Theoretical investigation of the direct observation of anharmonic coupling in CDCl3 in the time domain with femtosecond stimulated Raman scattering

Energy flow between spectral components in 2D broadband stimulated Raman spectroscopy

We introduce a general theoretical description of non resonant impulsive femtosecond stimulated Raman spectroscopy in a multimode harmonic model. In this technique an ultrashort actinic pulse creates coherences of low frequency modes and is followed by a paired narrowband Raman pulse and a broadband probe pulse. Using closed-time-path-loop (CTPL) diagrams, the response on both the red and the blue sides of the broadband pulse with respect to the narrowband Raman pulse is calculated, the process couples high and low frequency modes, which share the same ground state. The transmitted intensity oscillates between the red and the blue side, while the total number of photons is conserved. The total energy of the probe signal is periodically modulated in time by the coherence created in the low frequency modes.

Quantum theory of time-resolved femtosecond stimulated Raman spectroscopy: direct versus cascade processes and application to CDCl3

We present a quantum mechanical wave packet treatment of time-resolved femtosecond stimulated Raman spectroscopy (FSRS), or two-dimensional (2D) FSRS, where a vibrational coherence is initiated with an impulsive Raman pump which is subsequently probed by FSRS. It complements the recent classical treatment by Mehlenbacher et al. [J. Chem. Phys. 131, 244512 (2009)]. In this 2D-FSRS, two processes can occur concurrently but with different intensities: a direct fifth-order process taking place on one molecule, and a cascade process comprising two third-order processes on two different molecules. The cascade process comprises a parallel and a sequential cascade. The theory is applied to the 2D-FSRS of CDCl(3) where calculations showed that: (a) the cascade process is stronger than the direct fifth-order process by one order of magnitude, (b) the sidebands assigned to C-Cl E and A(1) bends, observed on both sides of the Stokes C-D stretch frequency, are not due to anharmonic coupling between the C-D stretch and the C-Cl bends, but are instead due to the coherent anti-Stokes Raman spectroscopy (CARS) and coherent Stokes Raman spectroscopy (CSRS) fields produced in the first step of the cascade process, (c) for each delay time between the femtosecond impulsive pump and FSRS probe pulses, the line shape of the sidebands shows an inversion symmetry about the C-D stretch frequency, and this is due to the 180(∘) phase difference between the CARS and CSRS fields that produced the left and right sidebands, and (d) for each sideband, the line shape changes from positive Lorentzian to dispersive to negative Lorentzian, then to negative dispersive and back to positive Lorentzian with the period of the bending vibration, and it is correlated with the momentum of the wave packet prepared on the ground-state surface by the impulsive pump along the sideband normal coordinate.

Femtosecond stimulated Raman scattering for polyatomics with harmonic potentials: application to rhodamine 6G

The perturbation theory of stimulated Raman scattering (SRS), with Raman pump on minus pump off and heterodyne detection along the probe direction, is reviewed. It has four third-order polarization terms, labeled as SRS or inverse Raman scattering (IRS): SRS(I), SRS(II), IRS(I), and IRS(II). These four polarizations have a wave packet interpretation. The polarizations, with homogenous and inhomogeneous broadening included, can be written as integrals over four-time correlation functions, and analytic formulas are derived for the latter for multidimensional harmonic potential surfaces with Franck-Condon displacements in the modes which facilitates the calculation of the SRS cross sections. The theory is applied to understand recent experimental results on the femtosecond SRS (FSRS) of a fluorescent dye, rhodamine 6G (R6G), where the Raman pump pulse is about 1 ps long, and the probe pulse is about 10 fs. The calculations compared very well with the R6G experimental results for off-resonance and resonance FSRS spectra spanning both Stokes and anti-Stokes bands, and for negative and positive pump-probe delay times on resonance.