第13讲_圆形镜共焦腔、一般稳定球面腔

1、112mnmnmnmn 2202200( , )22SrmmimmnmnnSSrrrCLee0,2mnSrCLfL其中为镜面的极坐标为归一化常数为共焦腔长度为镜面上的光斑半径 00122!()()! !( - )!111122 22knmnkmmmnmLmkk n kLLmLmmm 为缔合拉盖尔多项式(21)/2i kLmnmne对应本征值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 有确有确定的定的等价等价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方形镜稳定腔的谐振频率：方形镜稳定腔的谐振频率：同理可得圆形镜稳定腔的谐振频率：同理可得圆形镜稳定腔的谐振频率：12121 arccos2mnqcqmng gL121arccos0qmng g 121arccos()qKg gmnK12arccos0,/2g g12KK12arccos/g g22/(2)/NafaL0SL220SaNN 镜面面积镜面上的光斑面积比值越大，衍射损耗越小220220iSiSaa22iefiSiaN定义为稳定球面腔的有效菲涅尔数222111121111221122()()(1)()efSaaRL RRLagNg gRL RLLg222222122221222211()()(1)()efSaaRL RRLagNg gRL RLLg21111201222222212012111111efef