Three-wave dissipative brillouin solitons

Abstract

Stimulated Brillouin backscattering of an electromagnetic c.w. pump wave into a red-shifted Stokes wave through a dissipative material acoustic wave, as governed by the nonlinear space-time three-wave resonant model, gives rise to backward-traveling solitary pulses, which are experimentally obtained in long fiber-ring cavities. Stability analysis of the inhomogeneous stationary Brillouin mirror solution in a c.w.-pumped cavity exhibits a one-parameter Hopf bifurcation. Below a critical feedback, a time-dependent oscillatory regime occurs, and we get self-organization of a localized pulsed regime. Experimental results and a dynamical simulation confirm this scenario. A stable continuous family of super-luminous and sub-luminous backward-traveling dissipative solitary pulses is obtained through a single control parameter. A parallel analysis in an unbounded one-dimensional medium shows that the integrable three-wave super-luminous symmetrical soliton is unstable for small dissipation, and that it cascades to a turbulent multi-peak structure. The general non-symmetrical and non-integrable case is dependent only on the exponential slope of the wave front of the backscattered Stokes wave, thus providing the stable super- and sub-luminous dissipative solitary attractors. An overview of the experimental results for a large set of input pump powers and Stokes feedback conditions shows a remarkable agreement with the numerical simulations of the three-wave coherent partial differential equations model. © 2008 Springer-Verlag Berlin Heidelberg.