Analytic results for the electrostatic T-matrix and polarizability of finite cylinders

The T-matrix for electromagnetic scattering is most commonly computed using the Extended Boundary Condition Method (EBCM), but this approach is numerically unstable for finite cylinders of high aspect ratio. In the electrostatics limit, we show that this instability is caused by catastrophic cancellations in the numerical calculations of oscillatory integrals. We find that the problematic integrals can instead be evaluated by integrating over the complement surface that extends from the cylinder to infinity. The resulting integrals are stable and we are then able to compute the electrostatic T-matrix accurately. The polarizability of the finite cylinder is then derived from this T-matrix and validated against results obtained via discretization. As an alternative, we also investigate the T-matrix on a basis of spheroidal harmonics, which is stable on its own and converges more quickly than on the spherical basis. Since the integrals are analytic, we moreover derive a simple analytic approximation based on truncation of the T-matrix on this basis. Beyond the direct benefits of analytic expressions for the electrostatic cylinder polarizability, this work should pave the way for a stable formulation of the full-wave T-matrix/EBCM approach for cylinders.