Optical turbulence in multiple stimulated Brillouin backscattering

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Abstract
Driven stimulated Brillouin rescattering, obtained by multiline laser light, each satellite line downshifted by twice the acoustic frequency ωs, is an efficient way to reduce stimulated Brillouin reflection (Colombant et al. 1983; Montes 1985). For long enough interaction lengths the nonlinear dynamics leads to optical turbulence. We consider a six wave coherent model whose wave frequencies are ω1 and ω3 = ω1 − 2ωs for the principal and auxiliary pump waves, ω2 = ω1 − ω2 and ω4 = ω1 − 3ωs for the backscattered waves, and ωs for the forward- and backward-traveling sound waves. The sound wave is weakly damped and its velocity is neglected (limit cs/c = 0). The space-time evolution is studied numerically. The model depends upon several parameters of nonlinearity. Increasing the interaction length L we observe: (1) a stationary regime for L smaller than a critical value Lcrit; then (2) an oscillatory behaviour appears through a Hopf bifurcation at L = Lcrit which becomes (3) more and more anharmonic and (4) finally chaotic for large L.