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

Abstract

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.

Analysis of femtosecond stimulated Raman spectroscopy of excited-state evolution in bacteriorhodopsin

“…It is off-resonance FSRS, and the principal contribution is from the RRS͑I͒ term. 19,22 In principle, we do not need to use all 29 modes in Table I, but only those in the range of 800-1700 cm −1 relevant to the experiment; nevertheless, we included them all in the calculations and the results are the same. The shape of the ultrashort probe pulse is not critical so long as its spectrum spans the range 840-960 nm for observing the FSRS spectrum.…”

“…As in the experiment, the probe precedes the Raman pump by 1 ps. The method for calculating the FSRS for polyatomics with harmonic potentials from the ground vibrational state is described in Niu et al 22 In this case, its offresonance FSRS where the contribution is wholly from the RRS͑I͒ term with vibrational coherence ͉0͗͘1͉ on S 0 and associated vibrational dephasing time T 2 that affects the linewidths. Since its FSRS from the stationary ground vibrational state, we set ␥ 0 = 0, and for off-resonance FSRS the wave packet dynamics on the excited state S 1 is short lived by the uncertainty principle and so ␥ 1 is less important and we can set ␥ 1 =0.…”

“…The theory of FSRS from the ground state surface has been given earlier in terms of eight Feynman dual time-line diagrams. 19,22 Here, we use the familiar FWMEL diagrams of Lee and Albrecht 24 to describe FSRS from the excited state surface applicable to BR ‫ء‬ . The eight diagrams contributing to FSRS, 19,22 grouped as SRS, SRS͑I͒ and SRS͑II͒, and IRS, IRS͑I͒ and IRS͑II͒, are shown in Fig.…”

“…For the other terms, SRS͑II͒ also has three diagrams, while IRS͑I͒ and IRS͑II͒ have one each, where the role of the probe pulse is reversed from that for SRS͑I͒. The quantum theory of FSRS has been used to successfully explain the inversion symmetry in the FSRS Stokes and anti-Stokes spectrum, 19,20 to simulate off-resonance and resonance FSRS spectra of rhodamine 6G in comparison with experiment, 22 and to simulate how FSRS can provide direct observation of anharmonic coupling in CDCl 3 . 23 Recently, McCamant et al 11 used FSRS to study the photoisomerization dynamics in the excited state of BR.…”

What are the intensities and line-shapes of the twenty four polarization terms in coherent anti-Stokes Raman spectroscopy?

“…From the Feynman dual time-line diagrams, one can conveniently write down the expressions for the third-order polarizations. 33 The polarizations for the twenty four terms can be expressed by the overlap of wave packets on the bra and ket side when no decoherence life time is taken into account. 33,34 The third order polarizations for diagrams Aa, Dc and Ca, Bb are given by…”