Diffraction of light by ultrasonic waves I. General theory

Abstract
In this paper, following Darwin's (1924) treatment of the reflexion and refraction of light on a transparent homogeneous medium, the problem of the diffraction of light by ultrasonic waves is formulated in terms of the scattering of electromagnetic waves by a periodically perturbed medium. This leads to an integral equation which has been solved for E-polarization with the help of a trial solution for the electric disturbance in the medium in the form of a double infinity of plane waves. The condition that the trial function be a solution of the integral equation leads to (a) the frequencies and the directions of the diffracted spectra and (b) three infinite sets of linear algebraic equations for the amplitudes N$_{lm}$ and other unknowns occurring in the trial solution. The expressions for the intensities of the diffracted spectra involve the various unknowns of the trial function and can be immediately written down once these unknowns have been determined from the equations. The solution of the equations (b) by approximate methods, calculation of intensities for special cases and comparison of various theoretical results with available experimental data are dealt with in part II which follows. A summary of the main results obtained there is given in the Introduction (section 1) of the present paper.

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