Three-Wave Backward Optical Solitons

Abstract

Three-wave solitons backward propagating with respect to a pump wave are generated in nonlinear optical media through stimulated Brillouin scattering (SBS) in optical fibers or through the non-degenerate three-wave interaction in quadratic (χ (2)) nonlinear media. In an optical fiber-ring cavity, nanosecond solitary wave morphogenesis takes place when it is pumped with a continuous wave (c.w.). A backward dissipative Stokes soliton is generated from the hypersound waves stimulated by electrostriction between the forward pump wave and the counterpropagating Stokes wave. Superluminous and subluminous dissipative solitons are controlled via a single parameter: the feedback or reinjection for a given pump intensity or the pump intensity for a given feedback. In a c.w. pumped optical parametric oscillator (OPO), backward picosecond soliton generation takes place for non-degenerate three-wave interaction in the quadratic medium. The resonant condition is automatically satisfied in stimulated Brillouin backscattering when the fiber-ring laser contains a large number of longitudinal modes beneath the Brillouin gain curve. However, in order to achieve quasi-phase matching between the three optical waves (the forward pump wave and the backward signal and idler waves) in the χ (2) medium, the nonlinear susceptibility should be periodically structurated by an inversion grating of sub-μm period in an optical parametric oscillator (OPO). The stability analysis of the inhomogeneous stationary solutions presents a Hopf bifurcation with a single control parameter which gives rise to temporal modulation and then to backward three-wave solitons. Above OPO threshold, the nonlinear dynamics yields self-structuration of a backward symbiotic solitary wave, which is stable for a finite temporal walk-off, i.e. different group velocities, between the backward propagating signal and idler waves. We also study the dynamics of singly backward mirrorless OPO (BMOPO) pumped by a broad bandwidth field and also with a highly incoherent pump, in line with the recent experimental demonstration of this BMOPO configuration in a KTP crystal. We show that this system is characterized, as a general rule, by the generation of a highly coherent backward field, despite the high degree of incoherence of the pump field. This remarkable property finds its origin in the convection-induced phase-locking mechanism that originates in the counter-streaming configuration: the incoherence of the pump is transferred to the co-moving field, which thus allows the backward field to evolve towards a highly coherent state. We propose other realistic experimental conditions that may be implemented with currently available technology and in which backward coherent wave generation from incoherent excitation may be observed and studied

Model for coherence transfer in a backward optical parametric oscillator

“…According to the velocity-locking mechanism, the process of coherence transfer becomes more efficient when the group velocity of the co-propagating waves are matched [8], but this requires another choice of resonant frequencies for the backward MOPO [27]. In order to take advantage of a type I configuration in PPKTP, it is more convenient to chose the signal wave as the backward field, so that the group velocities of the co-propagating pump and idler waves may be matched exactly, v p = v i .…”