Generalized modal analysis of waveguides and resonators with discrete exterior calculus

A generalized modal analysis with discrete exterior calculus for 2-D or 3-D electromagnetic system is presented. For an arbitrarily shaped inhomogeneous system, discrete exterior calculus provides a simple way to formulate the problem based on a triangular or tetrahedral discretization. In this paper, circumcenter dual is adopted to achieve diagonal discrete Hodge star operators. We also consider signed dual volumes for all dimensions to keep the correctness and accuracy of discrete Hodge star operators. Traveling modes of inhomogeneous waveguides and resonant cavity modes are numerically calculated to validate this method.