Scattering by a dielectric cylinder of arbitrary cross section shape

TLDR

The study assumes a harmonic incident wave with electric vector parallel to the cylinder axis and field intensities independent of axial distance, and it treats the total field inside the dielectric as an unknown solved via a linear system rather than approximated by the incident field. The paper develops theory and equations for the scattering pattern of a dielectric cylinder with arbitrary cross‑section shape. The authors formulate analytic expressions and solve a linear system to determine the total field inside the cylinder, enabling calculation of the scattering.

Abstract

The theory and equations are developed for the scattering pattern of a dielectric cylinder of arbitrary cross section shape. The harmonic incident wave is assumed to have its electric vector parallel with the axis of the cylinder, and the field intensities are assumed to be independent of distance along the axis. Solutions are readily obtained for inhomogeneous cylinders when the permittivity is independent of distance along the cylinder axis. Although other investigators have approximated the field within the dielectric body by the incident field, we treat the total field as an unknown function which is determined by solving a system of linear equations. In the case of the dielectric cylindrical shell of circular cross section, this technique yields results which agree accurately with the exact classical solution. Scattering patterns are also presented in graphical form for a dielectric shell of semicircular cross section, a thin homogeneous plane dielectric sheet of finite width, and an inhomogeneous plane sheet. The effects of surface-wave excitation and mutual interaction among the various portions of the dielectric shell are included automatically in this solutiom