Brillouin Scattering in Cubic Crystals

Using a helium-neon laser light source and a high-resolution grating spectrograph we have studied, at room temperature, the Brillouin spectrum of light scattered from three alkali halide crystals: KCl, RbCl, and KI. By suitable orientation of the crystal axes relative to the incident beam we have obtained the frequency and the velocity of thermally excited phonons of ∼3000 Å wavelength in longitudinal and "mixed" acoustic phonon branches as a function of the direction of propagation in the [110] plane. From these data we have determined for each crystal, entirely in the absence of acoustic excitation, the elastic constants $C_{11}$, $C_{12}$, and $C_{44}$ for microwave (8-15 kMc/sec) sound waves with an accuracy from 0.25% to 4%. The elastic constants so determined are in very good agreement with investigations made in the ultrasonic region using externally generated sound waves of frequency ∼10 Mc/sec. This agreement indicates the absence of dispersion in the sound-wave velocity over three orders of magnitude change in the sound-wave frequency. We also present the theory for the scattering of light from thermally excited sound waves in a cubic crystal. This theory predicts the intensity, polarization, and spectral distribution of the scattered light as a function of the incident and scattered directions in the crystal. By treating the phonons quantum-mechanically at temperatures comparable to the scattering phonon frequency, we have also obtained expressions for the temperatures dependence of the scattering valid at very low temperature. The theory is in quite good agreement with our measurements of the relative intensity of the scattering from phonons in the longitudinal and "mixed" acoustic modes.