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Optics Letters

Phase conjugation in a flame

John Pender, Lambertus Hesselink

Published Jun 1, 1985• 71 citations
Publisher

Abstract

The first observation to our knowledge of degenerate four-wave mixing in a sodium-seeded flame is reported. In addition, the theoretical dependence of the phase-conjugate output on the sodium concentration is verified experimentally, demonstrating the potential of this procedure for use as a diagnostic tool to measure species concentration in combusting or noncombusting media.

DOI
10.1364/ol.10.000264

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The first observation to our knowledge of degenerate four-wave mixing in a sodium-seeded flame is reported. In addition, the theoretical dependence of the phase-conjugate output on the sodium concentration is verified experimentally, demonstrating the potential of this procedure for use as a diagnostic tool to measure species concentration in combusting or noncombusting media.
Two-photon resonant parametric four-wave mixing and a newly developed variant called seeded parametric four-wave mixing are used to detect trace quantities of sodium in a flame. Both techniques are simple, requiring only a single laser to generate a signal beam at a different wavelength which propagates collinearly with the pump beam, allowing efficient signal recovery. A comparison of the two techniques reveals that seeded parametric four-wave mixing is more than two orders of magnitude more sensitive than parametric four-wave mixing, with an estimated detection sensitivity of $5\ifmmode\times\else\texttimes\fi{}{10}^{9}$ atoms/cm3{\mathrm{cm}}^{3}cm3. Seeded parametric four-wave mixing is achieved by cascading two parametric four-wave mixing media such that one of the parametric fields generated in the first high-density medium is then used to ``seed'' the same four-wave mixing process in a second medium in order to increase the four-wave mixing gain. The behavior of this seeded parametric four-wave mixing is described using semiclassical perturbation theory. A simplified small-signal theory is found to model most of the data satisfactorily. However, an anomalous saturationlike behavior is observed in the large signal regime. The full perturbation treatment, which includes the competition between two different four-wave mixing processes coupled via the signal field, accounts for this apparently anomalous behavior.
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.