ABSTRACT A uniform real-time theory of spectroscopy was developed, which can treat one-photon and two-photon processes with a femtosecond pulse or a CW pulse excitation in a consistent picture. Applying this theory to second order spontaneous emission, unlike the previous approaches, the transient emission rate obtained from our theory can correctly reduce to Kramers-Heisenberg-Dirac expression in CW limit without any approximation. In continuum Raman, for a pulse shorter than the molecular dissociation time, apart from the normal Raman-like (RL) scattering, the fluorescence-like (PL) peak that remains fixed occurs as the incident light is tuned near the electronic on-resonance frequency. Furthermore, in a strong field, the range of excitation frequency giving FL emission is great than in a weak field. We also give an approximation by which the calculation of the spectroscopy with long pulse excitation becomes very easy while the accuracy is remained. The theory is expanded to density phase system, and the decay rate of vibrational relaxation is given to predict the typical characters of time-resolved fluorescence depletion.
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