Applicability of the Rayleigh hypothesis to real materials

Abstract

The validity of Rayleigh's hypothesis with permeable media is investigated. For the two-dimensional transmission problem, the extinction theorem and boundary integral equations are obtained within a common framework, for the surface with periodic corrugations. The surface field functions are found from the integral equations; these functions can be analytically continued to complex values of the coordinates. Then the extinction theorem provides a criterion for the validity of Rayleigh's hypothesis. We find that it is valid for all materials, absorbing or otherwise, when 2\ensuremath{\pi}h/D0.448. Here h is the depth and D the period of the sinusoidal surface. Criteria of this nature have previously been established only for the Dirichlet problem, with the assumption that the medium of incidence was also nondissipative. Accurate application of Rayleigh's method requires accurate knowledge of both the interface geometry and the material properties. In particular, when ``perfect-conductor'' formulas are used to measure the dielectric constant and calibrate the corrugation depth of gold gratings, significant errors are introduced into the data. Such distortions may be the true cause of discrepancies observed when Rayleigh-type calculations are applied to light scattering from real metals with rough surfaces.