Complex Resonances of a Hard Rectangular Cavity Coupled to a Half-Space Through a Narrow Aperture

Electromagnetic coupling through a small slot into a two-dimensional rectangular cavity is computed via a simple Ritz-Galerkin expansion of the aperture field for the case of transverse electric (TE) polarization. One term expansions for each of the symmetric and antisymmetric dynamic aperture fields use the exact solutions for harmonic potentials that solve the related Neumann problem of a slot in a hard plane. Source-free solutions exist at discrete, complex-values of the frequency variable. These eigenfunctions of the negative Laplacian are improper modes and several of the low-order, complex resonances are found from zeros of the variational expression that relates the aperture field to the excitation. The complex resonances are perturbations of the real, closed-cavity resonances and their presence is unmistakable in the net stored energy in the cavity under plane-wave excitation from the exterior half-space.