Spontaneous Brillouin Scattering Spectrum and Coherent Brillouin Gain in Optical Fibers

Brillouin light scattering describes the diffraction of light waves by acoustic phonons, originating from random thermal fluctuations inside a transparent body, or by coherent acoustic waves, generated by a transducer or from the interference of two frequency-detuned optical waves. In experiments with optical fibers, it is generally found that the spontaneous Brillouin spectrum has the same frequency dependence as the coherent Brillouin gain. We examine the origin of this similarity between apparently different physical situations. We specifically solve the elastodynamic equation, giving displacements inside the body, under a stochastic Langevin excitation and in response to a coherent optical force. It is emphasized that phase matching is responsible for temporal and spatial frequency-domain filtering of the excitation, leading in either case to the excitation of a Lorentzian frequency response solely determined by elastic loss.