The diffraction of light by progressive supersonic waves. Oblique incidence of the light: III. The special case ϱ ⪢ 1

Abstract

Approximate expressions for the intensities of the diffracted light waves, in the case ϱ ⪢ 1 are derived from the formulae of the intensities, established by the exact solution of the system of difference-differential equations of Raman-Nath for the amplitudes of the diffracted light waves. Two cases are considered: (1) the angle of incidence φ is a Bragg angle; (2) φ is neither a Bragg angle, nor zero. In order to facilitate the computations in the latter case, a new notation is introduced for the coefficients of the Mathieu functions of fractional order and their characteristic numbers. From the obtained formulae, symmetry or asymmetry properties of the diffraction spectrum are derived; periodicity properties as well as extremal values for the diffraction lines are established, which are in agreement with experiments of Nomoto. The approximate solutions of Phariseau, Bhatia and Noble and David have been found.