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Acta Physica Sinica

LEVEL CROSSING EFFECT IN DEGENERATE FOUR-WAVE MIXING

FU PANG-MING, MI XIN, 中国科学院物理研究所

Published Jan 1, 1983• 0 citations
Publisher

Abstract

Third-order nonlinear susceptibility x(3)(-ω;ω,ω,-ω) is calculated in nearly-degenerate quasi-two-level system by perturbation method. We have studied the level crossing effect in degenerate four-wave mixing and compared it with the level crossing effect in resonance fluorescence. The possibility of using level crossing effect in degenerate four-wave mixing to measure the relaxation rate of upper and lower state is pointed out.

DOI
10.7498/aps.32.133

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Acta Physica Sinica•Jan 1, 1984•0 citations
Third-order nonlinear susceptibility x(3)(-ω;ω,ω,-ω) is calculated in nearly-degenerate quasi-two-level system by perturbation method. We have studied the level crossing effect in degenerate four-wave mixing and compared it with the level crossing effect in resonance fluorescence. The possibility of using level crossing effect in degenerate four-wave mixing to measure the relaxation rate of upper and lower state is pointed out.
The nonlinear susceptibility of a gas of molecules under level crossing in a single-mode laser field is calculated by an iteration procedure. The higher-order solutions up to the fourth order are explicitly given for arbitrary number of nearly degenerate levels. Contributions of the second-, third-, and fourth-order terms are discussed with particular emphasis on the third-order term. The third-order solution reveals the level-crossing effect in saturated absorption with the half-width almost twice as broad as the Lamb clip when the decay rates of the upper and the lower states are different to some extent. Finally the zero-field level-crossing experiment of methane at 3.39 µm by Luntz et al. is reexamined to result in the pressure broadening of its half-width to be 7.4 MHz/Torr.
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.