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 rough-surface scattering problems as well as the problem of propagation in the presence of a rough surface. For surface scattering problems it is known that as the angle of incidence approaches grazing incidence the tapered beam waist should be made larger; several criteria relating these two parameters have been proposed for both the Gaussian and the Thorsos tapers. Our two-dimensional scattering simulations with the oceanlike Pierson–Moskowitz surfaces show that when the width of the Gaussian or the Thorsos taper is fixed, the backscatter cross section for TE polarization is characterized by a distinctive and consistent anomalous jump as grazing incidence is approached. This observation has led to a refined version of one of the above-mentioned beam waist–angle of incidence criteria and its robustness is demonstrated. The approximate (non-Maxwellian) nature of the Thorsos–Gaussian taper also becomes evident in over-surface-propagation simulations with use of the boundary integral equation method. A certain inconsistency was observed between the surface field that we obtained by first defining the Thorsos–Gaussian-tapered field on a vertical plane and then propagating it to the surface and that obtained by defining the same tapered field directly on the surface. This effect, not previously appreciated, may be of importance when the rough-surface effects are rigorously incorporated into the propagation problem. We conclude with a detailed derivation of the Thorsos taper that points out all the approximations involved in it and the resulting limitations.
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