Reduction of degenerate four-wave mixing spectra to relative populations I. Weak-field limit

Diagrammatic perturbation theory combined with a spherical tensor treatment allows the degenerate four-wave mixing (DFWM) signal resulting from an isotropic molecular sample to be decomposed into a sum of three multipole moments in the weak-field (no saturation) limit. The zeroth moment gives the relative internal-state population contribution, the first moment the orientation contribution, and the second moment the alignment contribution to the DFWM spectra. This treatment makes explicit how the magnitude of the DFWM signal depends on the polarizations of the other three beams and the collisional relaxation caused by the environment. A general expression is derived for the DFWM signal for an arbitrary geometric configuration of the beams (arbitrary phase matching geometry). Under the assumption that the rates of collisional relaxation of the population, the orientation, and the alignment are the same, simple analytic expressions are found for the most commonly used experimental configurations, which should facilitate the practical analysis of DFWM spectra