Two-dimensional analysis of optical waveguides with a nonuniform finite difference method

A nonuniform finite difference method is presented for an analysis of arbitrarily-shaped optical waveguides. By introducing preconditioning of discretised coefficient matrices by similarity transformations, it has become possible to improve the accuracy of the solution without paying any penalty in terms of computing time. From the comparison between the exact analytical method and the nonuniform finite difference method for an analysis of planar slab waveguides, it has been clarified that the mesh refinement near the material interfaces plays a dominant role in determining the accuracy of solutions. Furthermore, the nonuniform finite difference method is used to model buried-channel waveguides and is compared with the effective-index method