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Optics Letters

Multiresonant behavior in nearly degenerate four-wave mixing: the ac Stark effect

Duncan G. Steel, Richard C. Lind

Published Dec 1, 1981• 53 citations
Publisher

Abstract

We have experimentally studied the effects of pump-probe detuning in nearly degenerate four-wave mixing. The data show multiresonant behavior as a function of the pump-probe detuning at both low and high intensities. At low intensities, the structure is the result of Doppler motion. At high intensities, five-peak structure is observed and is explained by the standing-wave modulation of the ac Stark splitting of the atomic levels.

DOI
10.1364/ol.6.000587

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We have experimentally studied the effects of pump-probe detuning in nearly degenerate four-wave mixing. The data show multiresonant behavior as a function of the pump-probe detuning at both low and high intensities. At low intensities, the structure is the result of Doppler motion. At high intensities, five-peak structure is observed and is explained by the standing-wave modulation of the ac Stark splitting of the atomic levels.
We present an experimental study of cw nearly degenerate four-wave-mixing emission in a Doppler broadened Rb atomic system. With the fixed detuning of an intense pump laser for the Rb D2{\mathit{D}}_{2}D2​ line, the nearly degenerate four-wave-mixing emission exhibits three peaks as a probe laser is scanned across the same Rb D2{\mathit{D}}_{2}D2​ line. The observed three-peaked spectrum can be interpreted as the resonances in the energy structure of the dressed atomic states.
The use of resonantly enhanced four-wave mixing to generate high reflectivity phase-conjugate waves is discussed. A physical understanding of the mechanisms underlying the nonlinear response for a simple two-level system is presented followed by a discussion of the complicating effects of pump absorption, pump depletion, unbalanced pumps, and thermal motion. Modifications of the theory to describe four-level behavior are presented and compared with experiments. The application of nearly degenerate four-wave mixing to narrow-band filtering complicated by the A. C. Stark effect is dis-cussed along with examples of experimental observations.
The coherent optical response of high quality microcavities containing quantum wells is investigated. The dynamics of the ac Stark effect is investigated by degenerate pump–probe experiments, by exciting the quantum well excitons at various intensities and detunings. The evolution from a simple dynamical excitonic Stark shift to a splitting is clearly observed, even when the excitation is degenerate with the continuum states. The experimental results agree well with the predictions of a theoretical model based on the semiconductor Maxwell-Bloch equations.
Intracavity nearly degenerate four-wave mixing in amplifying media has been demonstrated to be a powerful technique to get very high conjugated reflectivities. A physical interpretation of this process is given in terms of interactions among pump (ω), probe (\omega- \delta\omega), or conjugated (\omega + \delta\omega) waves with optically induced refractive index modulations or gratings. Mixing experiments performed at the milliwatt level inside a (GaAl)As semiconductor laser operating above or below threshold have demonstrated very high conjugated reflectivities (a factor of 103-104) together with a 10 percent energy conversion efficiency. The appearance of additional peaks related to the ac Stark effect and observation of bistability on probe and conjugated beams also make this mixing process interesting for the study of instabilities occurring in lasers.
This work presents a theoretical analysis of the Autler-Townes splitting pattern in the four-wave mixing signal generated in a three-level cascade Doppler-broadened system. We employ the density matrix formalism to write the Bloch equations and solve them numerically. The solutions allow us to compare the response of the upper level population and the generated signal coherence for homogeneously and nonhomogeneously broadened systems. Our results reveal an AC Stark shift in the nonlinear signal when the frequency of the strong or weak laser beam is scanned, in contrast to what is observed in the fluorescence. Furthermore, we present experimental data for the four-wave mixing signal in a hot rubidium vapor for the copropagating configuration of the laser beams that drive the $5S\ensuremath{\rightarrow}5P\ensuremath{\rightarrow}5D$ transition. The behavior of the AC Stark displacement and signal amplitude as a function of laser power indicates a good agreement between the model and the experimental results.