General gyrotropic finite element formulation with loss

A four-transverse-field formulation for a lossless Hermitian tensor material was introduced previously for an arbitrary direction of applied bias field. This method is extended here to include loss, which is critical in modelling experimental devices and which causes variational functionals for gyrotropic waveguides to become non-Hermitian. The functional is developed from Maxwell's equations before demonstrating its stationary properties at the boundary value problem solution. Using the finite element method, the functional is implemented and then validated against various waveguide structures. For the first time, the Et - Ht formulation has been explicitly applied to lossy gyroelectric waveguide cross-sections. This method has important implications for the study and design of future phase shift and control components used in sub-millimeter wave and terahertz systems. Copyright © 2006 John Wiley & Sons, Ltd.