On a synthesis of field scattered by a perfectly conducting obstacle and Rayleigh´s hypothesis

If one considers the stationary boundary-value problem of wave scattering by an obstacle with an arbitrarily shaped surface, the Rayleigh hypothesis signifies the possibility of representing scattered waves by means of Rayleigh´s series everywhere outside the surface of the scatterer. A method of rigorous solution of the scattered-field-synthesis problem is proposed for a 2-D external point-source excited case. The boundary condition corresponds to a perfectly conducting finite obstacle with a smooth analytic boundary. Some simple geometrical restrictions on the location of the analytical continuation´s singularities supply the necessary and sufficient conditions for the Rayleigh hypothesis to be valid.<>