Electrodynamic modeling of slot gratings by the generalized scattering matrix method – spherical wave decomposition

Abstract

An algorithm is presented for the electrodynamic analysis of a two-dimensional waveguide slot array of finite dimensions. To solve the boundary value problem, the generalized scattering matrix method is used. The complex problem for a structure with large electrical dimensions is divided into two subproblems: wave scattering on one lattice element and the interaction of waves within the lattice. In accordance with this method, the electromagnetic field of a solitary lattice element is represented in the form of an expansion in incident and scattered spherical waves. The solution to the first subproblem is given by the scattering operator, which relates the amplitudes of the incident and scattered waves. The solution to the second subproblem yields an interaction matrix that relates the amplitudes of waves incident on the mth array element with the amplitudes of waves scattered by the nth element. Application of the scattering operator and interaction matrix to the analysed lattice leads to a system of linear algebraic equations for the amplitudes of the scattered waves. A non-periodic slot grating, focused in the Fresnel zone, containing up to a thousand elements is analysed. The obtained numerical results are in good agreement with the known behaviour of focused leaky wave gratings. Possible areas of application of the method are discussed.