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Femtosecond broadband stimulated Raman spectroscopy theory

Femtosecond broadband stimulated Raman spectroscopy (FSRS) is a new technique that produces lifetime-limited (time-resolved) vibrational spectra from either the ground or excited electronic states of molecules, free from background fluorescence with very short data acquisition times. The semiclassical coupled-wave and quantum-mechanical descriptions of FSRS will be presented and the connection between the two will be discussed. A new technique, femtosecond stimulated Raman spectroscopy (FSRS), has been developed [14] that (a) circumvents the traditional transform limit which restricts spontaneous Raman to the ps time domain, (b) is free from background fluorescence, and (c) enables observation of vibrational spectra of either the ground or ultrafast (~100 fs) excited electronic states with lifetime limited spectral resolution. FSRS uses two NIR-pulses: a narrow bandwidth (1-3 ps, ~803 nm, 30-1500 nJ) Raman pump, and a continuum Stokes probe pulse (30-50 fs, 840-950 nm, <20 nJ) to the red of the pump covering vibrations in the range 450-2100 cm. When both pump and probe pulses are incident on the sample simultaneously, sharp Raman gain features are observed on top of the continuum probe spectrum, as exemplified in Fig. 1 for ground electronic state FSRS of cyclohexane. Fig. 1. (a) The spectra of Raman pump and Stokes probe pulses for a typical FSRS experiment on cyclohexane. The Raman pump-off spectrum is shown as the dotted line. With the Raman pump-on, the Raman gain peaks from the cyclohexane are clearly visible in the output Stokes probe spectrum (solid line). (b) The ratio of the Stokes probe spectrum with and without the Raman pump gives the Raman gain spectrum. How do we explain the Raman gain features in Fig.1 [5]? The medium is taken to be a collection of oscillators. The intense electric field, given by a sum of pump p and Stokes s fields, , where z is the axis of light propagating through the medium and t is the time, drives a coherent vibration Q(z ,t) in the medium described by the equation of motion, ) , ( ) , ( ) , ( t z E t z E t z E s p + =