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Journal of the Optical Society of America B

Phase Conjugation with the Use of Transverse Optical Pumping

J. Mlynek, E. Köster, Jurgen Kolbe, W. Lange

Published Jan 1, 1984• 1 citation
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Abstract

Recently, level degeneracy effects have been considered in phase conjugation (PC) through resonant degenerate four-wave mixing with special attention paid to sublevel coherences in atomic ground states.1,2 We report on detailed studies on usual and intracavity PC in atomic Na vapor (D1 line) using ground-state depopulation pumping and Zeeman coherences as a versatile nonlinear mechanism. Our measurements are found to be in good agreement with the results of a simple analytic nonperturbative treatment for a homogeneously broadened coupled four-level system.

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Recently, level degeneracy effects have been considered in phase conjugation (PC) through resonant degenerate four-wave mixing with special attention paid to sublevel coherences in atomic ground states.1,2 We report on detailed studies on usual and intracavity PC in atomic Na vapor (D1 line) using ground-state depopulation pumping and Zeeman coherences as a versatile nonlinear mechanism. Our measurements are found to be in good agreement with the results of a simple analytic nonperturbative treatment for a homogeneously broadened coupled four-level system.
An analytic nonperturbative treatment of degenerate four-wave mixing is presented to study Zeeman-coherence effects in phase conjugation. The counterpropagating pump waves are taken to be orthogonally circularly polarized and interact with different Zeeman sublevels. The nonlinear medium is modeled in terms of a homogeneously broadened, folded three-level system. Particular attention is paid to the phase-conjugate spectrum obtained by varying the Larmor frequency associated with the Zeeman splitting. A level-crossing resonance is found to occur in the saturation regime and manifests itself as a narrow peak or dip depending on various level decay rates. Even for a purely absorptive system, the Zeeman coupling of the ground-state degenerate sublevels is shown to produce significant phase-conjugate reflectivities at pump intensities much lower than those required for a two-level system.
The effect of Zeeman coherence on phase conjugation is investigated in the saturation regime by using a nonperturbative analysis of resonant degenerate four-wave mixing with orthogonally polarized pump beams in a A-type homogeneously broadened three-level system. The dependence of the phase-conjugation efficiency on phase-interrupting collisions and pump imbalance is particularly studied. Significant phase-conjugate reflectivities can be obtained at pump intensities much below those required for a two-level system.
Considers phase conjugation through degenerate four-wave mixing in a Λ-type three-level system under certain simplifying assumptions, the most restrictive among them being the assumption of symmetrical detuning of the pump from the two lower lying sublevels. When compared to an absorbing resonant two-level system, it is found that significantly higher values of the phase-conjugate reflectivity are possible at pump intensities well below saturation provided the sublevel splitting is less than a homogeneous linewidth. The physical mechanism responsible for phase conjugation is coherent population trapping arising from two-photon-induced atomic coherence between the two sublevels.
Nonlinear effects of sublevel coherence on resonant backward-degenerate four-wave mixing are analyzed in the saturation regime of an inhomogeneously broadened and optically thin gas medium, composed of \ensuremath{\Lambda}-type three-level atoms. No limitations are set to the pump-field intensities, and an analytical approach is presented in the Doppler limit and efficient transverse-optical-pumping regime. It is shown that coherent population trapping due to strong pump-field coupling has a negligible incidence in phase conjugation, while interference of two imbalanced coherent-population-injection channels determines the mixing process. Level-crossing emission resonances are found to exhibit particular line-shape characteristics: (1) an insensitivity to power shifts, (2) strong power-broadening accompanied by incomplete line splitting, or (3) field-induced line-broadening inhibition. The conditions under which these effects should be observable are identified, and their dependence on pump imbalance is remarked.
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.