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

Abstract

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.

Laser diagnostics and minor species detection in combustion using resonant four-wave mixing

“…The generated signal is then orthogonally polarized to the strong pumps and so use of a crossed polarizer in the detection path leads to improved rejection of noise from scattered pump radiation. The effect on the signal is described by a J-dependent geometrical factor G(J); a function of the relative polarization and the ΔJ of the transition, which modifies the basic A&L result for both weak and strong pump fields [77,78].…”

“…The generated signal is then orthogonally polarized to the strong pumps and so use of a crossed polarizer in the detection path leads to improved rejection of noise from scattered pump radiation. The effect on the signal is described by a J-dependent geometrical factor G(J); a function of the 50 relative polarization and the ΔJ of the transition, which modifies the basic A&L result for both weak and strong pump fields [77,78].Absorption by the medium may be a problem when using strong resonance lines to enhance the DFWM signal. In particular the distortion of relative intensities of different molecular lines caused by line-centre absorption will affect values of temperature or concentration derived from the signals [79,80].…”

Two-color resonant four-wave mixing: A tool for double resonance spectroscopy

“…1) into a general REWM signal equation separates into the analysis of the numerators, which contain the four transition moments summed over all possible magnetic sublevels, and the resonant denominators, which contain the spectral response and can be removed from the summations because the dipolar dephasing rates are indpendent of M. The M-level sums may be re-ordered so that for each two-color RFWM process the numerators reduce to a four-photon matrix element, which, for the schemes in Figs. 21 for DFWM and will not be described in detail here. This method provides a well developed and efficient way of using the inherent symmetry of the system and allows the separation of the molecular properties from purely geometric factors.…”

Excited-state Structure and Dynamics of Nitric Oxide probed by Resonant Four-wave Mixing Techniques

“…Toward this end, a description of two-colour LIGS based on an extension of work on DFWM (Williams et al 1994b) that combines timeindependent diagrammatic perturbation theory with spherical tensor analysis has very recently been developed and applied to measurements of intensities and line shapes in two-colour RFWM experiments on C3 and HCO (Williams et al 1995). These methods look very promising for quantitative interpretation of line intensities observed by using typical experimental arrangements and a variety of polarisation configurations.…”