Slow dynamics and multipair self phase-locked oscillation in the divide-by-3 cw optical parametric oscillator

This study investigates the slow dynamics and multipair self phase-locked oscillation in the divide-by-3 continuous-wave optical parametric oscillator (OPO). This work also reports on a different regime of operation, when the SLOPO is slightly frequency detuned from exact by-3 division by changing the PPLN phase-matching temperature. When /spl delta/ is equal or multiple of the cavity free spectral range /spl Delta//spl nu//sub s/, cascade injection-locking of many resonant mode pairs (up to 5-6) has been observed by spectral analysis of the SPLOPO output, as a premise to a cw mode-locked OPO operation. Such a simultaneous multipair stable oscillation is precluded in a conventional OPO due to gain saturation. The maximum number of phase-locked pairs is limited by the pumping power. The potential of the device as a generator of multipartite quantum entangled pairs, as well as in 3-phase-encoded spiral wave transverse pattern formation are discussed.

Nonlinear dynamics of conventional optical parametric oscillators (OPOs) has been extensively investigated in the past from the point of view of spatio-temporal instabilities and transverse pattern formation in a highly nonlinear dissipative system. By conventional, we refer to an OPO medium consisting of a single down-conversion medium. It was shown that such an OPO can display either bistability or self-pulsing only in the triply resonant case, under extreme cavity detuning operation. Attempts to observe the Hopf instabilities, which periods scale in the 1–10 MHz range, have always been mitigated by the occurrence of dynamical thermal effects arising from the required high pumping threshold. Recently, we have introduced a new class of highly non-degenerate subharmonic OPOs (dividing the pump frequency by 3, i.e that also contains a second nonlinear crystal self-injecting the signal and idler waves via internal second-harmonic generation (SHG), leading thus to self phase-locked (SPL), phase diffusion-free oscillation [1]. A much richer dynamics of this SPLOPO device has been theoretically predicted [1]. The resonantly competing :X(2) processes was shown to induce intensity bistability for any cavity detuning 0, independently of the cavity resonance configuration. The stable upper branch can further destabilize via a Hopf bifurcation for a low pump input value relative to the oscillation threshold, especially for zero detuning oscillation for which a critically slowed-down dynamics is predicted as a consequence of the coalescence of the saddle-node point with the lasing threshold point as (hence co-existence of bistability and self-pulsing). The transition from non-SPL to SPL operations results in a strong intensity dip of the signal/idler intensities due to the nonlinear competition. Contrary to the conventional OPO subject to phase diffusion, parametric oscillation occurs with 3 equiprobable (stable) phase states associated to the same intensity state . All these predicted dynamical signatures were recently reported in a cw triply-resonant SPLOPO (threshold ~100mW) containing a dual-section PPLN chip carrying in cascade the OPO/SHG processes [2]. Fig.1a shows a typical SPL fringe dip within the SPLOPO mode cluster observed under cavity length scan, corresponding to signal-idler phase-locking at exact subharmonicity. The width and contrast of the dipped fringe, giving the phase/frequency locking range, depends on the nonlinear coupling strength controlled by the ratio of the two chip sections. The free-running SPLOPO could be biased on the dip without any mode pair hop during up to half an hour, whereas in non-SPL conditions mode hops of the conventional OPO are retrieved. When and (pump power ), the SPL fringe exhibits sustained small amplitude periodic pulsing in the 1–20 kHz frequency range as a consequence of the critically slowed-down dynamics. We also report on a different regime of operation, when the SLOPO is slightly frequency detuned from exact by-3 division (i.e. by changing the PPLN phase-matching temperature (Fig.1b) When 6 is equal or multiple of the cavity free spectral range , cascade injection-locking of many resonant mode pairs (up to 5–6) has been observed by spectral analysis of the SPLOPO output, as a premise to a cw mode-locked OPO operation. Such a simultaneous multipair stable oscillation is precluded in a conventional OPO due to gain saturation. The maximum number of phase-locked pairs was limited by the pumping power • The potential of the device as a generator of multipartite quantum entangled pairs, as well as in 3-phase-encoded spiral wave transverse pattern formation will be discussed. Fig. 1. (a) Time traces of signal and pump cluster when the cavity is dithered. The upper trace is the output of a length-biased confocal Fabry-Perot set to transmit the signal of mode-pair 5. (b) Resonant cascade multipair operation.