Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy

A phase-modulation technique for coherent Raman spectroscopy is used to measure both the real and imaginary parts of the third-order nonlinear susceptibility of gases. The Raman Q-branch resonance of ${\mathrm{D}}_2$ is calibrated by comparison to the Q-branch resonance of ${\mathrm{N}}_2$. By using ${\mathrm{D}}_2$ as an internal standard, the nonresonant electronic susceptibility of Ar and the sum of the electronic and molecular reorientation contributions to the nonresonant susceptibility of ${\mathrm{N}}_2$ are determined. The results of these measurements are compared to published data on the Q-branch Raman cross section of ${\mathrm{H}}_2$, to predictions from the theory of the optical (ac) Kerr effect, and to measurements of electronic hyperpolarizabilities. For the last-mentioned quantity, measurements from three-wave mixing, from field-induced second-harmonic generation, from third-harmonic generation, and from the electro-optic (dc) Kerr effect are intercompared and agreement at the 10% level is established. Formulas interrelating a number of different definitions of third-order susceptibilities found in the literature are presented.