Scattering of Plane Waves by Soft Obstacles. II. Scattering by Cylinders, Spheroids, and Disks

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Abstract
Approximate closed form analytical expressions are derived for the total and differential scattering cross sections of cylindrical, prolate spheroidal, and disk‐shaped scatterers which subject scalar plane waves to only a small phase shift. When a plane wave excites a sphere or infinite cylinder, the internal field of these objects can be expressed as an infinite series of bessel functions. By making an approximation in coefficient of the nth bessel function which is valid for either 2πa/λ0»n (a = sphere or cylinder radius, λ0 = wavelength of incident plane wave) or |m−1| «1 (m = λ0/λ1, λ1 = wavelength of plane wave in medium composed of material of scatterer), it is possible to obtain a closed form expression for the series. The scattered field is obtained by integrating over these internal fields. The scattered fields for long but finite cylinders and prolate spheroids are calculated by approximating their internal fields by those of infinite cylinders of the same radius. The scattered fields of thin disks are obtained by assuming the internal fields to be that of an infinite flat plate of the same thickness.

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