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Acta Physica Sinica

POLARIZATION ROTATION OF DEGENERATE FOUR-WAVE MIXING IN THE EXTERNAL MAGNETIC FIELD

Panming Fu, Xin Mi, 中国科学院物理研究所

Published Jan 1, 1982• 0 citations
Publisher

Abstract

We have discussed the polarization rotation of degenerate four-wave mixing in the external magnetic field. The third-order nonlinear susceptibility Xyxx(3) is calculated in the Jg=0→Je=1 transition. It consists of two components. The first component is due to the saturation effect of the population difference. The second component is due to the Zeeman coherence induced in the interaction between atom and field.

DOI
10.7498/aps.31.1113

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Acta Physica Sinica•Jan 1, 1984•1 citation
We have discussed the polarization rotation of degenerate four-wave mixing in the external magnetic field. The third-order nonlinear susceptibility Xyxx(3) is calculated in the Jg=0→Je=1 transition. It consists of two components. The first component is due to the saturation effect of the population difference. The second component is due to the Zeeman coherence induced in the interaction between atom and field.
A theory of resonantly enhanced degenerate four-wave mixing in two-level systems including the effects of atomic and photon angular momentum is presented in the absence of pump-induced saturation of the transition. It is shown that there exist three distinct quantum-mechanical amplitudes leading to the third-order polarization density. These quantum-mechanical amplitudes are shown to be sensitive to the states of polarization of the incident fields. The quantum-mechanical transport equation in the mmm representation is used to calculate the output signal in the various regimes of laser detuning, atomic linewidth, and polarization states of the radiation field for collinear interaction.
We present a study of atomic coherence effects in resonant degenerate four-wave mixing. We find for energy levels having magnetic degeneracies, the third-order nonlinear response resulting from two counterpropagating pump waves orthogonally polarized to an incident probe wave generates a signal whose polarization is phase conjugate to that of the incident probe wave. This effect is due to the coupling of different magnetic states resulting from coherent excitation giving rise to a net electric quadrupole. Experimental studies in Na on the D2 line at 5890 Å confirm the analysis.
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.
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.