XXXI. The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic

Abstract

It has been found possible to make a detailed mathematical and numerical study of the field structure at and near a line focus of a cylindrical electromagnetic wave train possessing any finite amount of cylindrical aberration of the first order. By a suitable choice of parameters all the possible wave-lengths and degrees of aberration can be expressed in terms of a single infinite integral of two independent parameters. Diagrams of the magnitude and phase of this integral are given, and only the final mathematical results are described.