激光原理与激光技术习题答案习题一(1)为使氦氖激光器的相干长度达到1m,它的单色性/应为多大?解:10101032861000106328.LRc(2)=5000Å的光子单色性/=10-7,求此光子的位置不确定量x解:hp2hphpxmRphx5101050007102(3)CO2激光器的腔长L=100cm,反射镜直径D=1.5cm,两镜的光强反射系数分别为r1=0.985,r2=0.8。求由衍射损耗及输出损耗分别引起的、c、Q、c(设n=1)解:衍射损耗:1880107501106102262.).(.aLs..cLc881075110318801686810113107511061010314322....QcMHz.Hz...cc19101910751143212168输出损耗:1190809850502121.)..ln(.rrlns..cLc881078210311901686810964107821061010314322....QcMHz.Hz...cc75107510782143212168(4)有一个谐振腔,腔长L=1m,两个反射镜中,一个全反,一个半反,半反镜反射系数r=0.99,求在1500MHz的范围内所包含的纵模个数,及每个纵模的线宽(不考虑其它损耗)解:MHzHz.Lcq15010511210328811]11501500[]1[qq005.0201.02TscLc781067.6103005.01MHzcc24.01067.614.321217(5)某固体激光器的腔长为45cm,介质长30cm,折射率n=1.5,设此腔总的单程损耗率0.01,求此激光器的无源腔本征纵模的模式线宽。解:cmL60155.130s106.3661030.01π0.6cL88c2.5MHz106.3663.1428cc121(6)氦氖激光器相干长度1km,出射光斑的半径为r=0.3mm,求光源线宽及1km处的相干面积与相干体积。解:0.3MHz10103Lc38c2221.42m)10π(3100.632810ADA241226sc331042.1mLAVccc习题二(1)自然加宽的线型函数为20220)(4)21(1),(ccHg求①线宽②若用矩形线型函数代替(两函数高度相等)再求线宽。解:①线型函数的最大值为cNg4),(00令ccc2)(4)21(12022ccc1)(821202cc21)(82022220161)(cc410cN21②矩形线型函数的最大值若为cmg4则其线宽为cmNg411(2)发光原子以0.2c的速度沿某光波传播方向运动,并与该光波发生共振,若此光波波长=0.5m,求此发光原子的静止中心频率。解:cvsz10cc15.02.0015.02.00m625.08.05.00MHzc86800108.410625.0103(3)某发光原子静止时发出0.488m的光,当它以0.2c速度背离观察者运动,则观察者认为它发出的光波长变为多大?解:mcccvz5856.0488.02.1488.0)2.01(100(4)激光器输出光波长=10m,功率为1w,求每秒从激光上能级向下能级跃迁的粒子数。解:hdtdPshcPhPdtdP/11051031063.610101198346(6)红宝石调Q激光器中有可能将几乎全部的Cr+3激发到激光上能级,并产生激光巨脉冲。设红宝石棒直径为1cm,长为7.5cm,Cr+3的浓度为2109cm-3,脉冲宽度10ns,求输出激光的最大能量和脉冲功率。解:JhLrVhW9108341522103.4106943103106.631020.0750.0053.14wtWP34.01010104.399(7)静止氖原子3S22P4谱线中心波长0.6328m,求当它以0.1c速度向观察者运动时,中心波长变为多大?解:mcccvz5695.06328.09.06328.0)1.01(100(9)红宝石激光器为三能级系统,已知S32=0.51071/s,A31=31051/s,A21=0.31031/s。其余跃迁几率不计。试问当抽运几率W13等于多少时,红宝石晶体将对=0.6943m的光是透明的?解:02123232AnSndtdn322123SAnn03233131313SnAnWndtdn)(323113132331313SAnnnSnAnW透明即n1=n2175733231322132312313318)105.0103(105.0103.0)()(sSASASAnnWS32A21W13A31习题三(1)若光束通过1m长的激光介质以后,光强增大了一倍,求此介质的增益系数。解:2lnln10IIzG(2)计算YAG激光器中的峰值发射截面S32,已知F=21011Hz,3=2.310-4s,n=1.8。解:222114221223222032109.1102103.28.114.341006.14mnSF(3)计算红宝石激光器当=0时的峰值发射截面,已知0=0.6943m,F=3.31011Hz,2=4.2ms,n=1.76。解:2241132212222220211084.2103.3102.476.114.34106943.04mnSF习题四(1)红宝石激光器腔长L=11.25cm,红宝石棒长l=10cm,折射率n=1.75,荧光线宽F=2105MHz,当激发参数=1.16时,求:满足阈值条件的纵模个数解:MHzHT45108116.11021cmlnLL75.1810)175.1(25.11)1(MHzLcq8001075.182103228101]180080000[]1[qTq(2)氦氖激光器腔长1m,放电管直径2mm,两镜反射率分别为100%、98%,单程衍射损耗率=0.04,若Is=0.1W/mm2,Gm=310-4/d,求①q=0时的单模输出功率②q=0+21D时的单模输出功率解:①05.004.0202.004.02TmmlGt/1105100005.05mmdGm/1105.121031034443105105.154tmGGmwSTIPs13.25)13(1.002.0114.35.0)1(222210②mweeSTIPiqs8.7)13(1.002.0114.3]1[2ln222)(2ln822200(3)氦氖激光器放电管长l=0.5m,直径d=1.5mm,两镜反射率分别为100%、98%,其它单程损耗率为0.015,荧光线宽F=1500MHz。求满足阈值条件的本征模式数。(Gm=310-4/d)解:025.0015.0202.0015.02TmmlGt/1105500025.05mmdGm/11025.1103103444410510254tmGGMHzDT21212ln4ln15002lnlnMHzLcq3005.02103288]13002121[]1[qTq(5)CO2激光器腔长L=1m,,放电管直径d=10mm,两反射镜的反射率分别为0.92、0.8,放电管气压3000Pa。可视为均匀加宽,并假设工作在最佳放电条件下。求①激发参数②振荡带宽T③满足阈值条件的纵模个数④稳定工作时腔内光强。(频率为介质中心频率0)经验公式:L=0.049p(MHz)、Gm=1.410-2/d(1/mm)、Is=72/d2(w/mm2)。解:①153.0)8.092.0ln(5.0ln2121rrmmlGt/11053.11000153.04mmdGm/1104.110104.1104.132215.91053.1104.143tmGG②MHzpL1473000049.0049.0MHzLT420115.91471③MHzHz.Lcq1501051121032883]1150420[]1[qTq④222/72.0107272mmwdIs2/87.515.872.0)1(0mmwIIs(6)氦氖激光器放电管直径d=0.5mm,长l=10cm,两反射镜反射率分别为100%、98%,不计其它损耗,稳态功率输出0.5mw,求腔内光子数。(设腔内只有0一个模式,且腔内光束粗细均匀)解:chTSTSIP2121cTShP2个716234103103.51031063.602.01063281.0105.022cTShPVV(7)CO2激光器腔长l=1m,放电管直径d=10mm,单程衍射损耗率d=0.5%,两镜面散射损耗率分别为1.5%,两镜透过率分别为2%、10%,其它损耗不计。当它工作在室温(300K)条件下时,求①激发参数②碰撞线宽及多普勒线宽,并判断它属于哪种加宽类型(设放电管中气压为最佳气压)③计算在最佳放电条件下稳定工作时,腔内的光强④若输出有效面积按放电管截面积的0.8计,此激光器的最大输出功率是多大?有关公式:Gm=1.410-2/d(1/mm)、Is=72/d2(w/mm2)、pd=2.67104PammL=0.049p(MHz)、D=7.1610-7021)(MT。解:①083.0)9.098.0ln(5.0015.0005.0ln015.0005.02121rrmmlGt/1103.81000083.05mmdGm/1104.110104.1104.13229.16103.8104.153tmGG②Padp3441067.2101067.21067.2MHzpL1311067.2049.0049.03MHzMTD5344300106.1021521560DL属于均匀加宽③222/72.0107272mmwdIs2/45.119.1572.0)1(0mmwIIs④04.02)015.0005.0(a2228.62514.3mmrSwalGSIPmsm49)04.010104.12(72.08.625.0)2(233221(8)He-Ne激光器放电管气压p=270Pa,上、下能级寿命分别为