Scattering of a plane wave by one-dimensional dielectric random rough surfaces—study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of a one-dimensional dielectric random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the diffraction amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The results of a Gaussian random process with a Gaussian roughness spectrum are compared to published experimental and numerical data. Comparisons are conclusive.