CLASSICAL-MODEL OF FEMTOSECOND TIME-RESOLVED ABSORPTION-SPECTRA OF DISSOCIATING MOLECULES

We present a simple classical model for understanding time-resolved absorption spectra of molecules that are in the process of dissociating. The model applies to absorption spectra that are obtained by measuring the spectral power density of an ultrafast, continuum probe pulse after transmission through the sample. We show that the classical model can yield results in good agreement with quantum-mechanical wave packet propagation calculations. In a close analogy with collisional line broadening, the time-resolved absorption spectra are shown to have an impact region near the separated-atom transition frequency and a far-wing region. The impact region is due to radiation emitted after the molecule has separated into atomic fragments, and the far-wing region is due to radiation emitted during the time of strong molecular interaction. The spectrum in the impact region depends upon an effective phase shift for a "partial" collision, which begins at the time that the probe pulse sweeps through the molecular transition frequency. For narrow wave packets, this phase shift can be directly measured, and the molecular transition frequency can be recovered as a function of time along the path of dissociation. For very broad wave packets, the time-resolved absorption spectra approach a statistical limit, in which the absorption line shape becomes an image in frequency space of the probaility density in configuration space at the time of excitation by the probe pulse. In all cases, the frequency-integrated absorption is proportional to the net population of molecules that are excited by the probe pulse. In principle, this result can be used to obtain the strength of the transition dipole moment as a function of internuclear separation. We also consider fluorescence induced by a short optical probe pulse, as in the experiments of Zewail and co-workers. Fluorescence measurements are shown to be fundamentally different from measurements of the transmitted spectral power density: fluorescence depends upon the net population excited by the probe pulse, whereas the transmitted spectral power density depends upon interference between the incident probe field and the polarization field. Thus these two experimental techniques are sensitive to different aspects of the dissociation process.