A variational mode solver for optical waveguides based on quasi-analytical vectorial slab mode expansion

A flexible and efficient method for fully vectorial modal analysis of 3D dielectric optical waveguides with arbitrary 2D cross-sections is proposed. The technique is based on expansion of each modal component in some a priori defined functions defined on one coordinate axis times some unknown coefficient-functions, defined on the other axis. By applying a variational restriction procedure the unknown coefficient-functions are determined, resulting in an optimum approximation of the true vectorial mode profile. This technique can be related to both Effective Index and Mode Matching methods. A couple of examples illustrate the performance of the method.