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Acta Physica Polonica A

Resonant Degenerate Four-Wave Mixing in SO2

Wenqi Wei, Z.Z. Lu, Q. Dong, Y.L. Sun, Lin Ma, Junru Liao, J.F. Liu, Xiaoping Xie, Wei Zhao

Published Jun 1, 2020• 0 citations
Publisher

Abstract

We report an experimental investigation of degenerate four-wave mixing spectrum of SO2.A novel beam-split technique is used to compensate the beam drift caused by the laser itself and disturbance from the environment.Degenerate four-wave mixing spectra of the transition B 1 B1 ← X 1 A11 for SO2 are obtained.The degenerate four-wave mixing signal intensity as a function of the total input laser energy is measured.The effects of the laser field intensity on the degenerate four-wave mixing spectrum are analyzed.Our results show that the degenerate four-wave mixing signal intensity rises with laser intensity and tends to saturate.Then, a dip begins to appear at resonance in the profile with increase in laser field.The existence of saturation for degenerate four-wave mixing signal intensity and spectrum profile confirms the prediction of previous theoretical work.

DOI
10.12693/aphyspola.137.1022

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We report an experimental investigation of degenerate four-wave mixing spectrum of SO2.A novel beam-split technique is used to compensate the beam drift caused by the laser itself and disturbance from the environment.Degenerate four-wave mixing spectra of the transition B 1 B1 ← X 1 A11 for SO2 are obtained.The degenerate four-wave mixing signal intensity as a function of the total input laser energy is measured.The effects of the laser field intensity on the degenerate four-wave mixing spectrum are analyzed.Our results show that the degenerate four-wave mixing signal intensity rises with laser intensity and tends to saturate.Then, a dip begins to appear at resonance in the profile with increase in laser field.The existence of saturation for degenerate four-wave mixing signal intensity and spectrum profile confirms the prediction of previous theoretical work.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.
Saturation effects in gas-phase degenerate four-wave mixing (DFWM) are investigated for conditions of interest for diagnostic applications in flames and plasmas. In particular, the case in which Doppler and collisional broadening are comparable, as is often the case for flame species such as NO and OH, is investigated. DFWM line shapes and signal intensities are calculated nonperturbatively and compared with high-resolution laser measurements. In the nonperturbative calculations the time-dependent density-matrix equations for a two-level system interacting with three laser fields are integrated directly on a grid of spatial locations along the phase-matching axis. The electric-field amplitude for the DFWM signal is determined by multiplying the time-varying, laser-induced polarization at each grid point by the appropriate phase factor and then by summing over all grid points. The calculations are in excellent agreement with measurements of DFWM line shapes and signal intensities for NO in a buffer gas of He over a wide range of He pressure. Under saturation conditions the pressure dependence of the DFWM signal is reduced greatly compared with the unsaturated case. The signal level is still dependent on the ratio of pure dephasing to quenching collisions, even for saturation conditions. From the standpoint of minimal dependence on collisional processes it appears that operation with pump-laser intensities approximately equal to the saturation intensity is optimal. The dependence of the DFWM line shape and signal intensity on the ratio of probe to pump-laser intensity is also investigated.
The effects of finite laser bandwidth on resonant degenerate four-wave mixing (DFWM) are calculated with use of a model in which the intense, counterpropagating pump beams are characterized by a chaotic field, the probe beam is weak and monochromatic, and the medium consists of a gas of two-level atoms. We present a steady-state solution in the limit where the pump-laser bandwidth exceeds all other atomic relaxation rates. Although the mean intensity due to the fluctuating fields is spatially independent (no steady-state standing-wave pattern is established), the analytic results indicate that, for intensities above the saturation intensity Isat{I}_{\mathrm{sat}}Isat​, spatially periodic saturation effects are important. Increasing bandwidth is shown to lead to an increase in the effective saturation intensity resulting in lower phase-conjugate reflectivity for IIsat{I}_{\mathrm{sat}}Isat​ than for coherent pump fields, in contrast to the results for narrow-bandwidth chaotic fields. The resonant DFWM line shape is also calculated and compared to the coherent result. We comment on the application of the model to other four-wave-mixing processes employing broad-bandwidth lasers.
Degenerate four-wave mixing (DFWM) spectroscopy is a promising diagnostic technique [1-3], but significant questions remain regarding its application for quantitative concentration measurements in combustion environments with typical laser systems. In this paper we present a summary of two numerical investigations with the goal of quantifying the measurement technique for common experimental situations. Specifically, we investigate both (1) probing a degenerate-level (multistate) resonance with a single-mode laser and (2) probing a two-state resonance with a multimode laser. DFWM signal levels are calculated by solving the time-dependent density matrix equations using direct numerical integration (DNI) [4, 5] for a two or more level system interacting with three laser beams.