Wave catastrophes: Types of focusing in diffraction and propagation of electromagnetic waves

Abstract

Theoretical and applied results obtained in the theory of diffraction and propagation of electromagnetic waves with the use of methods of wave catastrophes are reviewed. The basic concepts of the theory are considered: classification of wave catastrophes, methods for constructing uniform asymptotics applied to describe fields in such regions, and analysis of the field structure. A general description of classes of special functions involved in uniform asymptotic decompositions of wave fields, properties of these functions, and methods of their calculation are presented. Applied problems that are solved efficiently by means of methods of wave catastrophes are discussed.