Abstract

Electromagnetic scattering by a penetrable sphere is the canonical problem that lies at the heart of theories of the rainbow. It is relatively straightforward to solve this problem via separation of variables (often referred to as Mie theory in this context). This leads to a series which converges for all frequencies but which becomes computationally ineffective at high frequencies. As a consequence, there have been extensive attempts over the years to derive asymptotic solutions in the high-frequency regime and this has been very successful in improving our understanding of the complex phenomena which this physical problem exhibits. The challenge remains to extract all the phenomena direct from the Mie solution and to use the Mie solution to devise a numerical scheme that can compute the solution to arbitrary accuracy for high frequencies. The starting point for such an approach is the Watson transform. With this in mind, this talk will focus on perhaps the simplest relevant canonical problem, namely acoustic scattering by a circular cylinder with Dirichlet boundary conditions and describe what the challenges are to achieving the goal of a solution which is valid everywhere in the fluid domain and which can be used to compute that solution efficiently at high frequencies.