Spectral shape of stimulated Brillouin scattering in crystals

We derived a formula to describe the stimulated Brillouin spectral shape in crystals for various temperatures ranging from room temperature to liquid-helium temperature. We modeled a sample as a one-dimensional system with a finite thickness in which the optically induced phonon propagates, partly interacting with the pump and probe laser beams. When the sample length is shorter than the propagation distance (i.e., the mean free path) of phonons, the spectral shape becomes multipeaked due to the multiple phonon reflections in the sample. Such a situation can be realized in a thin film or a bulk sample at low temperatures. We experimentally measured the Brillouin gain spectra with a multipeak structure in TeO2 and PbMoO4 crystals at low temperatures. We found that these spectra were reproduced by our formula for both the coaxial and off-axis phonon propagations with respect to the laser beams. It was revealed that our formula is very useful in estimating the phonon attenuation coefficient from the observed spectra, which gradually change from Lorentzian shape to a multipeak spectrum with decreasing temperature.