NUMERICAL MODELLING OF WAVEGUIDE INTERFACE By

ii We develop a computational algorithm for solving the stationary Maxwell equation at the interface between two planar waveguides. The algorithm operates with arbitrary refractive index profiles on both sides of the interface and with arbitrary incident electric field from one side. The algorithm computes the reflection and transmission coecients for trapped waveguide modes, radiation waves and edge states localized at the interface. We use spectral decompositions for one-dimensional Schrodinger operators and diagonalization of two symmetric matrices. By solving a set of linear equations at the interface between two waveguides, the numerical solution represents a full picture of electric and magnetic field distributions in each waveguide. We also study absorbing layers in order to absorb outgoing waves from artificial boundary-reflected waveguides. By using a complexification of transverse space we introduce a thin absorbing layer on the boundaries of the computational domain