目录?
第一章 .............................................................................................................................................. 2?第二章 .............................................................................................................................................. 2?第三章 .............................................................................................................................................. 7?第四章 ............................................................................................................................................ 17?第五章 ............................................................................................................................................ 28?第六章 ............................................................................................................................................ 30?第七章 ............................................................................................................................................ 31?第八章 ............................................................................................................................................ 32?第九章 ............................................................................................................................................ 33?
?
第一章?
4
为使氦氖激光器的相干长度达到1km, 它的单色性??/?0应当是多少?
解:相干长度LC?
c
,??是光源频带宽度 ??c3*108m/s?????3*105Hz
LC1km
c
??22
(c/?)??
632.8nm???5?10
*3*10Hz6.328*10??????
c3*108m/s???
c
????
c
???
第二章?
2 3
如果激光器和微波激射器分别在??10?m,????500nm,?????3000MHz时输出1W连续功率,问每秒钟从激光上能级向下能级跃迁的粒子数是多少?
E?h??h
c
?P?NE?N?
P?hc
h?6.3*10?34J?s???c?3*108m/s解1:
N1W*1*10?5m19
1?6.3*10?34J?s*3*108m/s
?5.03*10/s
N1W*5*10?7m18
2?6.3*10?34J?s*3*108
m/s?2.5*10/sNPh??1W23
3?6.3*10?34
J?s*3000MHz?5.03*10/s解2:n?P*tP*t
h?? hc?当??10?m时 n?P*t*?h*c?1*1*10*10?66.63*10?34
*3*108?5.03*1019 当??500nm时 n?P*t*?h*c
?1*1*500*10?96.63*10?34
*3*108?2.51*1018 当??3000MHz时 n?P*th*??1*16.63*10?34
*3000*10
6?5.03*1023 4
设一对激光能级为E2,E1,f2?f1,相应的频率为?,波长为?,能级上的粒子数密度分别为n2,n1,求:
(1)当??3000MHz,???T?300K时,n2/n1?? (2)当??1?m,???T?300K时,n2/n1?? (3)当??1?m,???n2/n1?0.1时,温度T=?
nE2?E1
2f2k0T
n?e?
,f2?f1,k0?1.38*10?23J/K
1f1
解:E2?E1?h??hc/?
(1).????????????
n2
?en1
?
6.63*10?34J?s*3000MHz1.38*10?23J/K*300K
?e?4.799*10?1
?4
(2)?????1?m
?n2
?en1
6.63*10?34J?s*
3*108m/s
1*10?6m
1.38*10?23J/K*300K
?e?47.99?1.44*10?21?0 h?c
??n2
(3)????ekT?T??
n1
h?
c
??n?k?ln?2?
?n1?
?6252.9K
?n2
解2:?e
n1
E2?E1kbT
其中??
?
h*ch*ch*c
?E??h? ?
?EE2?E1?(1)
n2
?en1
?
h*ckb*T
6.63*10?34*3*1091.38*10?23*300
?e
?e?4.8*10?1
?4
??n2kbT
(2)?e?e
n1
h
c
?6.63*10?34*1.38*10
?23
3*108
10?6*300
?e?48?1.425*10?21?0 c
(3)
n2
?en1
h*c?kbT
?ln
n2
??? n1kbT
h
h*c6.63*10?34*3*108???6.26*103K 所以T???23?6n1.38*10*10*ln(0.1)kb?ln2n1
5
解:(1)?E?E2?E1?h*v?6.63*10(2) 6
n2
?en1
?
?34
3*108?20*?3.978*10J ?65*10
E2?E1kbT
?e
?
3.978*10?201.38*10?23*300
?e?9.6?6.773*10?5
n2f2?
解:(1)?*e
n1f1n2?n1
f2ef1
?
E2?E1kbT
其中:E2?E1?1.64*10?18J,T?2700K,n1?1020,
?
1.64*10?181.38*10?23*2700
f2
?4 f1
E2?E1kbT
?1020*4*e?1020*e?44?31.12
(2)P?h*v*108n2?(E2?E1)*108*n2?1.64*10?18*108*31.12?5.1*10?9w 7
2-7. 若激光工作物质的某一跃迁波长为100nm的远紫外光,自发跃迁几率A21?106s?1,求:(1)该跃迁的受激辐射爱因斯坦系数B21是多少?(2)为使受激辐射跃迁几率比A21大3倍,腔内的单色能量密度??应为多少?解:(1)A218?h?3=3?B21cc8?h()3c3??8?h?3A10?3106(100?10?9)316?13?2?B21=??6?10J?m?s8?h8?3.14?6.63?10?34(2)W104A104?106?11?3W10?B10??=4A10???????6.7?10J?m?s16B10B106?10 A218*?*h*v3
? 解:(1)3B21c
A21*c3106*(10?7)316?1 B21???6*10s3?34
8*?*h*v8*3.14*6.63*10
(2)受激辐射跃迁概率W21?B21?v自发辐射概率A21
B21*?v4*A214*106?113
R??4所以?v???6.67*10w/m 16
A21B216*10
8
A218*?*h*v38*?*h
?? 解:(1)??6?m由公式:33B21c?
激光原理作业答案 - 图文
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