Backward three-wave optical solitons

Backward symbiotic solitary waves in quadratic media with absorption losses are generated through the nonlinear non-degenerate three-wave interaction. We study these solitary waves in the particular case of a doubly backward quasi-phase matching configuration. The same mechanism responsible for nanosecond solitary wave morphogenesis in the c.w. pumped Brillouin-fiber-ring laser may act for picosecond pulse generation in a quadratic c.w. pumped optical parametric oscillator (OPO). The resonant condition is automatically satisfied in stimulated Brillouin backscattering when the fiber-ring laser contains a large number of longitudinal modes beneath the gain curve. However, in order to achieve quasi-phase matching between the three optical waves in the Χ⁽²⁾ medium, a nonlinear susceptibility inversion grating of sub-μm period is required. Such a quadratic medium supports solitary waves that result from energy exchanges between dispersionless waves of different velocities. We show, by a stability analysis of the non-degenerate backward OPO in the QPM decay interaction between a c.w. pump and backward signal and idler waves that the inhomogeneous stationary solution exhibits a Hopf bifurcation with a single control parameter. 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 signal and idler waves. We also study the dynamics of singly backward mirrorless OPO’s (BMOPO’s) pumped by an incoherent field, in line with the recent experimental demonstration of this OPO configuration. 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 two distinct phase-locking mechanisms that originate respectively in the convection and the dispersion properties of the fields. In both cases we show that 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 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.