The edge conditions and field representation theorems in the theory of electromagnetic diffraction

Abstract

In 1897 Rayleigh(14) pointed out that it is possible to obtain a family of solutions to certain problems in diffraction theory, notably those involving plane obstacles, by the simple operation of differentiation of some one solution. This, of course, alters the nature of the solution, especially so in the neighbourhood of a sharp edge. For, at an edge the parent solution may be finite and yet its derivative can become infinite. Further, such a differentiated solution may produce an infinite total energy in the neighbourhood of the edge. It is, therefore, natural to ask what conditions are required to make the solutions of these problems physically and mathematically acceptable and thus define the boundary-value problem uniquely.