Ultrafast saturation of electronic-resonance-enhanced coherent anti-Stokes Raman scattering and comparison for pulse durations in the nanosecond to femtosecond regime

Abstract

The saturation threshold of a probe pulse in an ultrafast electronic-resonance-enhanced (ERE) coherent antiStokes Raman spectroscopy (CARS) configuration is calculated. We demonstrate that while the underdamping condition is a sufficient condition for saturation of ERE-CARS with the long-pulse excitations, a transient gain must be achieved to saturate the ERE-CARS signal for the ultrafast probe regime. We identify that the area under the probe pulse can be used as a definitive parameter to determine the criterion for a saturation threshold for ultrafast ERE-CARS. From a simplified analytical solution and a detailed numerical calculation based on densitymatrix equations, the saturation threshold of ERE-CARS is compared for a wide range of probe-pulse durations from the 10-ns to the 10-fs regime. The theory explains both qualitatively and quantitatively the saturation thresholds of resonant transitions and also gives a predictive capability for other pulse duration regimes. The presented criterion for the saturation threshold will be useful in establishing the design parameters for ultrafast ERE-CARS.

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“…Also, it has been shown that in an electronic-resonanceenhanced CARS (ERE-CARS) configuration, where the probe pulse resonantly couples the ground and electronically excited electronic states of the molecule, a strong ns-duration probe can saturate the signal [163]. However, in a detailed theoretical study of ERE-CARS for different pulse regimes with durations ranging from 10 ns-10 fs, it was shown that the signal saturation threshold associated with probe pulse begins to increase for pulse durations shorter than the molecular decay and dephasing times; the threshold intensity was shown to increase quadratically with the inverse of the pulse duration [164]. It has also been shown that the saturation threshold of the pump and Stokes intensities for Raman coherence using ultrafast pulses has a similar dependence [106].…”

“…From careful theoretical analysis it was demonstrated that ERE-CARS is dependent on the coherencedephasing rate but independent of the electronic quenching rate, and such dephasing dependence can be overcome by operating near the saturation condition for probe coupling [163,253]. The saturation conditions for the probe pulse in ERE-CARS have been analyzed theoretically for pulse durations ranging from ns to fs [164]. It is observed that for pulse durations longer that collisional timescales, the threshold intensity for saturation is independent of the duration of the pulse; however, for pulse durations shorter than collisional timescales, the threshold intensity of saturation is inversely proportional to the square of the pulse duration.…”

Influence of coherent population trapping on Raman scattering

“…A generalized formulation is developed for determining the saturation thresholds for optical processes excited by ultrafast pulses based on the pulse area of the excitation pulse [30] and for different pulse shapes [31]. The condition was derived for the saturation threshold of a probe pulse in an ultrafast electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman spectroscopy (CARS) configuration [32]. Further, femtosecond fully resonant electronically enhanced CARS (FREE-CARS) has been demonstrated with orders of magnitude enhancement of the CARS signal, where all three input pump, Stokes, and probe pulses are resonant to electronic states of the molecules [33,34].…”