Abstract
The diffraction and propagation problems presented here fall broadly into the two categories of high frequency diffraction of electromagnetic waves by smooth objects and of low frequency diffraction of electromagnetic waves by objects with edges. In the former category the geometry of the problems is such that the variables may be separated and a solution obtained in the form of an eigenfunction expansion which is suitable at low frequencies. The Watson Transformation which is then employed enables the high frequency case (i.e. the case when the wave number is large) to be considered. In the latter category an integral equation approach is adopted and a solution to the boundary value problems is shown to rest upon the solution of a Fredholm integral equation of the first kind. Using a technique employed by W.E., Williams, the Fredholm integral equation of the first kind is reduced to a Fredholm integral equation of the second kind for which, after ensuring that edge conditions are satisfied, an approximate solution is obtained. This solution is useful at low frequencies (i.e. when the wave number is small) and when certain separation distances are considered large. In both classes of problems attention is, amongst other things, focused on the field at large distances from the scattering obstacles so that expressions for scattering coefficients and transmission coefficients, where appropriate, may be obtained.