Optical-parametric-generation process driven by femtosecond pulses: Timing and carrier-envelope phase properties

We investigate, both numerically and experimentally, the optical parametric generation (OPG) process in second-order nonlinear crystals driven by femtosecond pulses. We model the OPG process by solving the coupled second-order three-wave nonlinear propagation equations in the plane-wave limit, using noise fields to mimic the vacuum fluctuations. We focus on two parameters: (i) the temporal jitter between the OPG and the pump pulse; (ii) the carrier-envelope phase (CEP) relationship between the OPG and the pump pulse. Both numerical simulations and experiments support the following conclusions: (i) in the regime of low pump depletion the OPG pulse is synchronized with the pump, but its energy presents strong fluctuations; (ii) in the regime of high pump depletion, the energy of the OPG pulse stabilizes, but a temporal jitter with respect to the pump pulse is introduced; (iii) in both cases, the CEP relationship between pump and OPG pulses is completely random.