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Laser Applications to Chemical, Security and Environmental Analysis

The effect of laser pulse shape on the saturation of the forward degenerate four-wave mixing signal

Jae Won HAHN, Dai-Hyuk Yu, Jai-Hyung Lee, Joon-Sung Chang, Jae-Seok Ryu, Jae Won HAHN, Paul M. Danehy

Published Jan 1, 2001• 0 citations
Publisher

Abstract

We investigate the effect of laser pulse shape on the forward degenerate four-wave mixing(DFWM) in two-level media. Saturation behavior of the DFWM signal generated with the square top and Gaussian pulses are analyzed.
DOI
10.1364/lacea.2000.sac5

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We investigate the effects of the input laser beam’s temporal pulse shape on a forward degenerate four-wave mixing (FDFWM) signal, assuming two-level saturable absorbers. Under conditions in which the coherence time is far shorter than the pulse-duration, we can calculate the signal easily in the time and frequency domains. From this result it is shown that, when the pulse duration is longer than ten times the population relaxation time, the calculated signal intensity is almost the same as that obtained by assuming a steady state throughout duration of the laser pulse. With this assumption, we obtain the signal by summing all the steady-state signals at each time-domain grid point during the pulse. The calculation is performed with three input beam temporal pulse shapes: square, Gaussian, and typical Q-switched pulses. After reaching a maximum, the signal intensity decreases. The rates of the signal increase and decrease depend strongly on the temporal shape of the input beam. For the same average power, the square-pulse input saturates the absorber faster than the other pulses. These results indicate that the weak part of the pulse input plays an important role in generating the signal, yielding differences in saturation behavior of the signal intensity and the spectral line shape. We compare the calculations with experiments by fitting the saturation curve of the FDFWM signal of argon atoms in a radio frequency inductively coupled plasma. Also, the spectral line shape of the DFWM signal is fitted with the calculation by use of published experimental data.
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 steady-state theory of degenerate four-wave mixing (DFWM) with broad-bandwidth lasers is extended to treat the time dependence of the interaction allowing calculation of the intensity dependence and saturation behavior of DFWM with pulsed lasers. An experimental study of this intensity dependence as a function of laser bandwidth is reported, showing qualitative agreement with the theory. The line shape of DFWM induced by broad-bandwidth pump fields, probed by a monochromatic probe, is shown to have a Doppler-broadened profile in agreement with the theoretical predictions.
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.
This dissertation presents experimental and theoretical studies of transient degenerate four wave mixing (DFWM) in organic dyes. Chapter 1 is an introduction to DFWM. Chapter 2 describes DFWM experiments that were performed in the gain medium of a dye laser. Chapter 3 presents the theory of DFWM of short pulses in three level saturable media. Chapter 4 presents DFWM experiments of femtosecond pulses in the saturable absorber of a passively modelocked ring dye laser. Chapter 5 presents the theory of DFWM of ultrashort pulses in resonant media.