Dissipative three-wave structures in stimulated backscattering. II. Superluminous and subluminous solitons

Abstract

Stimulated Brillouin or Raman backscattering of a cw pump into dissipative material and Stokes waves, governed by the nonlinear space-time three-wave resonant model, gives rise to solitary pulses, which are experimentally obtained in long fiber-ring cavities. We show that the known superluminous symmetrical soliton solution is unstable for small dissipation, cascading to a turbulent multipeak structure. A stable single-peak dissipative soliton solution prevails for moderate dissipation (damping), and at a lower critical dissipation operates a pitchfork bifurcation, first yielding a stable bisolitary structure, and then multipeak space-time-dependent structures. Besides a continuous set of asymptotically stable superluminous and subluminous dissipative solitary attractors, the general nonsymmetrical and nonintegrable case is dependent only on the wave front exponential slope of the backscattered Stokes wave, in agreement with the solitary pulses observed in a Brillouin fiber-ring laser. These three-wave dissipative solitons result from the dynamical compensation between the wave-front slope dispersion and the pump depletion. We give an explicit solution for the particular integrable luminous velocity case. We also show that initial steep Stokes envelopes (like Gaussian profiles) evolve to the universal subluminous solitary attractor of paper I.