On the scattering of electromagnetic wabes by a dielectric cylinder

The scattering of $E$-polarized cylindrical electromagnetic waves by an infinitely long dielectric cylinder is investigated. For small incident wavelength the slowly converging series solution is converted to a sum of integrals. An expansion is performed so that the integrals may be divided into two classes depending on the relative locations of source and observation points. Those in the first class have points of stationary phase and an asymptotic evaluation gives contributions which are identified as those of geometric optics. The remaining integrals are evaluated as residue sums. A plot of normalized back-scattering cross section vs. normalized radius for $n = .4$ is given.