Development of a simple model for optical parametric generation

Optical parametric generation is treated as a particular case of parametric amplification of two waves at frequencies ω1 and ω2 from a pump wave ω3 propagating in a nonlinear crystal. This theory describes the configuration in which initial intensities for ω1 and ω2 at the input plane of the material are equal to zero. This research is based on the theory of optical parametric fluorescence. According to this quantum-mechanical model, there is a probability for a photon ω3 to be spontaneously scattered into photons ℏω1 and ℏω2, respectively. We introduce a critical length over which the first signal and idler photons are created. This new approach allows us to take into account optical parametric fluorescence not only at the entrance of material but also over its entire interaction length. We show that this can widely modify the calculated generated intensities. This model is applied to a KTP optical parametric generator and amplifier pumped by the second harmonic (532 nm) of a Nd:YAG picosecond laser.