Multiple Scattering of Radiation by an Arbitrary Planar Configuration of Parallel Cylinders and by Two Parallel Cylinders

The formal solution for the scattering of a plane wave by an arbitrary configuration of parallel cylinders previously presented is specialized to consider the case where all the axes lie in the same plane. The scattered wave is expressed as an infinite sum of orders of scattering, the first order being the usual single scattering approximation. It is shown that the far field form of the multiply scattered orders is symmetrical with respect to the plane of the configuration for minimum spacing large compared to wavelength. Hence, for the analogous configuration of bosses on a perfectly conducting plane, departures from the predictions of single scattering theory should occur primarily for the component polarized perpendicular to the elements. The problem of two cylinders is considered in detail, the multiply scattered orders being summed explicitly subject to the above conditions. Approximate solutions for radii very small compared to wavelength are derived, the wavelengths for which the effects of multiple scattering are greatest are investigated, and a criterion for the use of the single scattering hypothesis presented. Solutions for two bosses and a single cylinder parallel to a nonabsorbing plane are also stated. Both the electromagnetic and acoustic cases are treated.