Study of Eigenwaves of a Two-Dimensionally Periodic Lattice of Capacitive Metal Cylinders in Transparency Bands

Abstract—The article studies eigenwaves of an electromagnetic crystal in the form of a two-dimensionally periodic lattice of metal cylinders with capacitive gaps between two metal screens forming a plane waveguide. The standard system of electrodynamic modeling is used to study the dispersion characteristics of eigenwaves propagating in a structure in the first and second transparency bands in the self-oscillation mode. In the plane-wave excitation mode, the authors study the characteristics of an electromagnetic crystal layer infinite in one coordinate in its transparency bands. It is shown that the fundamental eigenwave of the structure in the first transparency band is a slow wave, the deceleration coefficient of which increases at the boundary of the first band gap. It has been established that in the second transparency band, under certain conditions, backward waves can occur with anomalous frequency dispersion of the propagation constant. The relationship between the conditions of the occurrence of backward waves and the frequency of the series resonance of the capacitive cylinder is shown.