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1、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 se
2、ction 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),In chapter 3 we foun
3、d that an atomic medium with an inverted population (N2N1) is capable of amplifying an electromagnetic wave if the latters 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
4、 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 amplificatio
5、n constant to decrease as a result of gain saturation.,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 ob
6、tains.,（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, 腔内光强Iq逐渐增加，同时由于饱,和效应，g(q,Iq) 将随Iq的增加而减少，但只要g(q,Iq) 仍比gt大，这一过程就将继续下去，即Iq 继续增加， g(q,Iq) 不断减小，直到,增益和损耗达到平衡， Iq不再,增加。这时，激光器建立了稳定工作状态。,当g0()gt时，dNl/dt0，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g0()增大，此时Iq必须增大到一个更大的值才能使g(q,Iq) 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
7、数总是等于gt 。 结论：在一定的激发速率下，即当g0()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Iq 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T1，稳态工作时增益系数也很小，近似认为I+=I-，腔内平均光强Iq=2 I+。 稳态情况下，,求得腔内平均光强为,?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,1）在T1时， ，a为往返指数净损耗因子，通常a1。上式改写为,2）光泵激光器 Pp及
8、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,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,The total loss encountered by the oscillating laser mode can conveniently be attributed to two different sources: (a) the inevitable residual loss due to absorption and scattering in the l
9、aser material and in the mirrors, as well as diffraction losses in the finite diameter reflectors; (b) the (useful) loss due to coupling of output power through the partially transmissive reflector. It is obvious that loss (a) should be made as small as possible since it raise the oscillation thresh
10、old without contributing to the output power.,The problem of the coupling loss (b), however, is more subtle. At zero coupling (that is, both mirrors have zero transmission) the threshold will be at its minimum value and the power emitted by the atoms will be maximum. But since none of this power is
11、available as output, this is not a useful state of affairs. If on the other hand, we keep increasing the coupling loss, the increasing threshold pumping will at some point exceed the actual pumping level. When this happens, oscillation will cease and the power output will again be zero. Between thes
12、e two extremes there exists an optimum value of coupling (that is, mirror transmission) at which the power output is a maximum.,3）最佳透射率及功率 输出功率和反射镜的透射率T有关。当T增大时，一方面提高了透射光的比例，有利于提高输出功率，同时又使阈值增加，从而导致腔内光强的下降。,在透射率T1时，令dP/dT=0，求出最佳透过率Tm,最佳输出功率,Maximizing P with respect to T by setting yields as the cond
13、ition for the mirror transmission that yields the maximum power output.,（1）q0 （多普勒非均匀加宽） I+和I-两束光在增益曲线上分别烧两个孔，对每一个孔起饱和作用的分别是I+或I-，而不是二者的和。 振荡模的增益系数为,2、非均匀加宽单模激光器的输出功率,激光器稳态工作时,（2）q=0 I+和I-两束光同时在增益曲线上中心频率处烧一个孔，烧孔深度取决于腔内平均光强I0。,稳定工作时振荡模的增益系数为,求得腔内平均光强为,输出功率,兰姆凹陷： 在单模输出功率P和单模频率q的关系曲线中，在q=0处，曲线有一凹陷，称作兰姆
14、凹陷。,由于两个烧孔在 时开始重叠，所以兰姆凹陷的宽度大致等于烧孔的宽度，即,兰姆凹陷形成的机制： 当q=0时，两个烧孔完全重合，此时只有z=0附近的原子对激光有贡献。虽然它对应着最大的小信号增益，但由于对激光作贡献的反转集居数减少了，即烧孔面积减少了，所以输出功率下降到某一极小值，Pq关系曲线在0处出现兰姆凹陷,凹陷的深度和激发参量gml/成正比，当gml/小时兰姆凹陷变浅，当gml/很小时，兰姆凹陷消失。,激光管的气压增高时，碰撞线宽增加，兰姆凹陷变宽、变浅。当气压高到一定程度，谱线加宽以均匀加宽为主时，兰姆凹陷消失,If the oscillation frequency is equa
15、l to0, only a single “hole” exists in the velocity distribution function of the inverted atoms. This “hole” is centered on Z=0. We may, thus, expect the power output of a laser oscillating at =0 to be less than that of a laser in which is tuned slightly to one side or the other of0 (this tune can be
16、 achieved by moving one of the laser mirrors). This power dip first predicted by Lamb is indeed observed in gas lasers. The phenomenon is referred to as the “Lamb dip” and is used in frequency stabilization schemes of gas lasers.,3、多模激光器的输出功率,在非均匀加宽激光器中，每个模式各自消耗表观中心频率与其频率相应的激活粒子。如果模间隔足够大，各个模式相互独立，分别计算每个纵模的输出功率，总的输出功率是各模输出功率之和。 在均匀加宽激光器中，由于各模式相互影响，必须由多模速率方程求出输出功率。在矩形线型函数及各模损耗相同的假设下，得出其输出功率可由
