Electromagnetic modelling of material loaded cavity resonators with a filling hole for complex resonant frequency determination

The electromagnetic modelling of cavity resonators loaded with dielectric material is important with respect to corresponding material measurements. In this paper, a variational technique is employed to determine the complex resonant frequencies of the loaded cavity resonator. Inhomogeneous impedance boundary conditions are considered to take the effects of lossy walls and the filling hole of the resonator on the resonance into account. An eigenmode expansion of the magnetic field appearing in the variational formulation results in a nonlinear eigenvalue problem in terms of the complex resonant frequency. An iterative scheme is employed to solve the nonlinear eigenvalue problem. Given an initial guess, the nonlinear eigenvalue problem is approximated by a quadratic eigenvalue problem. The approximated quadratic eigenvalue problem is transformed to a generalized eigenvalue problem that is solved by using the generalized Schur decomposition. Also, the inverse problem, where the complex wavenumber is measured and the material parameter is to be determined, is discussed. In order to show the capabilities of the proposed method, the computed resonant frequencies are compared with measured data.