Complex eigenvalues of natural TM-oscillations in an open resonator formed by two sinusoidally corrugated metallic strips

The diffraction of an E-polarized plane wave from two finite sinusoidal gratings is investigated by a rigorous approach, based on the Method of Analytical Regularization. This allows us to analyse the problem in a wide frequency band without limitations on the depth of the sinusoidal corrugation, the wave size of the gratings, or their relative location. The homogeneous version of the equations obtained is used for accurate computation of the complex eigenvalues in an open resonator of Fabry–Perot type with sinusoidally corrugated strips. In the calculations, two types of structures were used: one is formed by parallel translation of the sinusoidally corrugated strips and the other is obtained by rotation of one of the strips in the first structure. For each relative location of the corrugated strips, the resonance excitation of the structure by an obliquely incident E-polarized plane wave is considered. Based on the calculation of the surface current density for different incidence angles, their specific values for optimal excitation of the complex modes are established.