The diffraction of light by progressive supersonic waves. Oblique incidence of light: I. Approximate solution of the Raman-Nath equations

Abstract

In the problem of the diffraction of light by a progressive supersonic wave at arbitrary incidence of the light, the method of solution of Kuliasko, Mertens and Leroy is employed by considering the coefficients of the Laurent expansion of an unknown generating function G (ζ, ν) as the amplitudes of the diffracted light beams. The integration of the system of difference-differential equations of Raman-Nath is reduced to the integration of a partial differential equation in G. Approximate solutions are obtained for: (1) ϱ = 0; (2) small values of ϱ (ϱ ⪡) by means of a power series in ϱ and a double series in ϱ and 2 a sin ϱ, leading in the second approximation to maxima as well as to minima of the first-order intensity, if the angle of incidence equals the Bragg angle.