Modeling the spontaneous Brillouin scattering spectrum of microstructured optical fibers
Résumé
Brillouin light scattering can describe the diffraction of light waves by either 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 [1]. The latter arrangement is notably used for Brillouin sensing in fibers [2]. In experiments with classical optical fibers, but also with microstructured fibers and microwires, it is generally observed experimentally that the spontaneous Brillouin spectrum has the same frequency dependence as the coherent Brillouin gain [3,4]. We examine the origin of this similarity between apparently different physical situations. We specifically solve the elastodynamic equation, giving the evolution of phonons, under a stochastic Langevin excitation and in response to a coherent optical force, using a finite element method [5,6]. From this analysis, we observe that phase matching is responsible for both temporal and spatial frequency-domain filtering of the excitation, leading in either case to the excitation of a Lorentzian frequency response whose width is determined by elastic losses. When isolated elastic modes are present, – which applies typically to microstructured fibers, nanoscale waveguides, and microwires, – we obtain an expression for the Brillouin linewidth that depends explicitly on the modal properties. Furthermore, we exemplify numerically how the stochastic force modeling the Langevin excitation is spatially filtered by the elastodynamic equation to produce the isolated mode near its eigenfrequency.