WAVE PACKET ANALYSIS OF FEMTOSECOND STIMULATED RAMAN SPECTROSCOPY

Abstract

Femtosecond stimulated Raman spectroscopy (FSRS) is described here by both the classical coupled wave approach and by the quantum theory with wave packet analysis. The classical coupled wave approach is restricted to off-resonance FSRS, but the quantum theory also applies to the resonance regime. The quantum theory describes FSRS by the third-order polarization with eight perturbative terms which are pictured with Feynman dual time-line diagrams as well as the complementary four-wave mixing energy level diagrams. The eight terms can be placed into four sets — SRS(I), SRS(II), IRS(I), IRS(II) — where SRS stands for stimulated Raman scattering and IRS stands for inverse Raman scattering. In the SRS(I) set, there are three terms which are similar to the resonance Raman scattering and hot luminescence terms in spontaneous Raman scattering. The remaining five terms in SRS(II), IRS(I) and IRS(II) entail “absorption” of the probe pulse, and these are absent in spontaneous Raman scattering because of the vacuum probe field but they are present in FSRS. The SRS(I) set accounts for the sharp Stokes Raman lines while the IRS(I) term accounts for the sharp anti-Stokes Raman lines in the FSRS spectrum. We illustrate the theory with calculations on (a) the resonance FSRS of Rhodamine 6G and (b) the FSRS from a coherent vibrational state prepared by an impulsive pump pulse in CDCl3. The calculated results compare well with experiment, and it is shown that in the case of FSRS on CDCl3 there is a cascade effect involving two molecules that makes a dominant contribution to the FSRS spectra.