Resonant Reflectance Anomalies: Effect of Shapes of Surface Irregularities

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Abstract
It was recently shown that hemispherical pits or bumps on an otherwise flat surface of a sample of isotropic material may cause marked anomalies in reflectance near resonant frequencies of the material, such as reststrahlen bands in ionic dielectrics and plasma frequencies in metals. The anomalies occur even when such irregularities are much smaller than the wavelength of the reflected radiation, so that incoherently scattered radiation is negligible. The effect is due to localized resonances that are somewhat displaced in frequency from the bulk optic modes of the material by electric boundary conditions. The sharp right angle at the rim of a hemispherical pit or bump might have been suspected of giving exceptional results. In this paper, the problem is solved in a different way to demonstrate that pits and bumps with well-rounded edges produce anomalies of approximately the same magnitude and frequency characteristics as hemispherical pits and bumps. The effect is derived classically. Spatial dispersion and dielectric nonlinearity are assumed to be negligible. The effects of very slight roughness on the reflectance curves of lithium fluoride and of aluminum are described as illustrations.

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