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Physical Review A

Effects of atomic motion on the polarization properties of phase conjugation by two-photon-resonant degenerate four-wave mixing

Martti Olavi Kauranen, Robert W. Boyd

Published Jul 1, 1991• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.44.584

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Conference on Lasers and Electro-Optics•Jan 1, 1998•1 citation
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.
We have studied the polarization properties of phase conjugation by degenerate four-wave mixing resonantly enhanced by the sodium 3S1/2 → 6S1/2 two-photon-allowed transition. As predicted by third-order theories, this interaction leads to simultaneous conjugation of the optical wave front and state of polarization (vector phase conjugation) when the pump intensities are sufficiently weak. However, qualitatively different polarization behavior is observed for pump intensities near or above the two-photon saturation intensity.
We develop a semiclassical theory of the polarization properties of phase conjugation by two-photon resonant degenerate four-wave mixing. The theory includes the effects of saturation by the pump waves. We solve the density-matrix equations of motion in steady state for a nonlinear medium consisting of stationary atoms with a ground and excited state connected by two-photon transitions. As an illustration of the general results, we consider an S0{S}_{0}S0​\ensuremath{\rightarrow}S0{S}_{0}S0​ two-photon transition, which is known to lead to perfect polarization conjugation in the limit of third-order theory. We show that the fidelity of the polarization-conjugation process is degraded for excessively large pump intensities. The degradation can occur both due to transfer of population to the excited state and due to nonresonant Stark shifts. Theoretical results are compared to those of a recent experiment [Malcuit, Gauthier, and Boyd, Opt. Lett. 13, 663 (1988)].
We develop a semiclassical theory of phase conjugation by two-photon-resonant degenerate four-wave mixing. Our theory treats both the tensor nature of the interaction and the effects of saturation of the atomic system. Previous theories that include saturation effects have treated only the scalar case,1 while theories that include polarization properties have treated the problem only in lowest-order perturbation theory.2 We consider an S → S two-photon transition. This interaction is of Interest because it has been predicted theoretically2 and shown experimentally3 that in the limit of nonsaturating pump waves this interaction leads to the simultaneous conjugation of the wavefront and polarization of the incident probe wave (vector phase conjugation).
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.
Summary form only given. Previously, we have used four-wave mixing via coherent population trapping to achieve optical phase conjugation (OPC) with high gain, using two dye lasers and a sodium vapor cell. The /spl Lambda/ transition used involved the two hyperfine ground states and one excited state, so that two different optical frequencies were needed to satisfy the two-photon resonant condition between the probe and one of the pump beams. Later, we demonstrated in rubidium that a single hyperfine transition with Zeeman sublevels is enough to achieve OPC with equally high gain, thus eliminating the need for high-frequency sideband generation. However, in order to guarantee that the diffraction from the grating is primarily dispersive, the backward pump beam had to be detuned by about 60 MHz from the probe and the forward pump. One of the key disadvantages of such a nondegenerate scheme is that applications such as phase-conjugate mirrors are hard to implement. Here, we report the observation of optical phase conjugation in rubidium with equally high gain, but all the frequencies are degenerate.