A relation between the vibrational nonlinear refractive index coefficient \({{n}_{2}}(\omega )\) and the vibrational cubic susceptibility \({{\chi }^{{(3)}}}(\omega ';\omega ',\omega , - \omega )\) has been analytically derived involving well-known optical, spectral, and thermal matter parameters. This relation allows one to estimate the nonlinear phase shift of low-power probe radiation at the frequency \(\omega '\) , which propagates in the field of a high-power terahertz pump wave at the frequency \(\omega \) . Theoretical estimates of the nonlinear susceptibility \({{\chi }^{{(3)}}}(\omega ';\omega ',\omega , - \omega )\) for water and fused silica for terahertz Kerr effect measurements have been obtained in good agreement with experimental data.
