Spurious internal fields in scattering by a cylinder

Abstract

Numerical computations of scattering of electromagnetic waves by hollow conductors can produce spurious internal fields. This well-known effect is examined in detail, at an elementary level, for two-dimensional scattering by a circular cylinder. A plane electromagnetic wave of fixed frequency is scattered from a perfectly conducting hollow circular cylinder. The scattered wave may be regarded as produced by a current density in the cylindrical boundary, which can be readily computed from standard theory. Alternatively, the boundary may be divided into N discrete intervals and the current density may be computed by expressing an appropriate integral equation in discretized form. There is then a difference between the computed and exact current densities that is purely an artefact of the discretization. Provided the radius is not chosen to correspond to an internal resonance, the error in the current density does approach zero as N increases, but in an unusual way: if the radius is just below a resonance value, it can increase to large values before it decreases. As well as giving some error in the computed scattered field, a conspicuous consequence is a spurious internal field, which consists of a mixture of standing waves, not normal modes of the cylinder except at resonance, one from each Fourier component of the incident plane wave.