Scattering by an Infinite Elliptic Metallic Cylinder

Abstract

The scattering of a plane electromagnetic wave by an infinite elliptic metallic cylinder is considered. Two different methods are used for the evaluation. In the first the electromagnetic field is expressed in terms of elliptical-cylindrical wave functions. In the second, a shape perturbation method, the field is expressed in terms of circular-cylindrical wave functions only, while the equation of the elliptical boundary is given in polar coordinates. Analytical expressions are obtained for the scattered electromagnetic field and the various scattering cross-sections, when the solution is specialized to small values of the eccentricity h = c/2a, (h ≪ 1), with c the interfocal distance of the elliptic cylinder and 2a the length of its major axis. In this case exact, closed form expressions are obtained for the expansion coefficients g⁽²⁾ and g⁽⁴⁾ in the relation S(h) = S(0)[1 + g⁽²⁾h² + g⁽⁴⁾h⁴ + O(h⁶)] expressing the scattered field and the scattering cross-sections. Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters.

Keywords:

• electromagnetic scattering
• elliptic metallic cylinder
• scattering cross sections
• perturbation method