On Finite Element Methods for Inhomogeneous Dielectric Waveguides

We investigate the problem of computing electromagnetic guided waves in a closed, inhomogeneous, pillared three-dimensional waveguide at a given frequency. The problem is formulated as a generalized eigenvalue problem. By modifying the sesquilinear form associated with the eigenvalue problem, we provide a new convergence analysis for the finite element approximations. Numerical results are reported to illustrate the performance of the method.