A variational analysis of anisotropic, inhomogeneous dielectric waveguides

The authors derive a variational formulation for anisotropic, dielectric waveguides using only the (E/sub x/, E/sub y/) or (H/sub x/, H/sub y/) components of the electromagnetic field. They show that the (E/sub x/, E/sub y/) formulation is completely equivalent to the (H/sub x/, H/sub y/) 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.<>