The Rayleigh hypothesis and analytical properties of wave fields

The basic published literature concerning the application of the Rayleigh-series method in wave-diffraction studies is reviewed. Attention is given to rigorous studies of the analytical properties of wave fields and the applicability of analytical representations of fields by Rayleigh series, Sommerfeld integrals, and wave potentials. These studies yield theorems on the existence of solutions of direct and inverse diffraction problems. This survey includes discussions of mathematical formulations of characteristic problems of diffraction, wave diffraction by a single scatterer and by a periodic surface, and numerical methods for the solution of diffraction problems on the basis of the Rayleigh hypothesis.