中文摘要：

在引入光场与掺杂分布的重叠因子及忽略放大自发辐射（ASE）和光纤损耗的情况下,通过求解掺Yb^3＋光纤放大器（YDFA）的能级速率方程和光传输方程,得到了在稳态条件下YDFA的速率-传输方程组的解,推导出了泵浦阈值、放大器增益、最佳光纤长度的表达式.研究了泵浦光、信号光、掺杂浓度、最佳光纤长度、最佳光纤长度下增益之间的内在联系.最后对数值模拟结果进行了分析和讨论.

英文摘要：

The rate equations and light propagation equations were solved under the steady-state condition. In order to get the solution, the overlapping factors between the mode fields and the ytterbium dopant distribution is introduced, and the ASE and the loss inside the fiber is neglected. On the basis of the solution,the expressions of the pump threshold,gain and optimum fiber length were obtained. The relations were analyzed among the pumping power, input signal, ytterbium-doped concentration, optimum fiber length and gain of the optimum fiber length. The simulation results were discussed.