Calculation procedures for variational, Born and exact solutions for electromagnetic scattering from two randomly separated dielectric Rayleigh cylinders

The exact solution, the Born approximation, and its variational improvement are obtained for the scattering of electromagnetic waves from a random ensemble of systems, each consisting of two Rayleigh cylinders. The cylinders are parallel, of infinite length, and of equal radius. Their separation varies randomly among ensemble members except that the cylinders cannot overlap. The intent is to test a recently developed vector stochastic variational principle. The exact solutions are obtained for the average differential scattering cross sections of both the transverse electric (TE) and transverse magnetic (TM) fields relative to the cylinder axes with normal plane wave incidence. The corresponding variational approximations are obtained using a recently reported computational alternative to the more familiar dyadic Green's function solution. They are in essential agreement with the exact TE and TM solutions, whereas the Born results are not. In particular, the variational results accurately account for multiple scattering, which is significant in the exact TE, but not TM, solution, and also account for the difference in geometric polarizability between the two solutions.