Application of finite-difference method for numerical investigation of eigenmodes of anisotropic optical waveguides with an arbitrary tensor

In this paper 3D finite-difference methods is developed for analyzing anisotropic optical waveguides. An eigenvalue matrix equation is derived through considering simultaneously four transverse field components. The numerical results show that the proposed scheme is highly efficient and yields complex effective indices while requiring match less computer memory and calculation time than the commonly used methods. Algorithm is used to study modes on a electrooptic polymer waveguide and a liquid-crystal optical waveguide with arbitrary director orientation, clearly demonstrated in the numerical examples.