Two-dimensional open resonators with cylindrical mirrors

The paper presents a theoretical analysis of the spectral characteristics of two-dimensional open resonators consisting of a finite number of open screens coinciding with parts of surfaces of circular cylinders in the case when the resonance wavelength is commensurable with the characteristic size of the structure. A rigorous method of the Riemann-Hilbert problem is used to obtain the solution to the Maxwell equations for the resonator. Consideration is given to a confocal open resonator, coupled resonance volumes (H-polarization), and long-wave resonance regimes. A method is proposed for improving the Q of long-wave resonance regimes of two-layer open structures.