Stimulated emission pumping spectroscopy via two-color resonant four-wave mixing

Abstract

We present a combined theoretical and experimental study of the application of two-color resonant four-wave mixing (RFWM) to stimulated emission pumping (SEP) spectroscopy. The theoretical approach employs time-independent, diagrammatic perturbation theory and a spherical tensor analysis in an extension of a recent treatment of degenerate four-wave mixing [Williams, Zare, and Rahn, J. Chem. Phys. 101, 1072 (1994)]. The resulting signal expression for two-color RFWM separates the molecular properties from purely laboratory-frame factors determined by the polarizations of the input beams and the rotational branch types of the SEP PUMP and DUMP transitions. This expression is valid in the limit of weak fields and for molecules in which the total angular momentum (omitting nuclear spin) is a good quantum number. In addition, we demonstrate that the spectral response for tuning the DUMP laser is a simple Lorentzian in free-jet experiments. We test our theoretical results and demonstrate the applicability of RFWM-SEP to jet-cooled, transient species in experiments on C3 and HCO. Using the well-studied à 1Πu–X̃ 1Σ+g system of C3, we illustrate and compare the two possible schemes for RFWM-SEP. These are defined as ω1=ω2 (PUMP) and ω3=ω4 (DUMP) or ω1=ω4 (PUMP) and ω2=ω3 (DUMP), where ω1, ω2, and ω3 are the input frequencies and ω4 is the signal frequency. Using the B̃ 2A′–X̃ 2A′ system of HCO, we obtain RFWM-SEP spectra that probe ground-state vibrational resonances lying above the low threshold for dissociation to H+CO. Varying the polarization of the input beams or PUMP rotational branch produce dramatic effects in the relative intensities of rotational lines in the RFWM-SEP spectra of HCO; these effects are well-described by our theoretical analysis. Finally, RFWM-SEP spectra of HCO resonances that are homogeneously broadened by dissociation are consistent with the theoretically predicted Lorentzian line shape; the full widths for these levels are in good agreement with those determined via unsaturated fluorescence depletion SEP.