DIFFRACTION OF LIGHT BY SOUND WAVES

Abstract

Diffraction of light by a sinusoidal sound wave is discussed in detail. Assuming that the sound column modulates only the phase of the incident light in both time and space, the frequencies, wavevectors, and intensities of the diffracted waves are obtained for normal incidence. A transition length (width of sound beam) is defined, above which all diffraction effects disappear due to destructive interference. Constructive interference is obtained, however, provided the light is incident at the Bragg angle, in which case the diffracted beam appears to be reflected from the acoustic wavefronts. The transition length thus separates the region of multiple -order (Raman -Nath) diffraction from the region of single -order (Bragg) diffraction. It is found to be directly proportional to the square of the acoustic wavelength and inversely proportional to the optical wavelength. In the case of Bragg diffraction, the energy is exchanged sinusoidally between the diffracted and undiffracted beams. Owing to the finite width of the sound beam, the Bragg condition is relaxed, and the effect can be used to control the direction and phase of the diffracted beam or to determine the angular distribution of the acoustic power. Next, a particle picture of diffraction in terms of photons and phonons is given. The diffraction process is described as a single as well as a multiple three -particle interaction. The effects of finite optical and acoustic beamwidths and variation of acoustic frequency are considered in terms of momentum conservation. Finally, an analysis based on Maxwell's equations for an arbitrarily polarized light beam propagating in an arbitrary direction is given using the partial -wave approach. A set of coupled difference- differential equations for the diffracted amplitudes is derived from the optical wave equation and analytic solutions are obtained in the Raman-Nath and Bragg regions of diffraction. The results for normal and Bragg incidence are obtained as special cases. Limits of the two regions are defined, thus giving a transition region in which numerical solutions can be obtained.