On retrieving the electric fields of point-like scatterers in the presence of a large dielectric cylinder by means of the Foldy-Lax approximation

In this work, the scattering problem pertaining to the excitation of a dielectric cylinder surrounded by a cluster of significantly smaller, assumed point-like scatterers, by a field due to a line-source is considered. In particular, by considering a line-source parallel to the z-axis, the corresponding electric fields are perpendicular to the xy-plane, allowing the original 3D vector problem to be reduced to a 2D scalar problem. Furthermore, the multiple-scattering problem is reduced to a single-scattering problem of excitation of a dielectric sphere by an arbitrary distribution of electric dipoles, by means of the Foldy-Lax approximation. Specifically, by assuming that each point-like scatterer elicits fields similar to that of line-sources that disect the xy-plane on a point in the interior of each scatterer, the recovery of the electric fields of the point-like scatterers is enabled through an inverse-problem scheme utilizing measurements of the surface electric fields. To that end, the surface-field measurements at specific angles of observation are manipulated into a matrix form, so that a linear-system for the unknown point-scatterer fields can be devised. Furthermore, a dense cluster approximation of the scattering cross section attributed to the cluster's scatterers is obtained when certain conditions are met, while explicit numerical results demonstrating the accuracy and stability of the method, are presented.