Effects of collisions on electronic-resonance-enhanced coherent anti-Stokes Raman scattering of nitric oxide

Abstract

A six-level model is developed and used to study the effects of collisional energy transfer and dephasing on electronic-resonance-enhanced coherent anti-Stokes Raman scattering ͑ERE-CARS͒ in nitric oxide. The model includes the three levels that are coherently coupled by the three applied lasers as well as three additional bath levels that enable inclusion of the effects of electronic quenching and rotational energy transfer. The density-matrix equations that describe the evolution of the relevant populations and coherences are presented. The parametric dependencies of the ERE-CARS signal on collisional energy transfer and dephasing processes are described in terms of both a steady-state analytical solution and the numerical solutions to the governing equations. In the weak-field limit, the ERE-CARS signal scales inversely with the square of the dephasing rates for the electronic and Raman coherences. In accord with published experimental observations ͓Roy et al., Appl. Phys. Lett. 89, 104105 ͑2006͔͒, the ERE-CARS signal is shown to be insensitive to the collisional quenching rate. Parametric dependencies on quenching, rotational energy transfer, and pure electronic dephasing are presented, demonstrating reduced collisional dependence for saturating laser fields.

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

“…This technique is capable of obtaining a few orders of magnitude enhancement of the CARS signal as compared to traditional CARS with a nonresonant probe [3][4][5]. Also, since the ERE-CARS technique is inherently quenching independent [6,7], this technique has been employed very successfully using nanosecond lasers for measuring the concentration of minor species such as NO [2,6,[8][9][10][11][12], which is a tracer pollutant in combustion processes [13]. However, since the resonant probe in the ERE-CARS configuration interacts strongly with the molecules, the saturation limit of the probe intensity is lower than that in conventional CARS [14].…”

“…Note that the saturation threshold of the probe-pulse intensity in a traditional CARS is much higher than the ERE-CARS setup because of far weaker off-resonance interaction of the probe with the molecular transition [21]. Although saturation of ERE-CARS with long-pulse excitation has been extensively studied [7,14], the saturation of the ultrafast ERE-CARS is never discussed.…”

“…As noted in Refs. [7,15], a significant repumping can occur during the duration of the excitation pulse that has been really helpful for the quenching independence of the ERE-CARS signal in NO. However, for a pulse duration on the order of the dephasing time scale of the molecule, the underdamping condition is not a sufficient condition for saturation of the ERE-CARS signal.…”

“…For a detailed discussion about the decays and dephasing parameters used in the modeling of the NO molecule, see Ref. [7]. Furthermore, note that a short pulse may couple multiple rotational states in each vibrational manifold simultaneously because of the broad bandwidth associated with the pulse that affects the saturation dynamics of the CARS signal [21].…”

Collision‐independent detection of molecular two‐photon excitation by time‐resolved parametric four‐wave mixing

“…In this expression, ω nm and Γ nm represent the wavenumber and electronic‐dephasing rate, respectively, associated with the allowed NO TPA transitions to rotational states, n , within the v ′ = 0 manifold of the A 2 Π electronic state, whereas I nm represents the corresponding state‐to‐state TPA cross sections calculated following procedures detailed previously . Rovibronic‐state‐resolved electronic‐dephasing rates have not been reported for gas‐phase NO; therefore, a constant Γ nm of 0.29 cm −1 (corresponding dephasing rate is 5.5 × 10 10 s −1 ) is assumed for all contributing transitions; this empirically determined parameter is consistent with the electronic‐dephasing rates reported (5.3–5.6 × 10 10 s −1 ) for electronically excited NO in the presence of N 2 and CO 2 gases at room temperature and atmospheric pressure . An expression analogous to Eqn , with a corresponding NR response function, , is used to account for NR contributions; however, in this case, the dephasing time constant, (2 πcΓ NR ) − 1 ,  is assumed to be significantly shorter than the pulse durations, and a π /2 phase shift, via φ NR , is introduced.…”