Diffraction coefficients related to cylindrically curved soft-hard surfaces

Abstract

The author considers the two-dimensional problem of scattering of the field due to a point source by a circularly cylindrical shell which is ''hard'' on one side and ''soft'' on the other. For convenience the shell is assumed to occupy \(\rho =a\), \(0<\phi <\infty\), and consequently Fourier integral techniques over \(\phi\) may be used. The problem is reduced to a matrix Hilbert equation, which can be solved by Hurd's technique. The Hankel functions involved are replaced by their Debye approximations and the various types of waves - edge waves, whispering gallery modes, creeping waves - are discussed. It is pointed out that the diffraction of the incident ray may be obtained by modelling the edge locally as the edge of the tangent half-plane.