三能级光纤激光器速率方程组的阈值解析解

 在考虑了泵浦损耗及激光损耗的情况下，解析求解了阈值泵浦下的三能级光纤激光器速率方程组，获得了泵浦功率阈值的显函数解析表达式，泵浦功率沿光纤变化的隐函数表达式，以及用功率变化表示的各个能级的粒子数密度随位置变化的显函数表达式。并利用这些表达式对光纤激光器的阈值特性进行了研究，研究表明：泵浦功率阈值随泵浦损耗系数增大而增大；激光上能级粒子数密度随归一化位置呈下降趋势，而下能级粒子数密度的变化与此相反；泵浦功率阈值越大(光纤长度越长),净增益系数随归一位置下降就越快。所获得的结果适用于单包层和双包层光纤激光器。

Solving rate equations including backgroud losses applicable to threshold pumped fiber lasers with three-energy-level dopants

An analytical expression of the threshold pump power of the fiber laser with three-energy-level dopants has been obtained from rate equations including loss coefficients of the pump and laser radiations.And the rate equations describing the threshold pumped fiber lasers have been analytically solved,following the derivation of the implicit expression specifying the pump power variation along the fiber and explicit expressions of the position dependent population densities on the three energy levels in terms of the pump power variation.With these expressions,threshold characteristics of the fiber lasers have been studied.The threshold pump power grows monotonously with the increase of the loss coefficient of the pump radiation.The population density of the upper level decreases with the normalized fiber position and that of the lower level increases with the normalized fiber position.For lasers with higher threshold pump power(or longer fibers),the net gain coefficient decreases faster than that with a lower threshold pump power.