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Le Journal de Physique Colloques

POLARIZATION DEPENDENT PROPERTIES OF BACKWARD FOUR-WAVE MIXING

S. Saikan

Published Mar 1, 1983• 0 citations
Publisher

Abstract

Theoretical analyses have been made of polarization-and angular momentum-dependences of backward four-wave mixing in atomic lines. These results were also applied to the problem of "vectorial" phase-conjugation in atomic vapours. Experimental demonstration of the vectorial phase-conjugation was carried out in D2 resonance line of sodium. Concerning the phase-conjugation spectroscopy in condensed matter, it has been proposed to detect X(3)1221 component to eliminate thermal grating effect.

DOI
10.1051/jphyscol:1983214

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Theoretical analyses have been made of polarization-and angular momentum-dependences of backward four-wave mixing in atomic lines. These results were also applied to the problem of "vectorial" phase-conjugation in atomic vapours. Experimental demonstration of the vectorial phase-conjugation was carried out in D2 resonance line of sodium. Concerning the phase-conjugation spectroscopy in condensed matter, it has been proposed to detect X(3)1221 component to eliminate thermal grating effect.
We present the theory of resonant backward degenerate four-wave mixing in gaseous media for Doppler-broadened degenerate two-level systems. The degeneracy of the atomic levels as well as the influence of the polarization of the incident fields are taken into account within the framework of a tensorial formalism. The amplitude, line shape, and polarization of the reemitted phase-conjugate field are calculated up to the third order in the incident fields. The velocity average is performed in the approximation of large Doppler linewidths. One considers in detail the influence of depolarizing relaxation processes and the effects of pump-probe angular separation. In particular, the importance of the residual Doppler effect (shortening of the lifetime of the optically induced gratings by the atomic motion) associated with the pump-probe angle is emphasized. We show that the polarization of the reemitted fields is governed by very simple laws as soon as the residual Doppler effect overcomes the lifetimes of the atomic levels. Phase-conjugate mirrors can be simply characterized by a linear dichroism (parallel pump polarizations) or a birefringence (cross-polarized pumps). Vectorial phase conjugation is also analyzed, in the case of counter-rotating circular polarizations of the pumps. Finally, the case of two-photon transition is studied and compared with the case of a resonant transition.
We have studied the polarization properties of phase conjugation by degenerate four-wave mixing utilizing the 3S\ensuremath{\rightarrow}4S two-photon-allowed transition of sodium. We have observed high-fidelity vector phase conjugation (simultaneous conjugation of the optical wave front and the state of polarization) at a reflectivity of \ensuremath{\sim}1% for the case where the states of polarization of the two counterpropagating pump waves were circular and counterrotating. High-fidelity polarization conjugation with high reflectivity was obtained only when the forward pump wave was much stronger than the backward pump wave. To explain these results, it is necessary to include the effects of grating washout due to atomic motion in the theoretical analysis.
It is often desirable that a phase conjugate mirror be able to correct for polarization distortions in addition to correcting for wavefront aberrations. Such a device is called a vector phase conjugate mirror. It has been predicted within the context of the third-order theory that vector phase conjugation can be achieved by degenerate four-wave mixing using atomic two-photon transitions between S-states.1 We recently developed a theory of the polarization properties of two-photon resonantly enhanced degenerate four-wave mixing which can treat saturation effects due to pump waves.2 Our results show that for the case of linear and parallel pump wave polarizations, vector phase conjugation occurs with high quality and high reflectivity for two-photon transitions for which the nonresonant Stark shift is very small. We have also found that for the case of circular and counterrotating pump wave polarizations, perfect vector phase conjugation occurs for equal pump wave intensities. We have studied experimentally the effects of saturation and Stark shifts for S → S two-photon transitions of atomic sodium. We have found that high fidelity vector phase conjugation can be obtained.
Experimental and theoretical investigations were made of the polarization characteristics of a four-wave phase-conjugate mirror utilizing the 3S1/2–3P3/2 transition in sodium atoms and different combinations of linearly and circularly polarized external waves. A good agreement was established between the experimental results and a theory developed allowing for the optical transfer of atoms between magnetic sublevels and for a residual Doppler broadening due to the noncollinearity of the wave vectors of the interacting waves.