Unfortunately, owing to the nonlinear nature of the rate equations, it is difficult to obtain the exact analytical expressions.
然而，由于速率方程组的非线性特性，很难对之严格求解。
参考来源 - 端面抽运准二能级双包层光纤激光器的理论探讨·2,447,543篇论文数据，部分数据来源于NoteExpress
文中给出放大器的速率方程组的解，并在此基础上导出理想放大器的前三阶导数的解析表达式。
By finding out the solutions to the rate equations of the amplifiers, the analytical expressions of the derivatives, up to the third order, of Pout with respect to Pin have been deduced.
在考虑了俄歇效应的情况下，用行波速率方程组研究了半导体激光器的输出功率与端面反射率的关系。
Taking into account the Auger effect, the output-enhancement coatings applied to the facets of the semiconductor lasers have been investigated using a set of travelling wave rate equations.
在考虑了有限的下能级寿命和激光能级与晶格场的相互作用的基础上，对四能级激光的速率方程组进行了求解。
The rate equations for a continuous four level laser are solved in this letter, taking into account the finite lower level lifetime and the crystal field splitting of the laser levels.
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