Galerkin’s Spectral Method in the Analysis of Antenna Wall Operation

In this paper, a solution to the problem of electromagnetic field scattering on a periodic, constrained, planar antenna structure placed on the boundary of two dielectric media was formulated. The scattering matrix of such a structure was derived, and its generalization for the case of an antenna with a multilayer dielectric substrate was defined. By applying the Galerkin spectral method, the problem was reduced to a system of algebraic equations for the coefficients of current distribution on metal elements of the antenna grid, considering the distribution of the electromagnetic field on Floquet harmonics. The finite transverse dimension of the antenna was considered by introducing, to the solution of the case of an unconstrained antenna, a window function on the antenna aperture. The presented formalism allows modeling the operation of periodic, dielectric, composite antenna arrays.