Numerical simulation of waveguides of arbitrary cross-section

Finite difference equations are derived for the simulation of dielectric waveguides using an H-z-E-z formulation defined on a nonuniform triangular grid. The resulting equations may be solved as a banded eigenproblem for waveguide structures of arbitrary shape composed of regions of piecewise constant isotropic dielectric, and all transverse fields then computed from the solutions. Benchmark comparisons are presented for problems with analytic solutions, as well as a sample calculation of the propagation loss of a hollow Bragg fiber.