Effect of diffraction on the electrodynamic characteristics of two-dimensional coaxial Bragg resonators

The electrodynamic properties of coaxial two-dimensional Bragg resonators with two-dimensional distributed feedback are analyzed. These resonators are made of coaxial waveguide sections with doubly periodic corrugation, which provides coupling and mutual scattering of four partial waves. Two of them propagate along the waveguide, while the other two propagate in the transverse (azimuthal) direction. It is shown that the high azimuthal index selectivity of two-dimensional Bragg resonators may be related to a qualitative difference in topology of the dispersion characteristics of azimuth-symmetric and asymmetric normal waves propagating in infinite waveguides of such a geometry. For the finite-length systems used as two-dimensional Bragg resonators, the eigenmode spectrum is found for two types of boundary conditions that correspond to the limiting cases of perfectly matched (open) systems and, conversely, of systems closed for the extraction of transverse electromagnetic fluxes. Perimeter-to-length ratios of the resonator at which the Q factor of the fundamental azimuth-symmetric mode is greater than those of the other modes are determined. The applicability domain of the geometrical approach, which was earlier applied to two-dimensional Bragg resonators, is discussed.