The T-matrix revisited

We consider electromagnetic scattering from penetrable cylinders of general cross section. After summarizing the basic T-matrix equations the low-frequency case is examined, which leads for nonmagnetic materials to the exact result T=iR-R(2) in the Rayleigh limit, satisfying both reciprocity and energy constraints. Here elements of R are given by integrals of regular wave functions over the cylinder surface. A "Rayleigh expansion" is then found that is convergent throughout the Rayleigh region and the lower end of the resonance region and requires no matrix inversion. For bodies of high aspect ratio, there is a problem with significance loss during numerical integration, due to large oscillatory terms. A class of surfaces has now been found for which these terms can be removed, however, enabling us to treat aspect ratios up to 1,000:1. These methods are expected to apply also in three dimensions.