Estimation of third-order nonlinear optical susceptibility $\chi ^{(3) }$of synthetic Cu$_{2}$O crystal

High-quality crystals of Cu$_{2}$O were prepared by an improved method for thermally oxidizing metallic copper. We report the nonlinear refractive index (n$_{2})$ and the nonlinear two-photon absorption coefficient ($\beta )$ of the resultant crystals. The following techniques were utilized: i) Z-scan, ii) third-harmonic generation, and iii) intensity-dependent interferometry. The third-order susceptibility ($\chi ^{(3)})$ of a material plays important role in optical signal processing including switching, altering the frequency and the transmission characteristics. A comparison between the third-order nonlinear susceptibilities of a standard nonlinear reference material, carbon disulfide (CS$_{2})$ and Cu$_{2}$O will be made.