An application of a variational principle for scattering by random rough surfaces

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Abstract
This paper constitutes a first step in the application of a recently developed variational principle to the study of scattering from random rough surfaces. The variational principle has been applied here to assess and extend the range of validity of the perturbation approximation for the scattering of a horizontally polarized electromagnetic wave by a random configuration of non‐overlapping parallel hemicylindrical bosses of equal radii protruding from a conducting plane. The results for this model of a rough surface suggest that, besides extending the range of validity of the perturbation approximation, the variational approach also provides an improved first‐order correction at the long‐wavelength limit in the expansion of the reflection coefficient in powers of the scatterer concentration.

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