Abstract

Explicit closed-form expressions are obtained for the scattering of a plane wave by a semielliptic groove in a perfectly conducting ground plane, in the low-frequency limit. They are valid for arbitrary polarization, arbitrary incidence and scattering directions, and arbitrary eccentricity. The problem is complicated by the fact that the Mathieu eigenfunctions are complete but not orthogonal over the semisurfaces upon which the boundary conditions are fixed. Complete separation of the coefficients for the scattered field is possible only in the low-frequency limit. Simple results are obtained for the special cases of a very narrow groove, very shallow groove, and a semicircular groove.

© 1970 Optical Society of America

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Equations (73)

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