Some New Aspects of the Reflection of Electromagnetic Waves on a Rough Surface

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Abstract
The reflection of a plane‐electromagnetic wave from a rough perfect conductor is investigated. The roughness is represented by hemispherical bosses whose radii and mutual distances are small relative to the wavelength. This problem is solved taking into account the electromagnetic interaction of the bosses. Aside from throwing some light on the limitations of approximate methods, the present solution reveals some effects not known before. For grazing incidence and vertical polarization the interaction has a drastic influence in that it causes a complete phase reversal of the reflected wave, near a 45 degree incidence the influence of the roughness vanishes. These effects do not occur for horizontal polarization. An approximate treatment for the case of the imperfect conductor is indicated. The analogous case for the acoustic wave is also developed and shows similar behavior. The effect of the roughness is shown to be equivalent to a boundary condition for the wave equation. Extension of the method to a more general type of roughness, and to the case of statistical and asymmetric shapes and distributions, is briefly discussed.

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