Electromagnetic scattering by an infinite elliptic dielectric cylinder with small eccentricity using perturbative analysis

Abstract

The scattering of a plane electromagnetic wave by an infinite elliptic dielectric cylinder is examined using two alternative methods. In the first the electromagnetic field is expressed in terms of elliptical-cylindrical wave functions while in the second, a shape perturbation method is applied by expressing the field in terms of circular-cylindrical wave functions only and the equation of the elliptical boundary 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> the interfocal distance of the elliptic cylinder and 2a the length of its major axis. In this case the scattered field and the scattering cross-sections expressions have the form of S(h) = S(0)[1+g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(2)</sup> h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(4)</sup> h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> + O(h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> )], where the expansion coefficients g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(2)</sup> and g <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(4)</sup> are given by exact, closed form expressions. Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters.