Electromagnetic wave propagation over large rough surfaces at low grazing angles
Although there is extensive literature on theoretical and numerical techniques for the rough surface scattering problem, there is relatively little work done on the analysis of the statistical properties of the scattered field, which is the core component of this dissertation. Scattering of electromagnetic waves from one-dimensional perfectly conducting large rough surfaces at low grazing angles is considered. Two different approaches, one based on the parabolic equation techniques and the other based on an exact full wave integral equation, are investigated.
For the parabolic equation modeling of the forward scattering over a rough surface, we are mainly concerned with the mean field. Efficient Fourier split-step solutions are carried out and results are compared to the experimental data showing reasonably good agreements for surfaces with moderate roughness. Meanwhile a recently published analytical approach, the mean Green’s function technique for computing the mean scattered field, is numerically evaluated through direct comparisons with other methods. Unfortunately numerical computations reveal that the scattered field calculated by this technique is not accurate particularly for the equivalent admittance.
In the second method, the surface is assumed to be periodic resulting in a surface integral equation over only one single period. The new integral equation is discretized using the method of moments and is solved using the generalized conjugate residue algorithm with the help of the fast multipole method. Numerical results based on Monte Carlo simulations show that the mean scattering amplitude vanishes in non-specular directions and it is uncorrelated between different scattering angles, resulting in a scattered field whose autocorrelation function depends only on the position difference. Unlike the scattering amplitude, the scattered field does follow some form of non-delta-like autocorrelations and it decorrelates more rapidly when the surface is rougher. It is also shown that the fluctuating part of the reflection coefficient in the specular direction does not always follow a Rayleigh distribution unless the Rayleigh parameter is large. It is however always Rayleigh distributed in non-specular directions. The fluctuating part of the scattered field on the other hand always follows a Rayleigh distribution.