Abstract

The Mathieu function series solution for the scattering of a plane wave by a perfectly conducting elliptic cylinder is used to derive explicit long-wavelength approximations (k = 2π/λ∼0) for arbitrary polarization, for arbitrary angles of incidence and observation, and for arbitrary eccentricity. We obtain closed-form approximations for the scattering coefficients of the elliptic modes which yield series correct to order k6 on expansion; similarly, for the far-field scattering amplitudes. The corresponding series for the scattered intensity and total scattering cross section are given to order h5 for E parallel to a generator, and to order k7 for E perpendicular. Analogous results are also obtained for the semielliptic protuberance on a ground plane. For this case the series for the intensities and cross sections for both polarizations are correct to order k7. Numerical results obtained from series approximations, from closed forms, and from tables of functions, are given.

© 1964 Optical Society of America

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