Stable computation of the electromagnetic T-matrix for high aspect ratio cylinders

We analyze the stability of computing the T-matrix with the Extended Boundary Condition Method for electromagnetic scattering for long or flat cylinders. Some integrals in the auxiliary Q-matrix are unstable due to an oscillatory integrand over the longer side. As proposed by Waterman for the acoustic case [J. Acoust. Soc. Am. 125, 42 (2009)], we expand the integrands in powers of the size parameter, and find that the negative powers integrate to zero exactly when the surface is extended to infinity, hence the cancellations. To work around this, we split the integrals into low and high powers, integrate the high powers normally, and integrate the low powers over the complement of the cylinder surface that extends from the edge to infinity. Stable methods of matrix inversion are also explored. Overall, this approach provides stable computation of the T-matrix and physical properties such as optical cross sections over a much wider range of aspect ratios.