线线下下方方，向向轴轴线线下下方方出出射射，光光线线遇遇到到凹凹面面球球面面半半径径，光光线线遇遇到到凸凸面面12L101L131n2n12100nn141n2n1212210()nnnnn RR151021RR161011ff1712101nLnL1n2n1n181121211ABCDDCAqBqqBCqDqAq或或1q2q19ABMCD往往返
3、返矩矩阵阵：abcdMXX特特征征方方程程：()00ME XABXCD1ADBC2()10AD 2021,2122ADAD121122ADADAD 为为复复数数稳稳定定腔腔：-1-1为为实实数数非非稳稳腔腔：或或211210102211ABdbabCDcacdRR abcd1R2R2211211222222222abAadb cBbdb dRRdbadbbCa cacDb cadRRRRRR 22111AqBqCqD2111122DAADiqBB211111iqR2112212BBRDAAD231211bbGaGdRR222121212221222421aGbGABCDaG GGa GG Ga
4、Gb1212120110G GG GG G稳稳定定腔腔条条件件：非非稳稳腔腔条条件件：或或24122jiij1iiiGRRbGG G 212120121212212120222112G1GG2G1 GGG2 GbGG GaaG GbGGddG 21012121212022211222bGaGLGa GaGGbG dGLGd GdGG25*1122gGgGLb*12*1212110g gg gg g稳稳定定腔腔条条件件：00非非稳稳腔腔条条件件：或或261*22j*iijgg 1 g giiiRRL *2121202*ji12*2j02*ji12g g1 g ggg 1 g gggg 1 g g
5、iiiiiLL RLRLL R2721,22122121221221221ADADMADADMADADMM M放放大大倍倍数数：abcd1R2R1O2O01L02L28abcd1R2R1O2O01L02L1DCRBRAR211122DAADRBB29abcd1R2R1O2O01L02L2121212211122ADADADMMDAADRBB30abcd1R2R1O2O01L02L2221212211122ADADADMMDAADRBB 312121(1)1112qqzqqF自自由由空空间间传传播播：（ ）过过薄薄透透镜镜：求证：稳定腔的判据为：求证：稳定腔的判据为：120()()1bbadRR
6、求证：对于高斯光束求证：对于高斯光束32一、热透镜腔二、基模动态稳定腔三、基模动态稳定望远镜腔四、类透镜介质中的高斯光束332201( ),(0)2n rn r正透镜正透镜负透镜负透镜lr22221cos()sin()1, ( )(1)2sin()cos()1c ()s ()1, ( )(1)2s ()c ()zzn r rzzh zh zn r r h zh z类类透透镜镜介介质质中中的的传传播播矩矩阵阵：正正透透镜镜：负负透透镜镜：34lr00001cos()sin()sin()cos()1()()()()lln n zlch lsh ln n sh lch l考考虑虑两两端端面面的的折折
7、射射后后，类类透透镜镜的的传传播播矩矩阵阵：正正透透镜镜：负负透透镜镜：351222111212121212121212121212122210101011111blnnnnnncdn Rnn Rnnnnlln RnbcdnnnnnnllnRRnR Rn R厚厚透透镜镜的的传传播播矩矩阵阵：a aa al1R2R361R2Rl1h2hf212121211011110101111hhfhhhhhffhff等等效效矩矩阵阵：T=T=11122121122221212121121212()()()()111n lRhn RRnn ln lRhn RRnn lnnnnlfnRRnR R37200001
8、1sin122fn ln lllhtgn n212110021cos()sin()s111in()cos()hhhhzzn n zzhffhff38222020200,( )(1),0,2nnn rnrnnnn正正透透镜镜负负透透镜镜hhf2012lfhn ln39hhf1d2d1R2R1Df光光焦焦度度： 4012010201L02L*12*1212(1)1iiijiiidggDdRddgRLddDd d 411122*2ji120*01212gg 1 g gg g1 g giiiL R L1*2*j2*iijgg 1 g giL*1212202*ji12*2j02*ji12g g1 g g
9、gg 1 g gggg 1 g giiiii LL RLRLL R42*121稳稳定定腔腔条条件件：00g g*121211221201111111iijg gg gDRdRdDdRdDdd , ,临临界界条条件件：或或临临界界光光焦焦度度：43*1222211211()d dgggggddg122211d dgkddg21gkg21gkg44451111ABCD2222ABCD3R2R1R1M2Mf311()(1)ssRRdn输输出出镜镜的的“匹匹配配”条条件件：46稳定腔球面输出镜如图所示：为使输出面处的等稳定腔球面输出镜如图所示：为使输出面处的等相位面为平面，（光从左向右传播）求证：相位
10、面为平面，（光从左向右传播）求证：211()(1)RRdn2R1Rdn47*121稳稳定定腔腔条条件件：0 0 g g10ddf基基模模动动态态稳稳定定条条件件：12*221*112gg 1 g gL2*112*12221122BBggBgB482*112*12221122BBggBgB2*112*12221122ddggdgd1212*1212BBddg g 或或热不灵敏热不灵敏腔条件腔条件深度热稳腔条件深度热稳腔条件49激光输出方向激光输出方向10d 501d2dl l1M2Mf1f2f1212fMflff 望望远远镜镜系系统统放放大大率率：离离焦焦量量：51*1122112Bg gB20
11、 2211112221221122112111222221221121212dffflffl dlffdfdffflfdfffflfffl dlffdfdfffflff f f522201( ),(0)2n rn r22002( )(1)21nn rnrnfn l热热透透镜镜：201fn l5302202022220002200202222000cos()sin(),0sin()cos()c ()s (),0s ()c ()nnnzznnnnnnnzznnnnnnhzhznnnnnnnhzhznnn正正透透镜镜：负负透透镜镜：54220002222020022000222202001cos()sin(),0sin()cos()1c ()s (),0s ()c ()nnzznnn nnnnn nzznnnnhzhznnn nnnnn nhzhznn正正透透镜镜：负负透透镜镜：552201n fn0020nn 020nn 20nzn0220f2562201n fn0020nn 020nn 20nzn02257020nzn00220min220()21nnzarctgfnnfRnfn最小曲率半径处：最小曲率半径处：58
