Numerical simulations and backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces with the sparse-matrix canonical grid method

Abstract

Numerical simulations exhibiting backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces (three-dimensional scattering problem) are presented. The Stratton–Chu surface integral equation formulation is used with the method of moments to solve for the tangential and normal components of surface fields. The solution of the matrix equation is calculated efficiently by using the sparse-matrix canonical grid (SMCG) method. The accuracy of the solution is assessed by comparing the bistatic scattering coefficients obtained from the SMCG and the matrix inversion method. Also, a sufficient sampling rate is established with respect to the dielectric constant below the rough-surface boundary. Numerical simulations are illustrated for moderate rms heights of 0.2 and 0.5 electromagnetic wavelengths with rms slopes of 0.5 and 0.7. The magnitude of the relative permittivity ranges from 3 to 7. With use of the SMCG method, scattered fields from a surface area of 256 square wavelengths (98,304 surface unknowns) are found. For a rms height of 0.5 wavelength and a correlation length of 1.0 wavelength, backscattering enhancement is observed in both co-polarization and cross polarization. However, in the case in which the rms height is 0.2 wavelength and the correlation length is 0.6 wavelength, backscattering enhancement is observed in cross polarization only.