激光束传输与变换第十二讲

1、HBEDBDtBEtDJH00tDH00222222HknHEknE11| 2kunakalm)(exp)()()(000000100010tirkJkauiHrkJHrkJEmimimziimriim)(exp) 1()() 1(10200000200000tzarkinarkuJiuniHHEmemmemzemrem)(exp)()()(0100000010tzirkJHrkJkauiErkJEmiimimimziimr)(exp) 1()(/11020000002020tzarkinarkuJiuHnHnEmemmememzemr)(exp)(sin)()(sin)(12)()(cos)

2、(12)(00210221tzilrkJkauiElrkJnkruirkJElrkJnlkauirkJElmillmizlmillmilirlmillmililm)(0000000cthlEHEHEHizlmizlmilmirlmirlmilm)(exp) 1()()(sin1)(sin)(cos20200tzarkinarkuJiulnElElElmelmllmezlmerlmelm)(00000002cthlEHEHEnHezlmezlmelmerlmerlmelmimimrmiimeeimzimimrimzEHtzirkJEHEHHEE00000100000)(exp)(0,0imrim

3、miimreeimzimzimrimEHtzirkJEHEEHHE00000100000)(exp)(0,0ilmirlmirlmilmlmilirlmlmililmeeizlmizlmEHEHtzilrkJEtzilrkJEHEHE00000101)(exp)(sin)()(exp)(cos)(0,aniaukillmlmlm122112anaullmlmIm122112)Re(2)Re(2)Im(322llmlmnau 空心圆柱波导本征模的衰减系数由以下主要因素决定：lm2/a3lmRe(nl)lmulm14 , 14blam 41 , 41222amnnbln 41 , 41222bln

4、namn )(exp2cos2sin2cos2sin00tzibylbylaxmaxmHEmlixmliyml0,0iziziyixHEHE(l、m为偶数)(l、m为奇数) )(exp2cos2sin2cos2sin00tzibylbylaxmaxmHEmliymlixml0,0izizixiyHEHE(l、m为偶数)(l、m为奇数) 1Re1611Re161Im142111Im14211222322232222222nnblnamnnbblnaammlml11Re161Re1611Im14211Im14211223222232222222nblnnamnbblnnaammlmlab)()(2

5、)()(2222123222312221222123222221nnnnnnarctgmnndnnnnarctgmnndcTMcTE2221222123222312221222123222)()(12)()(1nnnnnnnnarctgmdnnnnnnarctgmdcTMcTE)()(2int)()(2int22212322231122212221232212221nnnnnnarctgnndmnnnnarctgnndmTMTE-dd) xp(x(hd)B(hd)Ax -d (hx) B(hx)A x qx) (A(x)Eyexpsincos0sincos0exp221222222223220

6、00expsincos0cossin0expnhknpknq-dd) xp(x(hd)B(hd)Aipx -d (hx) B(hx)Aih x qx) (Aiq(x)Hz)/()()(2pqhqphhdtg-d x)(exp)sin()cos(0 xd- )sin()cos(0 x )exp()(dxphdDhdChxDhxCqxCxHy/()(4122322222321pqnhnnqnpnhnhdtg)(exp)(exp2112221211ziAiKzAziAiKzA) n(n a rnar nn(r)2121)exp()exp()exp()exp(1211212121iaurBJriaur

7、AJauuaiHiaurBJauaurAJriuaiHiaurBJauaurAJriuaiEiaurBJriaurAJauuaiErr)exp()exp()exp()exp(2222222222iawrDKriawrCKawwaiHiawrDKawawrCKriwaiHiawrDKawawrCKriwaiEiawrDKriawrCKawwaiErriEHABzz112222120222/1202222/122021)()()(annkuaknaknuaurBJuaiEaurBJuaiHaurBJHrz111101aurAJuaiHaurAJuaiEaurAJErz11111012022212)(knnu22212nnaV40483. 222221nnaVar )21 (ar0 21)(20202narnrn)0(2)()0(222nannddvg0dkdcLddLvLggddnncn122dndc