Simultaneous Four-Wave Mixing and Stimulated Raman Spectroscopy: Stark and Doppler Broadening.

Spectral line shapes obtained with four-wave mixing Raman spectroscopy (FWMRS) and stimulated Raman spectroscopy (SRS) are investigated experimentally and theoretically. While both techniques are commonly used as high-resolution spectroscopies, the systematic differences in their spectra have not been well explored. Using an experimental setup capable of simultaneous measurement of coherent Stokes Raman spectroscopy and inverse Raman spectroscopy spectra, we are able to perform a direct comparison between both classes of Raman spectroscopies and to reveal even minor differences in the resulting spectra. Experimental spectra of several lines in the vibrational Q-branch of molecular nitrogen (N_2) are obtained for different experimental conditions. At low pump intensities, after deriving the effect of Doppler broadening in these spectroscopies and taking the influence of neighboring lines into account, we are able to explain why FWMRS yields broader lines with peaks shifted relative to the peaks of SRS. At high pump intensities, we investigate the influence of optical Stark effect in focused Gaussian beams on both types of coherent Raman spectroscopy. Our experimental results demonstrate that SRS spectra show more Stark shift and broadening than their FWMRS counterparts. Our theory of signal generation in focused Gaussian beams leads to the calculation of theoretical Stark broadened spectra for both spectroscopies. While SRS spectra show excellent agreement with the theoretical calculations, simultaneously measured FWMRS spectra do not perfectly agree with our theory. We demonstrate that this discrepancy can be partly reconciled by the inclusion of a resonant fifth-order process in the previously third-order theory of FWMRS. Additionally we discuss the theory of phase modulation induced by rapid Stark tuning of molecular transition frequencies and its influence on both types of coherent Raman spectroscopy. We further suggest possible experiments to test our theory.