Possibility of the analytic solution of certain classical problems of diffraction theory

Two well known approaches (the integral equation method and the Johns method) in the reformulation of boundary value problems of diffraction theory into Wiener-Hopf-Fock equations make it possible to obtain an explicit analytic solution to a small number of problems whose geometry can be defined as a combination of semiinfinite domains. These approaches, however, do not exhaust the possibility of such reformulations. Other possibilities are demonstrated by the solution of two classical problems of electrodynamics, including the diffraction of a plane E-polarized wave obliquely incident on a plane ribbon grating and on a knife grating. It is shown that the number of explicit analytic solutions by the Wiener-Hopf-Fock method can also be increased by the use of diffraction problems whose geometry does not contain semiinfinite regions.