Scattering by an Infinite Dielectric Cylinder Having an Elliptic Metal Core: Asymptotic Solutions

The scattering of a plane electromagnetic wave by an infinite circular dielectric cylinder, containing an elliptic metallic one is considered in this work. The electromagnetic field is expressed in terms of both circular and elliptical-cylindrical wave functions, connected with one another by well-known expansion formulas. When the solution is specialized to small values of the parameter h = c/a, (h ≪ 1), where 2c is the interfocal distance of the elliptic conductor and 2a the length of its major axis, analytical expressions of the form S(h) = S(0)[1 + g
⁽²⁾
h
²
+ g
⁽⁴⁾
h
⁴
+ O(h
⁶
)] are obtained for the scattered field and the various scattering cross-sections. Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters.