Femtosecond transient absorption with chirped pump and supercontinuum probe: Perturbative calculation of transient spectra with general lineshape functions, and simplifications

Femtosecond transient UV/vis absorption spectra of molecules in solution show vibronic structure initially while pump and probe pulses overlap, superimposed on bands which broaden and shift on several time scales. Third-order perturbation theory is used simulate and understand such spectra under experimental conditions, i.e., with chirped pump pulses and 40-80 fs pump/probe correlation time. The electronic system is coupled to a solvent bath whose fluctuations enter through a lineshape function g(t). This approach has two advantages. (i) In the general case when g(t) is modelled realistically it provides a distinction of coherent and sequential contributions to early transient spectra. The time-zero stimulated emission band can be extracted, giving access to the relaxation function for the emission frequency. (ii) For limiting forms of g(t) corresponding to the Bloch approximation and to inhomogeneous broadening the threefold time integrals underlying the theory reduce to a single integral. In such cases the lineshape formulation of transient absorption spectra can be used for data fitting.