Galerkin finite element scheme with Bayliss-Gunzburger-Turkel-like boundary conditions for vectorial optical mode solver

A Galerkin finite element scheme furnished with 1st-order Bayliss–Gunzburger–Turkel-like boundary conditions is formulated to compute both the guided and leaky modes of anisotropic channel waveguides of non-magnetic materials with diagonal permittivity tensor. The scheme is formulated using transverse components of magnetic fields for nodal-based quadratic triangular elements. Results for some structures will be presented. The effectiveness of the boundary conditions will be illustrated using a step-index optical fiber with computational boundaries positioned near to the core, and the leaky modes computation of a leaky rib structure. In addition, a leaky mode solving of a six-hole "photonic crystal fiber" will be demonstrated. The computed results agree with their exact values (for optical fibers) and published results (for other structures).