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.
We present analytical signal expressions for each two-color resonant four-wave mixing ͑TC-RFWM͒ scheme that can be used for double-resonance molecular spectroscopy in the limit of weak fields ͑no saturation͒. The theoretical approach employs time-independent, diagrammatic perturbation theory and a spherical tensor analysis in an extension of recent treatments of degenerate four-wave mixing ͓S. Williams, R. N. Zare, and L. A. Rahn, J. Chem. Phys. 101, 1072 ͑1994͔͒ and TC-RFWM for the specific case of stimulated emission pumping ͓S. Williams et al., J. Chem. Phys. 102, 8342 ͑1995͔͒. Under the assumption that the relaxation of the population, the orientation, and the alignment are the same, simple analytic expressions are derived for commonly used experimental configurations. The TC-RFWM signal is found to be a product of a concentration term, a one-photon molecular term, a line shape function, and a laboratory-frame geometric factor. These expressions are intended to facilitate the practical analysis of TC-RFWM spectra by clarifying, for example, the dependence on beam polarizations and rotational branch combinations.
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