Specific properties of cubic optical parametric interactions compared to quadratic interactions

This paper is devoted to the phase matching and parametric gain properties of the χ⁽³⁾ mixing, and points out several specific behaviors whenever compared to χ⁽²⁾ interactions. For a given pulsation ω₄ and a fixed direction of propagation, phase matching simultaneously exists for numerous sets (ω₁,ω₂,ω₃). Two combinations of the interacting pulsations exist: ω₄=ω₁+ω₂+ω₃ and ω₄+ω₁=ω₂+ω₃, both with ω₄>ω₁,ω₂,ω₃. The second scheme has no equivalent among the three-wave processes; in this scheme, phase matching exists for all configurations of polarizations. It is then possible to make use of the largest elements of the χ⁽³⁾ tensor. Furthermore, in noncentrosymmetric crystals, solutions exist where nonzero χ⁽³⁾ nonlinear effective coefficient is associated with a zero χ⁽²⁾ nonlinear effective coefficient. Concerning the gain of χ⁽³⁾ parametric amplification, the conversion efficiency is analytically calculated for the most general case: it is nonzero only if at least three fields are incident on the crystal. The calculated gain allows us to deduce the oscillation threshold of a χ⁽³⁾ optical parametric oscillator and the effect of the pulse duration: the threshold is not independent of the parametric fluorescence field, so that it can only be calculated analytically for an injection-seeded optical parametric oscillator.