Modal analysis of nonuniform dielectric waveguide using semivectorial finite-difference time-domain method

This paper develops a compact two dimensional finite-difference time-domain method for the modal analysis of nonuniform planar dielectric waveguide. The proposed method is derived by replacing ∂/∂_z with -jβ, and approximating the Maxwell equations with semivectorial wave equation. By introducing the new techniques, complex variables are avoided in the calculations, and the number of variables is minimized in the computation domain. The dominant electric fields with two perpendicular polarizations are solved. Unsplit-field perfectly-matched-layer absorbing boundary condition is extended to this approach. Numerical examples are given to substantiate the theory. Excellent accuracy is obtained for the entire frequency spectrum, even near the cutoff region.