So , it is looked forward to being more perfect . in this thesis , beginning with the maxwell equation , we mainly do the following work based on the rigorous mathematical analysis : firstly , we present the rigorous nonorthogonal vectorial cmt for the isotropic waveguide under isotropic disturbances and anisotropic disturbances respectively . during the derivation , it is fully reflected the property of the vector and the universal fitness without any approximation 本论文从maxwell方程出发,在严格的数学分析基础上主要做了以下两方面的工作:第一,分别严格地推导出了各向同性光波导在各向同性微扰和各向异性微扰下的非正交矢量耦合模理论,在推导过程中,考虑到电磁场的矢量性和非正交性且没有用到任何近似,因此具有普遍适用性。