Temporal phase behavior from cascaded three wave mixing

Abstract

β–BBO crystal is an efficient material for three wave mixing processes like SHG, OPO or OPA. Different wave mixing processes that have the same wavevector matching condition can occur simultaneously. As an example, ω1 + ω2 → ω3 and ω3 − ω2 → ω1 or ω3 − ω1 → ω2 correspond to cascaded χ(2) effects where the initial pulse wavelengths are recovered. Choosing type I phase matching, we have studied the transient cascaded phase induced on the initial pulses. Compared with a direct Kerr n2 nonlinearity this cascaded phase shift is much more efficient (It is 50 times greater in β–BBO), and by detuning the phase matching one can also choose the phase shift sign[1]. Using a time resolved experiment [2], we have measured in the femtosecond regime the time dependence of the phase shift during sum and difference frequency generation and OPA processes. Due to group velocity mismatch between the pulses, the temporal dependence of the cascaded χ(2) phase is asymmetric with regard to the pulse temporal amplitude center. It results in an associate nonlinear chirp. This chirp, previously calculated[3,4] but never measured before to our knowledge, is difficult to compensate and limits the use of this efficient cascaded χ(2) n2.