第13講圓形鏡共焦腔、一般穩(wěn)定球面腔

1、112mnmnmnmn 2202200( , )22SrmmimmnmnnSSrrrCLee0,2mnSrCLfL其中為鏡面的極坐標為歸一化常數(shù)為共焦腔長度為鏡面上的光斑半徑 00122!()()! !( - )!111122 22knmnkmmmnmLmkk n kLLmLmmm 為締合拉蓋爾多項式(21)/2i kLmnmne對應(yīng)本征值0/SL 1argmnmn212kLmn 212mnmn212qkLmn 21 /22mnqcqmnL;24qnmccLL 211/0mnmn 222( , )0( )02( , )22( )( )( )mrmirzimzmnnrrErELeeezzz202

2、2( )1(1)21122zzfrkfmnf00112222SarctgzzLfLLf2( )zffR zfzfzz2( )zffR zfzfzzz=0z1z2R1R2L共焦腔211112222221( )()fRR zzzfRR zzzLzz 1201/1/1L RL RR1R2 z1 z2L0 f 共焦腔2111222221/RzfzRzfzLzz 2121122112122212()()()()()()()()()L RLzLRLRL RLzLRLRL RL RL RRLfLRLR 12120RLRLRR120,0RR1212,RL RLRL RL或1200zz 12121RLRLRR1

3、2()0L RRL20f 有確有確定的定的等價等價共焦共焦腔存腔存在在2( )fR zzz 1412120212()()()fL RL RL RRLLRLR121412221011121242122121/SSRRLLzfL RLRRLRRLLL RLRRL112211LgRLgR 141212021122142111214122121/11SSg gg ggRgRLggg gLggg g21200122SSVL12120200000212112121112224 14 1SggggVLVggggg gg g 2020001/22SVLL 0/SL 0000002121mnmnVVmnVV21

4、()( )mnzz 2( , )(1)arctan22mnrfzr zk zkfmnRfz 12211arctanarctanmnmnzzkzzmnff 1212arctanarctanarccoszzg gff2112()(1)arccosmnk zzmng g 12222(1)arccos2mnmnkLmng gq 1211 arccos2mnqcqmng gL方形鏡穩(wěn)定腔的諧振頻率：方形鏡穩(wěn)定腔的諧振頻率：同理可得圓形鏡穩(wěn)定腔的諧振頻率：同理可得圓形鏡穩(wěn)定腔的諧振頻率：12121 arccos2mnqcqmng gL121arccos0qmng g 121arccos()qKg gmnK12arccos0,/2g g12KK12arccos/g g22/(2)/NafaL0SL220SaNN 鏡面面積鏡面上的光斑面積比值越大，衍射損耗越小220220iSiSaa22iefiSiaN定義為穩(wěn)定球面腔的有效菲涅爾數(shù)222111121111221122()()(1)()efSaaRL RRLagNg gRL RLLg222222122221222211()()(1)()efSaaRL RRLagNg gRL RLLg21111201222222212012111111efef