Half-space Green's functions and applications to scattering of electromagnetic waves from ocean-like surfaces

Abstract

A mathematical model has been developed, based on the use of half-space Green's functions, that generalizes the Kirchhoff approximation in a way that produces polarization-sensitive estimates of the radar cross-section, and that also produces results that are consistent with perturbation theory. The mathematical description is founded on Tai's theory of dyadic Green's functions, and supplies the natural generalization to the electromagnetic case of a scalar analysis developed by Berman and Perkins. The results are presented here for the case of perfectly conducting boundary conditions, for surfaces which are otherwise, in their spectral properties, models of ocean-like surfaces. We also develop some identities, the transparency identities, involving the various surface integrals present in the theory, that allow us to simplify the theory compared to the Berman–Perkins approach. A striking prediction of even the non-iterated perfectly conducting model is that, although this model is consistent with perturbation theory, it predicts differences between horizontal and vertical polarization ocean background cross-sections of only a few dB for near-grazing incidence. This is in sharp contrast with perturbation theory, where the difference may be 40 dB or more. Near normal incidence the model produces estimates consistent with ordinary Kirchhoff theory. The treatment of the ocean background makes use of some new results on the nature of the correlation functions associated with ocean-like spectra, that allow us to construct simple analytical formulae for the Kirchhoff and half-space radar cross-sections for near-grazing incidence.