Lineshapes for resonant impulsive stimulated Raman scattering with chirped pump and supercontinuum probe pulses

Molecular vibrational coherence from impulsive stimulated Raman (SR) scattering, as observed by broadband transient absorption spectroscopy, is treated within the well-known third-order perturbation formalism. Shaped femtosecond optical pulses are used for the pump and supercontinuum probe fields. Dephasing is assumed to be homogeneous in the Bloch approximation. A key step requires threefold time integration over response functions and electric fields. For well-separated pulses the triple integral can be solved analytically, resulting in lineshape functions. These allow to describe the SR signal through absorption/emission/dispersion profiles which are associated with the inherent contributions. A clear physical interpretation of the amplitude and phase of the oscillatory signal is thereby obtained, and a direct connection with the vibronic structure of the molecular system is provided. Calculations for model molecular systems illustrate the spectral dependence of the vibrational coherence seen, for example, with perylene in cyclohexane. The nonoscillatory and oscillatory parts of the transient absorption spectra are compared to each other. Observed mode beatings are explained.