A variational analysis of anisotropic, inhomogeneous dielectric waveguides

Abstract

The authors derive a variational formulation for anisotropic, dielectric waveguides using only the (Ex, Ey) or only the (Hx, Hy) components of the electromagnetic field. They show that the (Ex, Ey) formulation is completely equivalent to the (Hx, Hy) formulation. In fact, they are the transpose problems of each other. Given the variational formulation, one can derive the finite-element solution quite easily. The authors also show how to derive a variational expression where the natural boundary conditions are incorporated as an optimal solution of the variational expression. The theory is illustrated with a simple implementation of a finite-element solution. The solutions agree with previous results, and there is no occurrence of spurious modes.