C. Durniak

Temporal walk-off for self-structuration of three-wave solitons in CW-pumped backward optical parametric oscillators

Stability analysis of the non-degenerate backward optical parametric oscillator in quasi-phase-matching decay interaction, between a CW-pump and counter-propagating signal and idler waves, proves that inhomogeneous stationary solutions exhibit a Hopf bifurcation, in contrast with the degenerate configuration. More importantly, we show that this Hopf instability gives rise to the generation of a backward three-wave soliton whose stable self-similar symbiotic structure is ensured by the group-velocity delay, or temporal walk-off, between the signal and the idler waves.

Unconditional temporal instability and self-pulse structuration in the phase-matched degenerate backward optical parametric oscillator

Stability analysis of the degenerate backward optical parametric oscillator in the phase-matching decay interaction, between a CW-pump and a sub-harmonic counter-propagating signal, proves that the inhomogeneous stationary solutions are always temporally unstable whatever the cavity length and pump power above threshold. The nonlinear dynamics exhibits self-pulse structuration of the backward signal with unlimited amplification and compression. Above a critical pulse steepening, dispersion saturates this singular behavior leading to strongly modulated solitary structures.

Three-Wave Backward Optical Solitons

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.

Modulated fronts in a modulationally stable LCLV cavity

This study reports on the occurrence of modulated structures with an intrinsic wavelength in a regime far from any modulational (i.e. Turing) instability. These modulations develop spontaneously from localized perturbations of the unstable homogeneous steady state that separates the two stable states of an hysteresis cycle. They occur in the wings of the traveling fronts and give eventually rise to a self-organized propagating pattern. This paper argues that the liquid crystal light valve nonlinear optical cavity is a strong candidate for this purpose.

Convection induced nonlinear phase modulations in optical systems

This study presents convection induced nonlinear phase modulations in optical systems. This investigation considers a degenerate optical parametric oscillator (DOPO) because convection (walk-off) arises naturally from the crystal birefringence that composes the optical device. Near to the threshold the nonlinear symmetry breaking is described by a Ginzburg-Landau model with an original dependence of the nonlinear self-coupling term upon convection. As a result, nonlinear travelling waves are no more symmetrical and the explicit analytical expressions of their intensities ratio with both convection and the distance from threshold are derived. Results show good agreement between the analytical and numerical results for the intensities ratio of the travelling waves that compose the signal field.