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给出求含有增益层与损耗层的突变与渐变折射率剖面多层平板波导导模的微扰理论与解析计算公式。举例讨论了导模模式的增益（或损耗）与结构参数和偏振的关系。本文方法较求解复本征值的打靶法等简便且节省机时。对于（半导体激光器与半导体激光放大器等）实际遇到的波导结构能给出精确数值结果，并可用以分析材料的增益系数或损耗对ＴＥ和ＴＭ模式及其增益的影响等问题。
The perturbation theory and analytical formula of multi-layer slab waveguide guided mode with abrupt and graded refractive index profile containing gain layer and loss layer are given. An example is given to discuss the relationship between the gain (or loss) of the guided mode and the structural parameters and polarization. The method proposed in this paper is more convenient and time-saving than the method of solving eigenvalue. Waveguide structures actually encountered with (semiconductor lasers and semiconductor laser amplifiers, etc.) can give accurate numerical results and can be used to analyze the effects of material gain factors or losses on TE and TM modes and their gains.