Analytic "α-Pole" Approach to an Electromagnetic Scattering Problem

We present an analytic formalism applied to the electromagnetic boundary-value problem consisting of a vertical semi-infinite conducting cylinder embedded in another conducting medium, with an upper half-space of a third material, in the presence of a normally incident plane electromagnetic wave from infinity. The cylinder and the medium may have arbitrary finite conductivities and dielectric constants. We use analyticity arguments and concepts based on Regge theory and Prony/SEM (singularity expansion method) formalism to construct an expansion for the fields. The expansion uses poles in the Fourier conjugate variable α to the vertical coordinate. A finite number of αpoles are taken as an approximation along with a truncation of the standard azimuthal expansion. The results satisfy Maxwell's equations in each region of space with given constitutive parameters. The boundary conditions between regions are approximately implemented by a leastsquares fitting procedure. Practical examples include a lossy cylindrical object in a conducting material (pictorially an "island" in an "ocean"), or a long metallic cylindrical object in the earth, with the upper half-space being air. Qualitative agreement with exact results is obtained.