Two-color resonant four-wave mixing: Analytical expressions for signal intensity

Abstract

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.

The effect of laser bandwidth on the signal detected in two-color, resonant four-wave mixing spectroscopy

“…Only straightforward computational modifications, however, are necessary to adapt the theoretical treatment developed below to different excitation schemes, a list of which is presented in Ref. 23.…”

“…However, the application of DPT has been carried out, so far, by assuming ideal experimental conditions. 23 Saturation effects arising from the utilization of high-intensity lasers are, for example, not accounted for by this theory. Neither are nonlinear phenomena such as the formation of nonresonant, laser-induced thermal, 25 acoustic 13 or electrostrictive 26 gratings consisting of modulations in the real part of the refractive index that occur, in relatively high-density media, as a result of the optical interference of intense laser beams.…”

“…[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Diagrammatic perturbation theory ͑DPT͒ has proven to be a very effective tool in analyzing the spectra obtained in gas-phase TC-RFWM. Analytic expressions for the signal line profile have been reported for a variety of TC-RFWM schemes used in double-resonance spectroscopy of bound 23 and quasibound 24 molecular states. However, the application of DPT has been carried out, so far, by assuming ideal experimental conditions.…”

“…The contribution of the laser bandwidth to the TC-RFWM signal profile is determined by a full frequencydomain calculation based on DPT and formulated as an extension of the theory presented in Refs. 23,24. Both Lorentzian and Gaussian line shapes are discussed with no assumption on the relative laser bandwidth and transition widths and the theoretical treatment addresses three-level systems featuring either discrete or quasibound states.…”

“…27 In addition, when the Doppler effect is taken into account, the singlemolecule contribution to (3) , explicitly calculated by DPT, must be integrated over the velocity distribution of the absorbing molecules and, as a consequence, the analytic character of the signal line profile is lost. 23 Finally, no attempt has been made to include in the DPT model the effect of finite laser bandwidths.…”