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Computation of Complex Eigenmodes for Resonators Filled With Gyrotropic Materials

Explicit expressions for the permittivity and inverse permeability tensor for gyrotropic materials are derived for the finite integration technique (FIT) in frequency domain. In contrast to the standard FIT, the material matrices exhibit nondiagonal elements. The obtained expressions are fully consistent with the standard FIT when applied to nongyrotropic materials. Furthermore, the manifestly Hermitian matrix structure in the lossless case enables numerically stable simulations. Since the gyrotropic characteristics notably depend on the bias magnetic field and on the frequency of the superimposed field, a dedicated solver to determine the field distributions in practical applications has been developed. In particular, emphasis has been put on the implementation to enable efficient computing. Finally, the extended formulation is applied to the computation of eigenmodes of biased cavity resonators of cylindrical and rectangular shape, which are filled with material exhibiting both gyromagnetic and gyroelectric characteristics. For the latter resonator, material losses are included. The validity of numerically obtained results is confirmed by comparison with semianalytical calculations.