An efficient and accurate semivectorial spectral collocation method for analyzing polarized modes of rib waveguides

A novel solution method based on the semivectorial spectral collocation method with domain decomposition is proposed to calculate the modal characteristics of rib waveguides. We formulate the scheme in terms of the transverse magnetic components H_x and H_y. The optical field expanded by a suitable set of orthogonal basis functions and the refractive index profile are all represented on a grid of discrete points in each subdomain. In addition, the a priori determination of the scaling factor of Laguerre-Gauss (LG) functions is introduced by means of the effective index method. The subdomains are then patched by imposing the continuities of longitudinal electric component E_z and magnetic component H_z at all internal dielectric interfaces. Because of the zero divergence constraint of magnetic field vector explicitly included, the occurrence of spurious modes is prevented. The present method is tested for various rib waveguide structures with lossless or lossy materials. Even with a coarse mesh, our results are still found to be in good agreement with those produced by other various full-vectorial methods, but without complexity of the latter approaches.