A new method to calculate wave scattering from rough surfaces at low grazing angles

A new method has been developed to study the electromagnetic fields scattered from one-dimensional perfect electric conducting arbitrarily rough surfaces which are planar in the mean. The technique allows for the calculation of the scattered fields in the low grazing angle regime, i.e., when the incident wave propagation vector approaches the horizontal to the mean surface plane, or in any situation which requires large number of current element unknowns, such as when surface length is very large compared to the incident electromagnetic wavelength or when the surface is very rough. The method presented in this work eliminates the matrix storage difficulties previously associated with solving this problem and significantly reduces the computation time, while providing a highly accurate solution over a large range of incident and scattering angles, as well as surface statistics. The technique reformulates the discretized Magnetic Field Integral Equation (MFIE) for the surface current by decomposing the Green's function or propagator matrix appearing in this equation into a sum of a lower and upper triangular matrix. This allows the original equation to be manipulated into a new discretized second kind integral equation, comprised of a new Born or source term and a new kernel, which can then be solved via iteration. We have found that the convergence rate of this new technique is very rapid, where typically only one or two iterations are required, and in most cases the iteration of the new integral equation is not even necessary due to the robust nature of the new Born term. Furthermore, we have never experienced a case in which the method failed to converge to the correct solution.