Matrix formulation of electromagnetic scattering

TLDR

A new method is proposed for computing the radar cross section and related field quantities when a smooth, perfectly conducting obstacle is illuminated by an incident electromagnetic wave. The method represents the scattered field as a distribution of electric dipoles on the obstacle surface, determines the surface current by enforcing that the scattered field cancels the incident field inside the obstacle, and yields coupled infinite matrix equations that are decoupled via Green's identity into two independent scalar problems. The resulting equations were specialized to axially symmetric obstacles and solved numerically on the IBM 7094 for several examples, with reciprocity, energy conservation, and resonant mode problems examined in matrix form.

Abstract

A new method is proposed for the computation of the radar cross section and other associated field quantities arising when a smooth, perfectly conducting obstacle is illuminated by an incident electromagnetic wave. The scattered wave is first represented by a distribution of electric dipoles over the surface in question, with the response from any dipole proportional to the induced surface current density at that point. The surface current is then determined by the "boundary condition" that the scattered wave, through interference, precisely cancels the incident wave inside the obstacle. One obtains in this mariner a pair of coupled (infinite) matrix equations for the surface current. Green's identity permits decoupling of the equations, reducing the problem to roughly the equivalent of two independent scalar problems. The equations have been specialized to axially symmetric obstacles and then solved numerically on the IBM 7094 for several examples of interest. Reciprocity and energy conservation are also examined and the resonant mode (interior) problem set up explicitly in matrix form.