In this paper a new approximate fast method of calculating the bistatic‐scattering coefficients of a multilayer structure with random rough interfaces was presented based on the Kirchhoff Approximation (KA) and the electromagnetic theory of stratified media. First, the electromagnetic scattering from a Gauss rough metal or dielectric surface was calculated by KA method and method of moment (MOM), and the effectiveness of KA method was confirmed and verified. Second, a new approximate fast method was presented to calculate electromagnetic scattering from a multilayer‐random‐rough surface based on electromagnetic reflection from multilayer parallel surfaces and KA. The calculated results by the new method were in good agreements with those by MOM, especially near the specular point. Finally, a comparison of the new method and MOM was carried out in consuming computing time, memory resources, and complexity. The comparison indicated that the new approximate method was faster by about 30–150 times than MOM. The new approximate fast method could avoid a large matrix inversion and greatly reduce the computation time and memory resources and thus improve the computational efficiency. It was an effective approximation fast analyzing method of electromagnetic scattering from multilayer rough surfaces.
Based on the Rayleigh hypothesis and Floquet's theorem, a vector method for studying electromagnetic wave scattering from a one-dimensional periodic conducting surface with tapered transverse magnetic (TM) wave incidence is presented. The fields are represented by vectors instead of scalars so that the vector behavior of scattering (such as cross polarization) can be naturally explored. The new formulation opens a wide range of applications of the method, concerning not only gratings used in TM polarization but also conical diffraction, crossed gratings, two-dimensional problems, photonic band gaps, nonlinear optics, etc. The numerical results are consistent with the T-matrix method in the particular case in which the plane of incidence is perpendicular to the generators of the surface. For the general case in which the plane of incidence is not perpendicular to generators of the surface, the proposed method obtains significant results that reveal cross-polarized and anisotropic characteristics in the scattering while the energy balance is kept satisfactory. This straightforward approach is much more efficient than the T-matrix; thus it is suitable to extend to other more involved periodic scattering problems.
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