深圳大学：《激光原理》课程教学课件（PPT讲稿）第四章 激光振荡特性 第三部分 输出功率与能量

三输出功率与能量. In section 4.1 we derived an expression for thethreshold population inversion at which the lasergain becomes equal to the losses. We wouldexpect that as the pumping intensity is increasedbeyond the point at which N,-N,=N, the laserwill break into oscillation and emit power. In thissection we obtain the expression relating thelaser power output to the pumping intensity. Wealso treat the problem of optimum coupling-thatis, of the mirror transmission that results in themaximum power output

三 输出功率与能量 • In section 4.1 we derived an expression for the threshold population inversion at which the laser gain becomes equal to the losses. We would expect that as the pumping intensity is increased beyond the point at which N2 -N1 =Nt the laser will break into oscillation and emit power. In this section we obtain the expression relating the laser power output to the pumping intensity. We also treat the problem of optimum coupling-that is, of the mirror transmission that results in the maximum power output

·激光器稳态工作的建立·连续或长脉冲激光器的输出功率(output power)·短脉冲激光器的输出能量(output energy)

• 激光器稳态工作的建立 • 连续或长脉冲激光器的输出功率 (output power) • 短脉冲激光器的输出能量(output energy)

In chapter 3 we found that an atomic mediumwith an inverted population (N,>N) is capableof amplifying an electromagnetic wave if thelatter's frequency falls within the transitionlineshape. Consider next the case in which thelaser medium is placed inside an opticalresonator

• In chapter 3 we found that an atomic medium with an inverted population (N2>N1 ) is capable of amplifying an electromagnetic wave if the latter’s frequency falls within the transition lineshape. Consider next the case in which the laser medium is placed inside an optical resonator

: As the electromagnetic wave bounces back andforth between the two reflectors it passed troughthe laser medium and is amplified. If theamplification exceeds the losses caused byimperfect reflection in the mirrors and scatteringin the laser medium, the energy stored in theresonator will increase with time. This causesthe amplification constant to decrease as a resultof gain saturation

• As the electromagnetic wave bounces back and forth between the two reflectors it passed trough the laser medium and is amplified. If the amplification exceeds the losses caused by imperfect reflection in the mirrors and scattering in the laser medium, the energy stored in the resonator will increase with time. This causes the amplification constant to decrease as a result of gain saturation

: The oscillation level will keep increasing untilthe saturated gain per pass just equals thelosses. At this point the net gain per pass isunity and no further increase in the radiationintensity is possible-that is, steady stateoscillation obtains

• The oscillation level will keep increasing until the saturated gain per pass just equals the losses. At this point the net gain per pass is unity and no further increase in the radiation intensity is possible-that is, steady state oscillation obtains

（一）激光器稳态工作的建立当g(v)>g,时，dN/dt>0，腔内光强不断增加。无限增加?如果腔内某一振荡模式的频率为V。，开始时，由于g(vg,lv)>g.，腔内光强Iv.逐渐增加，同时由于饱和效应，g(vg,Ivq)将随Ivg的增加而减少，但只要g(vg,lvg)仍比g,大，这一过程就将继续下去，即Ivg继续增加，g(vq,lvq)不断减小，直到g(vg,v。)=g,=8/1,增益和损耗达到平衡，Iv.不再增加。这时，激光器建立了稳定工作状态

（一）激光器稳态工作的建立 如果腔内某一振荡模式的频率为q，开始时，由于 q gt g I q ( ,  )  , 腔内光强Iq逐渐增加，同时由于饱 和效应，g(q ,Iq ) 将随Iq的增加而减少，但只 要g(q ,Iq ) 仍比gt大，这一过程就将继续下去， 即Iq 继续增加， g(q ,Iq ) 不断减小，直到 g I g l q t q ( ,  ) = = ,增益和损耗达到平衡，Iq不再 增加。这时，激光器建立了稳定工作状态。 当g 0 ()>gt时，dNl /dt>0，腔内光强不断增加。无限增加?

·当外界激发作用增强时，小信号增益系数g(v)增大，此时I必须增大到一个更大的值才能使g(vg,va)降低到g,并建立起稳定工作状态，因此激光器的输出功率增加。·稳态工作时的大信号增益系数总是等于gt·结论：在一定的激发速率下，即当g°(v)一定时，激光器的输出功率保持恒定；当外界激发增强时，输出功率随之上升，但在一个新的水平上保持恒定

• 当外界激发作用增强时，小信号增益系数g 0 () 增大，此时Iq必须增大到一个更大的值才能 使g(q ,Iq ) 降低到gt并建立起稳定工作状态， 因此激光器的输出功率增加。 • 稳态工作时的大信号增益系数总是等于gt 。 • 结论：在一定的激发速率下，即当g 0 ()一定 时，激光器的输出功率保持恒定；当外界激 发增强时，输出功率随之上升，但在一个新 的水平上保持恒定

(二)连续或长脉冲激光器的输出功率1、均匀加宽单模激光器??腔内平均光强Ivq在驻波型激光器中，腔内存在着沿腔轴方向传播的光I和反方向传播的光I，二者同时参与饱和作用如果T<<1，稳态工作时增益系数也很小，近似认为I=I.，腔内平均光强Ivg=2 I+gh(vg)d稳态情况下，gh(vg,Iv)=g,V求得腔内平均光强为s

（二）连续或长脉冲激光器的输出功率 1、均匀加宽单模激光器 ??腔内平均光强Iq 在驻波型激光器中，腔内存在着沿腔轴方向传播的光 I+和反方向传播的光I-，二者同时参与饱和作用 如果T<<1，稳态工作时增益系数也很小，近似认为 I+ =I-，腔内平均光强Iq=2 I+。 稳态情况下， 0 ( ) 1 ( ) q H q s q g I l I     = + 求得腔内平均光强为 0 ( ) ( ) 1 q H q s q g l I I       = −       ( , ) H q t q g I g   =

??输出功率设激光束的有效截面面积为A，则激光器的输出功率为g%(vg)lP= ATIAT-s21）在T<<1时，28=T+α，α为往返指数净损耗因子，通常α<<1。上式改写为2gh(ATIP2a+T

??输出功率 设激光束的有效截面面积为A，则激光器的输 出功率为 0 1 ( ) ( ) 1 2 H q s q g l P ATI ATI    +   = = −       1）在T<<1时， ，a为往返指数净损 耗因子，通常a<<1。上式改写为 2 =T +a 0 1 2 ( ) ( ) 1 2 H q s q g l P ATI a T     = −     +  

PTPgh(vg)A2)光泵激光器0n2Pg,V.S28ptptP,及Ppt分别为工作物质吸收的泵浦功率及阈值吸收泵浦功率，S为工作物质横截面面积耦合系数：no=To/28P=n.(P, -Pnt)=1ns称为斜率效率pt结论：一旦激光器确定了，斜率效率就确定了；输出功率随泵浦功率线性增加。上式对于放电激励的气体激光器例外

2）光泵激光器 Pp及Ppt分别为工作物质吸收的泵浦功率及阈 值吸收泵浦功率，S为工作物质横截面面积 0 ( ) H q p t pt g P g P  = 0 1 ( 1) 2 P pt p pt A T P P P S P     = − ( ) ( 1) p s p pt s pt pt P P P P P P = − = −   s称为斜率效率 结论：一旦激光器确定了，斜率效率就确定了； 输出功率随泵浦功率线性增加。 上式对于放电激励的气体激光器例外 耦合系数：0=T0 /2