Diffraction of Light by Ultrasound in Anharmonic Crystals

Abstract

Due to anharmonic effects an initially sinusoidal ultrasonic wave of finite amplitude gradually distorts as it passes through a crystal. In the present paper we calculate the asymmetry in the diffraction pattern formed by passing monochromatic light through a cubic crystal perpendicular to the direction of propagation of such a distorted longitudinal ultrasonic wave. The solution of the nonlinear wave equation for the crystal, obtained by iteration to first order in the nonlinear terms, is used in the diffraction integral to obtain an expression for the light amplitude in the diffraction pattern. The first-order intensities are computed for NaCl. In a typical case, a wave of strain amplitude 2×${10}^{-5\mathrm{}}$ produces a 10% difference in intensity between the first positive and the first negative orders. These results suggest a method for obtaining the third-order elastic constants of transparent crystals.