Degenerate four-wave mixing in noncentrosymmetric materials

This work treats degenerate four-wave mixing (DFWM) in noncentrosymmetric materials, taking into full account the fact that the DFWM signal arises from third-order nonlinear optical effects as well as from two distinct combinations of second-order effects: second-harmonic generation plus difference frequency generation and optical rectification plus Pockels effect. Because of these second order “cascaded” contributions, the DFWM signal becomes dependent on details of the experimental setup that do not normally matter for centrosymmetric materials, such as the wave vectors of the interacting beams and the pulse duration. The origin, consequences, and possible applications of these effects are discussed for both the “forward” and the “phase-conjugation” DFWM configurations. All second-order contributions are described quantitatively by introducing effective third-order susceptibilities, and their value is discussed using the example of two materials: ferroelectric ${\mathrm{KNbO}}_3$ and the organic salt $4-N,N-\mathrm{dimethylamino}-4^{\prime }-N^{\prime }-\mathrm{methyl}-\mathrm{stilbazolium}\mathrm{}\mathrm{tosylate}.$