Electromagnetic scattering patterns from sinusoidal surfaces

In this paper we present an analysis and calculation of scattering patterns from sinusoidal surfaces. An exact space harmonic representation is used for the field on the surface, and as a result, the calculation includes the effects of shadowing, diffraction, and multiple scattering. An asymptotic evaluation has been employed to obtain an exact expression for the scattering pattern as a product of the space harmonic scattering coefficients times the corresponding pattern functions. The formula obtained has been simplified for illuminated areas that are many wavelengths long and plotted for a variety of surface parameters. The present method for scattering pattern calculations can be considered to be complementary to methods using physical optics and point-matching techniques. In addition to the scattering pattern calculations the exact Bragg backscattering amplitudes have been computed and compared with their Rayleigh approximations.