Optical third-harmonic generation of fused silica in gas atmosphere: Absolute value of the third-order nonlinear optical susceptibility<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>χ</mml:mi></mml:mrow><mml:mrow><mml:mn/><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo><mml:mn/></mml:mrow></mml:msup></mml:mrow></mml:math>

We report on a calibration procedure based on third-harmonic generation, which yields absolute values for ${\ensuremath{\chi}}^{(3)}.$ By calibrating the nonlinear susceptibility ${\ensuremath{\chi}}^{(3)}$ of fused silica against the established, quantum chemically calculated second-order hyperpolarizabilities \ensuremath{\gamma} of various gases at different pressures, we determine reliable absolute values for fused silica. We propose a standard third-order nonlinear optical susceptibilities ${\ensuremath{\chi}}^{(3)}$ of fused silica ${\ensuremath{\chi}}^{(3)}(\ensuremath{-}3\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})=(2.0\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}{\mathrm{m}}^{2}{/\mathrm{V}}^{2}$ at the wavelength 1.064 \ensuremath{\mu}m and ${\ensuremath{\chi}}^{(3)}(\ensuremath{-}3\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})=(1.6\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}{\mathrm{m}}^{2}{/\mathrm{V}}^{2}$ at 1.907 \ensuremath{\mu}m. These results are in excellent agreement with the cascading experiments reported by Bosshard et al. [Phys. Rev. B 61, 10 688 (2000)].