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Applied Physics Letters

Multiplex nonresonant pump four-wave mixing

Eun Seong Lee, Dae Sik Choi, Jae Yong Lee, Jae Won HAHN

Published Jul 23, 2004• 6 citations
Publisher

Abstract

We propose a scheme of multiplex nonresonant pump four-wave mixing (NRP-FWM) process which is highly immune to saturation problems. The process is accomplished with two high-intensity pump beams detuned far from the resonance of the sample under investigation and a resonant probe beam as weak as possible not to give rise to nonlinear absorption. Only a single-broadband probe beam is used for the multiplex experiment to detect the electronic swan band spectrum of C2 molecules in a premixed acetylene–oxygen flame. Comparing the signal of the degenerate four-wave mixing (DFWM) experiment on the same sample, we found that the signal level at which the NRP-FWM starts to show saturation is about 250 times higher than in the case of the DFWM.

DOI
10.1063/1.1775293

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Degenerate four-wave mixing (DFWM) spectroscopy is a potentially powerful technique for quantitative measurement of minor species in gas-phase media [1-3]. In this paper we compare the DFWM signal levels and lineshapes obtained using two different phase-matching geometries: the phase-conjugate geometry and the forward phase-matched geometry. DFWM signal levels are calculated by solving the time-dependent density matrix equations using direct numerical integration (DNI) [4, 5] for a two-level system interacting with three laser beams. This numerical analysis includes the effects of molecular motion, intermolecular collisions, and high laser intensities, all of which have been shown to affect the DFWM signal level.

Laser Applications to Chemical, Security and Environmental Analysis•Jan 1, 1998•0 citations
We propose a scheme of multiplex nonresonant pump four-wave mixing (NRP-FWM) process which is highly immune to saturation problems. The process is accomplished with two high-intensity pump beams detuned far from the resonance of the sample under investigation and a resonant probe beam as weak as possible not to give rise to nonlinear absorption. Only a single-broadband probe beam is used for the multiplex experiment to detect the electronic swan band spectrum of C2 molecules in a premixed acetylene–oxygen flame. Comparing the signal of the degenerate four-wave mixing (DFWM) experiment on the same sample, we found that the signal level at which the NRP-FWM starts to show saturation is about 250 times higher than in the case of the DFWM.
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.
Degenerate four-wave mixing (DFWM) from laser-populated excited states, i.e., two-step DFWM (2S-DFWM), has been performed to investigate the possibility of increasing signal quality (i.e., strength or signal-to-noise ratio) when species with low transition probabilities or far-UV transitions are to be detected or when large beam areas are used. Gold atoms, aspirated into an air-acetylene flame, were chosen as a suitable species for this investigation. The 2S-DFWM signal strength was found to be comparable to the ordinary (one-step) DFWM signals for moderately high UV-light intensities but substantially better for low UV-light intensities. This finding implies that DFWM detection of species with lower transition probabilities in the first step as compared with gold (<10(-8) s(-1)) can benefit from the 2S-DFWM technique when moderate or low UV-light intensities are available. Additional possible advantages of using 2S-DFWM are also discussed.
A theoretical description for a forward degenerate four-wave mixing process in homogeneously broadened two-level absorbers with arbitrary intensities of all four beams is presented. Assuming no pump absorption and depletion, we obtain an analytical solution of forward degenerate four-wave mixing signal intensity in the limit of the strong pumps and weak probe and signal. In the case of low absorption or large detuning, this solution is shown to become equivalent to that of the phase-conjugate degenerate four-wave mixing derived by Abrams and Lind [Opt. Lett.2, 94 (1978)]. For arbitrary beam intensities and absorption parameters, the signal intensity is numerically calculated by solution of the coupled equations of complex wave amplitudes. Comparing the results of the numerical calculation with those of the analytical solution, we discuss the validity of using the analytical solution in practical experiments and show the saturation behavior that is due to the strong probe beam. The line shapes under the various ratios among the input beams and absorption parameters are also obtained and discussed.
The nonlinear response of resonant saturable materials giving rise to degenerate four-wave mixing (DFWM) has been shown both experimentally and theoretically to provide the potential for very large efficiencies for phase conjugation and Doppler-free spectra for high resolution spectroscopy. The geometry for this interaction consists of two counter- propagating pumps (Ef and Ep) and a probe (Ep) intersecting the pumps at some angle θfp. The simultaneous action of one pump and the probe produces spatial hole burning resulting in a spatial modulation of the saturating absorption and dispersion which scatters the remaining pump to produce the signal.
The use of picosecond lasers for degenerate four-wave mixing (DFWM) diagnostics of atmospheric pressure flames has been suggested as a means of overcoming the complicated collision-rate dependence of the DFWM signal in the nanosecond-laser pulse-length regime. In this paper DFWM spectroscopy in the regime in which the laser pulse length (τL) is less than the characteristic collisional time (τC) is investigated theoretically. DFWM signal levels for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integration of the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and by summing of the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision broadened and Doppler broadened are considered. DFWM signal generation for these two types of resonances in the fully transient regime (τL≪τC) is strikingly different. For a homogeneously broadened resonance, the DFWM signal persists long after the laser beam has passed through the medium. The decay rate of the DFWM signal is determined by the collision rate in the medium, and the integrated DFWM signal is still dependent on the collision rate even in this fully transient regime. However, when the Doppler broadening of the resonance is much greater than the collisional broadening, the DFWM signal decays with a fall time close to that of the laser pulse. For τL≪τC, we find that it is the laser spectral width, rather than the collisional width, that dictates the range of velocity groups with which the pulses effectively interact. The signal decays with a fall time close to that of the laser pulse because the excited velocity groups radiate out of phase with one another. In a medium in which the Doppler width is much greater than the collisional width, the DFWM reflectivity is independent of collision rate for τL≪τC, but the signal level is dependent on the Doppler width. Finally, we investigate the effect of different laser pulse lengths on reflectivity saturation curves for resonances with different levels of Doppler broadening.
Degenerate four-wave mixing (DFWM) spectroscopy is a potentially powerful technique for quantitative measurement of minor species in gas-phase media [1-3]. In this paper we compare the DFWM signal levels and lineshapes obtained using two different phase-matching geometries: the phase-conjugate geometry and the forward phase-matched geometry. DFWM signal levels are calculated by solving the time-dependent density matrix equations using direct numerical integration (DNI) [4, 5] for a two-level system interacting with three laser beams. This numerical analysis includes the effects of molecular motion, intermolecular collisions, and high laser intensities, all of which have been shown to affect the DFWM signal level.