Electromagnetic scattering patterns from sinusoidal surfaces

Abstract

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.

Application of beam simulation to scattering at low grazing angles: 1. Methodology and validation

“…Scattering from a large-amplitude sinusoidal surface whose wavelength is approaching that of the incident radiation is of interest in its own right. The subject has been explored extensively and continues to be active [McCammon and McDaniel, 1985;Jordan and Lang, 1979]. As with rough surface scatter in general, however, grazing incidence has been given little attention.…”

Note on the asymptotic approximation of a double integral with an angular-spectrum representation

“…However, if (x, y) is complex-valued but not differentiable everywhere in D, additional work is necessary to account for the contribution of the boundary stationary points to the asymptotic expansions of the double integrals [10,11]. 1 These boundary stationary points are certainly located in the vicinities of where (x, y) is not differentiable, i.e., branch points and singularities. Therefore, curves of stationary points are formed on the boundaries of the sub-domains {D j } ⊂ D which are disjoined with each other by the "deleted" neighborhoods of nondifferentiation.…”

“…Therefore, curves of stationary points are formed on the boundaries of the sub-domains {D j } ⊂ D which are disjoined with each other by the "deleted" neighborhoods of nondifferentiation. In addition, because (x, y) is complex-valued, approximation of the Laplace-type integrals should be 1 Generally, these boundary stationary points are the critical points of the second or the third kind. The critical points of the second type are points on the domain's boundary at which a level curve of (x, y) is tangential to ; while the critical points of the third type are points where has a discontinuously turning tangent.…”

“…The methods of steepest descent path (SDP) and stationary phase are commonly useful for the asymptotic evaluation of the complicated integrals in electromagnetics particularly in the far zone [1][2][3][4][5]. For the one-dimensional case, it seems no restrictions need to be enforced on the integrands to apply these classic asymptotic methods, although sometimes the construction of the SDP is difficult as also is the establishment of the uniform asymptotic expansions in the neighborhoods of the singularities of the integrands close to the saddle points [6,7].…”

Decoupling Approximations Applied to an Infinite Array of Fluid Loaded Baffled Membranes

“…In dimensionless variables :E = (:1:, y), the equation governing the pressure in the fluid IS \72 p + k2 p = () (1) where k = wA/ Ca and Ca is the sound speed in the fiuid. The spatial variables were made dimensionless by scaling with respect to A.…”