Application of the transmission line matrix method to the analysis of slab and channel optical waveguides

The applicability of the three-dimensional vectorial transmission line matrix (TLM) method to the analysis of optical waveguiding structures is demonstrated. Any waveguide geometry, even incorporating anisotropic materials, can be treated by taking into account the coupling between all optical field components. The application of the TLM method to optical waveguides is shown to be both efficient and accurate. The dispersion curve for the fundamental TE-like mode of a typical rib dielectric waveguide as well as its electric-field pattern is obtained by the use of the TLM method. Numerical comparisons with the integral-formulation technique, the effective-index method, the finite-difference analysis, the spectral-index method, and the beam-propagation technique are also included.