Exact Scattering from a Parabolic Cylinder Coated in an Isorefractive Sheath

The problem of an electromagnetic plane wave scattering off a perfect electrically conducting parabolic cylinder embedded in a confocal parabolic cylinder made of a material isorefractive to the surrounding space is solved and analyzed. The parabolic cylinder geometry is introduced, and a number of mathematical and physical relations required for the evaluation of the problem are discussed. A set of exact, analytic solutions of the scattering problem are derived. Utilizing these solutions, the numerical calculation of the scattered field is analyzed for realistic input parameters and asymptotic limits. Plots of the scattered wave in the far field are presented and discussed for different incident angles. In the process of generating results for the full isorefractive sheath problem, the solutions to simpler problems of the scattering from parabolic cylinders of different materials are discussed, and the near-field behaviors are plotted. This paper reveals a new, exact canonical solution to an electromagnetic scattering problem, one which can be used in benchmarking modeling software. It also presents an in-depth discussion of the convergent properties of the infinite sums which make up the expression of the scattered field, and provides a road map which can be followed in evaluating similar problems. The plots of the scattered fields prove to be interesting in their own right, but only begin to scratch the surface of the problem space. Thus, an interesting problem, which is but one of a rich field of study, is solved.