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1、,一 激光器的振荡阈值(threshold),Operation at threshold阈值反转集居数密度阈值增益系数连续或长脉冲激光器的阈值泵浦功率短脉冲激光器的阈值泵浦能量,（一）阈值反转集居数密度(population inversion density at threshold),能否产生振荡，取决于增益与损耗的大小。谐振腔的长度L往往大于工作物质的长度l，假设谐振腔中光束体积为VR，工作物质中的光束体积为Va，谐振腔中折射率均匀分布，则第l个模式的光子数变化的方程,假设光束直径沿腔长均匀分布,L为谐振腔光程长度,当 时，腔内辐射场可由微弱的自发辐射场增长为足够强的受激辐射场。考虑到
2、在阈值附近腔内光强很弱，相当于小信号情况，得出自激振荡的阈值条件为,不同模式具有不同的21(,0)值，频率为0的模式阈值最低，表示为,（二）阈值增益系数,激光自激振荡时，小信号增益系数满足,不同纵模具有相同的，因而具有相同的阈 值gt。不同的横模具有不同的衍射损耗，因而有不同的阈值，高次横模的阈值比基模大。,增益曲线,谐振腔模谱,激光器起振模谱,（三）连续或长脉冲（t02）激光器的阈值泵浦功率(pump threshold),Lasers are commonly classified into the so-called“three-level”or“four-level”lasers.,1
3、、四能级激光器的阈值泵浦功率,E3能级向E2能级无辐射跃迁的量子效率,E2能级向E1能级跃迁的荧光效率,总量子效率,复习以下概念,激光下能级E1是激发态，其无辐射跃迁几率S10很大，因而n10，,工作物质必须从光泵吸收n2t/(Fs)光子数，为此须吸收的泵浦功率称作激光器的阈值泵浦功率，以 Ppt表示,V为工作物质的体积，p为泵浦光频率,E2能级集居数密度的阈值为,当n2稳定于n2t时，E2 E1，即n2t/(2s),为保证稳定，单位时间内必须 E3E2，n2t/(2s),(A21+S21)n2t,E0E3，n2t/(Fs),For a four-level laser,the feature
4、 characterizing this laser is that the separation E1 of the terminal laser level from the ground state is large enough that at the temperature T at which the laser is operated,E1 kT.This guarantees that the thermal equilibrium population of level 1 can be neglected.If,in addition,the lifetime t1 of
5、atoms in level 1 is short compared to t2,we can neglect N1 compared to N2 and the threshold condition is satisfied when N2Nt.Therefore,laser oscillation begins when the upper laser level acquires,by pumping,a population density equal to the threshold value Nt.,参与激光作用的下能级是基态，有,一般有,须吸收的阈值泵浦功率为,2、三能级激光
6、器的阈值泵浦功率,采用与四能级系统类似的方法分析,A three-level laser is one in which the lower laser level is either the ground state or a level whose separation E1 from the ground state is small compared to kT,so that at thermal equilibrium a substantial fraction of the total population occupies this level.At a pumping le
7、vel that is strong enough to create a population N2=N1=N0/2 in the upper laser level,the optical gain is zero.To satisfy the oscillation condition the pumping rate has to be further increased until,（四）短脉冲激光器的阈值泵浦能量,若光泵激励时间很短，在激励持续期间E2能级的自发辐射和无辐射跃迁的影响可以忽略不计。在这种情况下，要使E2能级增加一个粒子，只须吸收1/1个泵浦光子。当单位体积中吸收的泵
8、浦光子数大于n2t/1 时，就能产生激光。,四能级系统须吸收的光泵能量的阈值为,三能级系统须吸收的光泵能量的阈值为,四能级激光器与三能级激光器的比较,三能级系统所需的阈值能量比四能级系统大得多：四能级系统的激光下能级为激发态，n10，只须把nt个粒子激励到E2能级就可使增益克服腔的损耗而产生激光；在三能级系统中，激光下能级是基态,至少要将n/2(f1=f2)个粒子激励到E2能级才能形成粒子数反转三能级系统激光器中光腔损耗的大小对光泵阈值能量（功率）的影响不大。四能级系统的阈值能量（功率）反比于发射截面21，而21又反比于荧光谱线宽度F，故阈值能量（功率）正比于F。,小结：,end,（f1=f2）,
