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Chinese Journal of Quantum Electronics

Elements hyperfine spectrum based on four-wave mixing

Zheng Tao

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The new method for isotope analysis based on degenerate four wave mixing(DFWM)is proposed for superfine structure researches and the quantum optics theoretical calculation is also introduced to get the percentage of isotopes.The self-oscillation frequency can be determined from the experimental phenomenon. Then,based on three order nonlinear polarizability,with quantum optics calculation of three ladder level system,the relationship of three order nonlinear polarizability and atomic density can be measured.

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The new method for isotope analysis based on degenerate four wave mixing(DFWM)is proposed for superfine structure researches and the quantum optics theoretical calculation is also introduced to get the percentage of isotopes.The self-oscillation frequency can be determined from the experimental phenomenon. Then,based on three order nonlinear polarizability,with quantum optics calculation of three ladder level system,the relationship of three order nonlinear polarizability and atomic density can be measured.
Nonlinear spectroscopic method based on degenerate four-wave mixing allows unusually sensitive measurement of isotopes and hyperfine profiles with sub-Doppler spectral resolution. Compared to other isotope capable methods including mass spectrometry, wave mixing offers a simple, more cost effective approach with minimal sample preparation steps. Since no two hyperfine profiles are alike, hyperfine-based isotope analysis offers unambiguous isotope information. Unlike mass-based methods such as mass spectrometry, frequency-based wave-mixing spectroscopy offers more information rich spectra. A non-planar 3-D wave-mixing optical setup generates a coherent signal beam in its own space and propagation direction. Hence, virtually 100% of the signal can be collected and detected conveniently. Using compact solid-state lasers and popular atomizers, a wave-mixing setup is relatively compact. Sub-Doppler spectral resolution can be further enhanced by using simple low-pressure atomizers. Ultrasensitive fingerprinting of important isotopes promises many potential applications.
The functional relations have been presented between the complex amplitude (including polarization) of reflected wave on the one hand and amplitudes, polarizations of pump and probe waves, the third-order nonlinear susceptibility on the other hand, for degenerate four-wave mixing (DFWM) in isotropic medium, in which the polarizations are linear and/or circular, and the geometry is collinear or non-collinear. In the non-collinear geometry, when the polarizations of pump waves are parallel to each other, one can determine the ratio x1111/x1221 from the angles between polarization directions of probe and reflected waves; when the polarizations of pump are circular polarizations of the same handedness, one can get the ideal complex conjugate wave in this geometry. In the collinear geometry, there are always some non-conjugate component in the reflected wave, and the functional relation between reflection coefficient of amplitude and the thickness of sample can have the form of tangent function, hyperbolic tangent function and linear function; when the polarizations of pump waves are parallel to each other and |x1221|> |x1122|, this geometry is capable of generating self-oscillation; when polarizations of pump are circular ones of different handedness, DFWM acts as an ideal plane-mirror for probe wave with circular polarization, etc. The results can be used to explain some well-known experimental results and provide some theoretical guidance for designing new experiments.
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.
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.
The spectral behavior of the third order nonlinear optical response of atomic sodium was studied. As a result, new kinds of frequency domain spectroscopy techniques were developed: nearly degenerate four-wave mixing, polarization nearly degenerate four-wave mixing, frequency domain three-state spectroscopy, and nonlinear Hanle effect in degenerate four-wave mixing. These techniques have provided new information on several areas of collision physics including: dephasing collisions (spectral broadening and frequency shift), velocity changing collisions, state changing collisions, and spin-flip collisions. (Author)