Solution of a diffraction problem - Solution of a diffraction problem. I The wide double wedge

Abstract

The problem of radiation from a semi-infinite parallel-plate waveguide, terminated by an infinite plane flange (‘double wedge’) is investigated in the k -representation. The problem is reduced to an infinite system ( S ) of linear equations. Part I deals with the case of a ‘wide double wedge’ (the width of the waveguide much greater than the wavelength). This may be considered as a perturbation of the problem of diffraction by a single rectangular wedge, the rigorous solution of which is known (Reiche 1912). In the k -representation, this solution satisfies an integral equation, which is a limiting form of system ( S ). This leads to an approximate solution of the wide double-wedge problem, which appears to be a very good approximation, except in the neighbourhood of critical frequencies of the waveguide. The diffraction patterns and the reflexion coefficient are evaluated in this approximation. The accuracy and limits of applicability of classical diffraction theory are discussed. In the neighbourhood of critical frequencies, strong reflexion appears. This is a new limiting case of the problem, which is connected with the theory of quasi-stationary currents. Neumann’s iteration method is applied to system ( S ), in order to investigate the possibility that Kirchhoff’s approximation is the first step of an accurate solution by successive approximations. The convergence of Neumann’s series is discussed.