Inverse Raman bands in ultrafast Raman loss spectroscopy

Ultrafast Raman loss spectroscopy (URLS) is equivalent to anti-Stokes femtosecond stimulated Raman spectroscopy (FSRS), using a broadband probe pulse that extends to the blue of the narrow bandwidth Raman pump, and can be described as inverse Raman scattering (IRS). Using the Feynman dual time-line diagram, the third-order polarization for IRS with finite pulses can be written down in terms of a four-time correlation function. An analytic expression is obtained for the latter in the harmonic approximation which facilitates computation. We simulated the URLS of crystal violet (CV) for various resonance Raman pump excitation wavelengths using the IRS polarization expression with finite pulses. The calculated results agreed well with the experimental results of S. Umapathy et al., J. Chem. Phys. 133, 024505 (2010). In the limit of monochromatic Raman pump and probe pulses, we obtain the third-order susceptibility for multi-modes, and for a single mode we recover the well-known expression for the third-order susceptibility, χ(IRS) ((3)), for IRS. The latter is used to understand the mode dependent phase changes as a function of Raman pump excitation in the URLS of CV.