Theory of time- and frequency-resolved resonance Raman and resonance fluorescence induced by realistic coherent pulses of arbitrary strength

Closed-form expressions are derived for the time-resolved and frequency-resolved resonance fluorescence (RF) and resonance Raman (RR) produced by coherent, realistic, quasi-rectangular pulses of arbitrary strength. Saturation effects, such as optical nutation, dynamic Stark splitting and dynamic Stark shifts of RF and RR are shown to be strongly dependent on the rise and fall times of the pulse. It is predicted that at high pulse intensities, optical nutation and the intensity of RF, but not of RR, disappear rapidly with increasing frequency offset Δω = ω - ω_mn of the average pulse frequency ω from the molecular transition frequency ω_mn. This result strongly influences the saturation effects in Doppler-broadened time- and frequency-resolved spectra and points to the necessity of revising the interpretation of recent experimental observations.