Abstract

In this paper, a semi-analytical technique to derive scattering coefficients of a three-dimensional multi-layered wall with doubly periodic interfaces is presented. First, the proposed method uses the periodicity of interfaces in the surface integral equation formulation to confine the integration interval to just one period. It also simplifies the formulation by using the extended boundary condition method (EBCM) and the spectral formulation of the background Green’s function. Then, each of the scattering coefficient matrices of interfaces and layers is treated as two-port networks, and the scattering matrix of the whole structure is derived using the scattering transfer matrix method. In a limiting case, the proposed method is validated by comparing the results to a two-dimensional semi-analytical approach that is available in the literature. Then for a single layer wall, the effects of side interfaces’ roughness, layer’s thickness, and dielectric constant on reflection and transmission coefficients are analyzed.

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