固體激光器諧振腔課件

1、1v5.0 預(yù)備知識v5.1 熱透鏡腔和基模動態(tài)穩(wěn)定腔2v基模高斯光束的基本性質(zhì)v光學(xué)傳輸矩陣vABCD法則v諧振腔的本征方程和穩(wěn)定性條件v穩(wěn)定腔與基模高斯光束vG參數(shù)等價腔v非穩(wěn)腔32222( )( )020( , )( )( )1( )krrikz R zzAA r zee zz zfzfR zffzzarctgf422( )rwze522220( )1zzf6( )zfR zffz722( , )( )2 ( )2 ( )kr r zkz zR zkrR zkzzarctgf總相移：總相移：幾何相移：幾何相移：徑向相移：徑向相移：附加相移：附加相移：820f9 00limz zz1021

2、1( )( )( )iq zR zz0qif211Re( )1Im( )R zqzq110101rrA BC D 離軸距離光線與軸線距離Rr符符號號規(guī)規(guī)則則：，出出射射點點位位于于軸軸線線上上方方，向向軸軸線線上上方方出出射射，出出射射點點位位于于軸軸線線下下方方，向向軸軸線線下下方方出出射射，光光線線遇遇到到凹凹面面球球面面半半徑徑，光光線線遇遇到到凸凸面面12L101L131n2n12100nn141n2n1212210()nnnnn RR151021RR161011ff1712101nLnL1n2n1n181121211ABCDDCAqBqqBCqDqAq或或1q2q19ABMCD往往返

3、返矩矩陣陣：abcdMXX特特征征方方程程：()00ME XABXCD1ADBC2()10AD 2021,2122ADAD121122ADADAD 為為復(fù)復(fù)數(shù)數(shù)穩(wěn)穩(wěn)定定腔腔：-1-1為為實實數(shù)數(shù)非非穩(wěn)穩(wěn)腔腔：或或211210102211ABdbabCDcacdRR abcd1R2R2211211222222222abAadb cBbdb dRRdbadbbCa cacDb cadRRRRRR 22111AqBqCqD2111122DAADiqBB211111iqR2112212BBRDAAD231211bbGaGdRR222121212221222421aGbGABCDaG GGa GG Ga

4、Gb1212120110G GG GG G穩(wěn)穩(wěn)定定腔腔條條件件：非非穩(wěn)穩(wěn)腔腔條條件件：或或24122jiij1iiiGRRbGG G 212120121212212120222112G1GG2G1 GGG2 GbGG GaaG GbGGddG 21012121212022211222bGaGLGa GaGGbG dGLGd GdGG25*1122gGgGLb*12*1212110g gg gg g穩(wěn)穩(wěn)定定腔腔條條件件：00非非穩(wěn)穩(wěn)腔腔條條件件：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放放大大倍倍數(shù)數(shù)：abcd1R2R1O2O01L02L28abcd1R2R1O2O01L02L1DCRBRAR211122DAADRBB29abcd1R2R1O2O01L02L2121212211122ADADADMMDAADRBB30abcd1R2R1O2O01L02L2221212211122ADADADMMDAADRBB 312121(1)1112qqzqqF自自由由空空間間傳傳播播：（ ）過過薄薄透透鏡鏡：求證：穩(wěn)定腔的判據(jù)為：求證：穩(wěn)定腔的判據(jù)為：120()()1bbadRR

6、求證：對于高斯光束求證：對于高斯光束32一、熱透鏡腔二、基模動態(tài)穩(wěn)定腔三、基模動態(tài)穩(wěn)定望遠鏡腔四、類透鏡介質(zhì)中的高斯光束332201( ),(0)2n rn r正透鏡正透鏡負透鏡負透鏡lr22221cos()sin()1, ( )(1)2sin()cos()1c ()s ()1, ( )(1)2s ()c ()zzn r rzzh zh zn r r h zh z類類透透鏡鏡介介質(zhì)質(zhì)中中的的傳傳播播矩矩陣陣：正正透透鏡鏡：負負透透鏡鏡：34lr00001cos()sin()sin()cos()1()()()()lln n zlch lsh ln n sh lch l考考慮慮兩兩端端面面的的折折

7、射射后后，類類透透鏡鏡的的傳傳播播矩矩陣陣：正正透透鏡鏡：負負透透鏡鏡：351222111212121212121212121212122210101011111blnnnnnncdn Rnn Rnnnnlln RnbcdnnnnnnllnRRnR Rn R厚厚透透鏡鏡的的傳傳播播矩矩陣陣：a aa al1R2R361R2Rl1h2hf212121211011110101111hhfhhhhhffhff等等效效矩矩陣陣：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正正透透鏡鏡負負透透鏡鏡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穩(wěn)穩(wěn)定定腔腔條條件件：00g g*121211221201111111iijg gg gDRdRdDdRdDdd , ,臨臨界界條條件件：或或臨臨界界光光焦焦度度：43*1222211211()d dgggggddg122211d dgkddg21gkg21gkg44451111ABCD2222ABCD3R2R1R1M2Mf311()(1)ssRRdn輸輸出出鏡鏡的的“匹匹配配”條條件件：46穩(wěn)定腔球面輸出鏡如圖所示：為使輸出面處的等穩(wěn)定腔球面輸出鏡如圖所示：為使輸出面處的等相位面為平面，（光從左向右傳播）求證：相位

10、面為平面，（光從左向右傳播）求證：211()(1)RRdn2R1Rdn47*121穩(wěn)穩(wěn)定定腔腔條條件件：0 0 g g10ddf基基模模動動態(tài)態(tài)穩(wěn)穩(wěn)定定條條件件：12*221*112gg 1 g gL2*112*12221122BBggBgB482*112*12221122BBggBgB2*112*12221122ddggdgd1212*1212BBddg g 或或熱不靈敏熱不靈敏腔條件腔條件深度熱穩(wěn)腔條件深度熱穩(wěn)腔條件49激光輸出方向激光輸出方向10d 501d2dl l1M2Mf1f2f1212fMflff 望望遠遠鏡鏡系系統(tǒng)統(tǒng)放放大大率率：離離焦焦量量：51*1122112Bg gB20

11、 2211112221221122112111222221221121212dffflffl dlffdfdffflfdfffflfffl dlffdfdfffflff f f522201( ),(0)2n rn r22002( )(1)21nn rnrnfn l熱熱透透鏡鏡：201fn l5302202022220002200202222000cos()sin(),0sin()cos()c ()s (),0s ()c ()nnnzznnnnnnnzznnnnnnhzhznnnnnnnhzhznnn正正透透鏡鏡：負負透透鏡鏡：54220002222020022000222202001cos()sin(),0sin()cos()1c ()s (),0s ()c ()nnz