Variational principles for electromagnetic resonators and waveguides

Variational expressions are presented for the propagation constants of a waveguide and for the resonant frequencies of a cavity directly in terms of the field vectors for situations not covered in the literature. These situations occur when the electromagnetic problem is not susceptible of a scalar formulation and are typified by the presence of inhomogeneous or anisotropic matter. The variational expressions are applied to several illustrative examples and the results are compared to known exact solutions. The variational expressions are also applied to the derivation of certain perturbation formulas, some of which were previously obtained by different methods.