Abstract

A surface-impedance boundary condition is obtained from first principles for problems involving the scattering of two-dimensional waves by cylindrical periodical surfaces of arbitrary shape. The analysis is performed in the context of the electromagnetic theory of gratings, but it is also applicable to other physical situations, leading to the solution of a two-dimensional Helmholtz equation with high values for index of refraction. The boundary condition deduced here is shown to be analogous to the one suggested by Leontovich for quasi-planar boundaries if Z₀ the quantity relating the field and its normal derivative at the boundary and depending only on the constitutive properties of the medium, is replaced by another quantity Z, which also depends on the local curvature of the surface. and on the polarization of the external fields; Z₀ is the zero-order term in the expansion of Z in terms of the curvature.

© 1988 Optical Society of America

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