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

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 c 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⁽²⁾h² + g⁽⁴⁾h⁴ + O(h⁶)], where the expansion coefficients g⁽²⁾ and g⁽⁴⁾ are given by exact, closed form expressions. Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters.