A vectorial variational mode solver and its application to piecewise constant and diffused waveguides

A Variational Vectorial Mode Solver for 3-D dielectric waveguides with arbitrary 2-D cross-sections is proposed. It is based on expansion of each component of a mode profile as a superposition of some a priori defined functions defined on one coordinate axis times some unknown continuous coefficient functions, defined on the other axis. By applying a variational restriction procedure the unknown coefficient functions are determined as an optimum approximation of the true vectorial mode profile. A couple of examples illustrate the performance of the method.