Limitations of pump-probe femtosecond time-resolved experiments: Time-dependent absorption and dispersion line shapes

In ultrashort (femtosecond) pump-probe spectroscopy, the pump pulse creates a nonstationary medium while the probe pulse propagates in such a medium. The analysis of this situation is performed in the framework of linear nonstationary optics. Constitutive equations and electrodynamics of the nonstationary media are analyzed. The propagation of the probe-pulse energy is characterized by the coarse-grained susceptibility introduced in the previous works of the authors [S. H. Lin and B. Fain, Chem. Phys. Lett. 157, 233 (1989); B. Fain, S. H. Lin, and N. Hamer, J. Chem. Phys. 91, 4485 (1989); B. Fain and S. H. Lin, Chem. Phys. 161, 515 (1992)]. The main objective of the paper is the derivation and analysis of the delay-time-dependent absorption and dispersion line shapes of the probe pulse. This line shape has a very specific form corresponding to phase-dependent Raman absorption (emission). The latter phenomenon is introduced and described in the present paper.