Non-phase-matched optical third-harmonic generation in noncentrosymmetric media: Cascaded second-order contributions for the calibration of third-order nonlinearities

Cascaded second-order contributions to third-harmonic generation are analyzed in detail, and are exploited to obtain reliable reference values for third-order nonlinear optical susceptibilities at several wavelengths. We describe the influence of boundary conditions on the measured properties for the case of high nonlinearity crystals such as ${\mathrm{KNbO}}_{3}$ and the organic salt 4-N, N${\ensuremath{-}\mathrm{d}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{o}\ensuremath{-}4}^{\ensuremath{'}}$-${N}^{\ensuremath{'}}$-methylstilbazolium toluene-p-sulfonate (DAST). Wavelength dispersion relations for the electronic third-order susceptibilities derived from third-harmonic generation experiments are discussed. Our reference standards allow a comparison of the third-harmonic generation results with measurements of the Kerr susceptibility determined with degenerate four-wave mixing and the z-scan technique and shows that ${\ensuremath{\chi}}^{(3)}(\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})>~{\ensuremath{\chi}}^{(3)}(\ensuremath{-}3\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})$ in the investigated wavelength range. The investigation of structure-property relationships between the perovskite crystals ${\mathrm{KNbO}}_{3}$ and ${\mathrm{KTaO}}_{3}$ indicates similar bond nonlinearities in these two compounds.