Diffraction by a cylinder with a variable surface impedance

Abstract

A solution is obtained for the two-dimensional electromgnetic Green function for a circular cylinder with a peripherally varying surface im pedance. The variations about an arbitrary constant impedance have a small amplitude a and a sinusoidal spatial dependence. A cylindrical wave formulation leads to a specification of the wave amplitudes in terms of an in-homogeneous, second-order difference equation with variable coefficients, which is solved by assuming the expansibility of the solution as a power series in α. The derivation is carried out by a characteristic Green function procedure which yields directly various alternative representations of the solution. Special emphasis is placed on image representations in an infinitely extended angular space, and on their utility for asymptotic evaluation in the quasi-optic wavelength range. These aspects are stressed in a discussion of the constant impedance cylinder result which constitutes the leading term (α 0 power) in the power series expansion.