Analysis of optical waveguide discontinuities using the Pade approximants

We propose a novel method to solve efficiently the dielectric waveguide discontinuity problems. The reflection and transmission fields are expressed in terms of the characteristic matrices and the incident field. Instead of solving eigen systems, the square roots of the matrices are approximated by the Pade approximants. Therefore, the proposed method requires much less computation time and memory. It can also solve discontinuity problems with arbitrary input field and arbitrary refractive index distributions.