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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Self-Oscillation Induced By Transverse Optical Zeeman Pumping In Degenerate Four-Wave Mixing

C. Schmidt-Iglesias, Gaspar T. Orriols, Francese Pi

Published Jul 10, 1987• 1 citation
Publisher

Abstract

It is shown that very high phase-conjugation efficiency and oscillation is attainable in the saturation regime of resonant degenerate four-wave mixing in Doppler-broadened gas media using transverse optical Zeeman pumping of the ground state as nonlinear mechanism. Our theoretical study predicts also the absence of frequency splitting in the saturated line shape of the vectorially phase-conjugate reflectivity of optically thin media.

DOI
10.1117/12.937121

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Journal of the Optical Society of America•May 1, 1983•67 citations
It is shown that very high phase-conjugation efficiency and oscillation is attainable in the saturation regime of resonant degenerate four-wave mixing in Doppler-broadened gas media using transverse optical Zeeman pumping of the ground state as nonlinear mechanism. Our theoretical study predicts also the absence of frequency splitting in the saturated line shape of the vectorially phase-conjugate reflectivity of optically thin media.
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.
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 phase-conjugate reflectivity attainable by degenerate four-wave mixing in an idealized saturable absorbing medium is calculated for arbitrary values of the laser intensity, laser frequency, and absorption path-length of the nonlinear medium. The influence of pump-wave absorption, including saturation and standing-wave effects, is included in the theory. The treatment is based on an analytic expression for the intensity distribution of the counterpropagating waves. The theoretical predictions differ substantially from those based on theories that ignore pump absorption effects. The results of the present calculation are used to predict the minimum laser intensity, absorption path-length, and detuning required to obtain unit reflectivity and self-oscillation.
A comprehensive theoretical analysis is developed for the vectorial phase conjugation using resonant four-wave mixing (FWM) in a highly degenerate rotational vibrational molecular system. The dynamic Stark shifts, saturation, and Doppler broadening are included for a realistic analysis. It is shown that the electromagnetically induced multilevel coherence controls the nonlinear wave mixing yielding interesting results for the phase conjugate (PC) reflectivity. It turns out that the efficiency of the PC reflectivity is decided by the relative phase of the Zeeman coherence and the population grating. When these two contributions are aligned in phase by a small detuning of the pump frequency, a large PC reflectivity ($~2020%) is obtained with moderate pump intensity (20~500mW/cm500 mW/cm500mW/cm{}^{2}$).
We present in this paper a theoretical study of the angular dependence of phase-conjugate emission via resonant degenerate four-wave mixing (FWM) in Doppler-broadened gas media. The nonlinear optical polarization is calculated through an expansion of the atomic density matrix up to the third order in the incident fields. One finds that, when the incident frequency is resonant for a single-photon transition, both strength and lineshape of the phase-conjugate emission strongly depend on the angle 0 between standing pump wave and probe wave. The emission intensity, maximum at grazing incidences, decreases rapidly by several orders of magnitude when 0 increases. Simultaneously the emission linewidth increases from homogeneous to Doppler width. Similar effects are predicted for nearly-degenerate FWM (different pump and probe frequencies). In particular, one shows that the bandwidth of the equivalent optical reflection filter undergoes a Doppler-broadening linearly increasing with sin θ. On the opposite, none of the above effects is predicted in two-photon-resonant FWM which does not exhibit any angular dependence.
We present a theoretical study of phase-conjugate (PC) emission by backward degenerate four-wave mixing (DFWM) processes in a resonant gas medium. In this study, high-intensity (pump) saturation and Doppler broadening are simultaneously taken into account. We develop a general formalism to deal with the saturation effects in the case of a three-level atom (with degenerate frequencies) and obtain analytical expressions of the PC field amplitude (after integration over the velocity distribution) under the following conditions: (1) the probe beam and one of the pump beams have intensities weak enough to be treated at the lowest perturbation order, whereas the other pump intensity is arbitrarily high; (2) the probe crosses the standing pump wave at grazing incidence. It is shown that the saturation induced by the forward pump (copropagating with the probe beam) leads to entirely different behavior of the nonlinear susceptibility from that induced by the backward pump (counterpropagating with the probe beam). This saturation anisotropy is specific to the inhomogeneous broadening of the gas medium, which is also responsible for the frequency splitting experimentally observed in the intensity line shape of the PC emission for large pump intensities. At saturation, this splitting is theoretically shown to be proportional to the Rabi frequency, with a proportionality coefficient critically dependent on the relaxation processes; in the case of a single-relaxation model, the splitting is equal to 1.5 times the Rabi frequency. The PC intensity line shape is demonstrated to be of dispersive origin in the case of backward saturation, whereas for forward saturation, narrow structures are predicted in both real and imaginary parts of the nonlinear susceptibility, also leading to the intensity line-shape splitting. One also finds that the reflectivity of PC mirrors based on resonant DFWM strongly depends on the origin of the saturation. For a saturating forward pump, the PC emission intensity tends toward zero with increasing pump intensities, and it reaches a finite (nonzero) limit in the case of backward saturation. Most of these predictions have been observed experimentally [ BlochD., Phys. Rev. Lett.49, 719 ( 1982)].