Issues related to the use of a Gaussian-like incident field for low-grazing-angle scattering

We study the suitability of a tapered plane-wave incident field, using both the Gaussian and the more advanced Thorsos tapers for low-grazing-angle ro ugh-surface scattering problems as well as the problem of propagation in th e presence of a rough surface. For surface scattering problems it is known that as the angle of incidence approaches grazing incidence the tapered bea m waist should be made larger; several criteria relating these two paramete rs have been proposed for both the Gaussian and the Thorsos tapers. Our two -dimensional scattering simulations with the oceanlike Pierson-Moskowitz su rfaces show that when the width of the Gaussian or the Thorsos taper is fix ed, the backscatter cross section for TE polarization is characterized by a distinctive and consistent anomalous jump as grazing incidence is approach ed. This observation has led to a refined version of one of the above-menti oned beam waist-angle of incidence criteria and its robustness is demonstra ted. The approximate (non-Maxwellian) nature of the Thorsos-Gaussian taper also becomes evident in over-surface-propagation simulations with use of th e boundary integral equation method. A certain inconsistency was observed b etween the surface field that we obtained by first defining the Thorsos-Gau ssian-tapered field on a vertical plane and then propagating it to the surf ace and that obtained by defining the same tapered field directly on the su rface. This effect, not previously appreciated, may be of importance when t he rough-surface effects are rigorously incorporated into the propagation p roblem. We conclude with a detailed derivation of the? Thorsos taper that p oints out all the approximations involved in it and the resulting limitatio ns. (C) 1999 Optical Society of America [S0740-3232(99)00301-4].