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Physical Review A

Physics in counterpropagating light-beam devices: Phase-conjugation and gain concepts in multiwave mixing

Martine Le Berre, Elisabeth Ressayre, Andree A. Tallet

Published Nov 1, 1991• 9 citations
Publisher

Abstract

The physics of Raman-type self-oscillations in highly dispersive saturable two-level-medium devices is revisited by using the gain and reflectivity matrices. The probe gain when two identical pumps counterpropagate through a two-level system is demonstrated to be very different from the gain for a probe in a one-way device, and typically peaked near a frequency twice the one-way Rabi frequency, while multiwave mixing displays a generalized mirror behavior of the atomic cell. The multimode instability in a Fabry-P\'erot interferometer is also discussed and shown to be mainly a result of counterpropagating probe coupling while the coupling between copropagating probe and idler is negligible.

DOI
10.1103/physreva.44.5958

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Physical Review A•Jun 1, 1991•24 citations
The physics of Raman-type self-oscillations in highly dispersive saturable two-level-medium devices is revisited by using the gain and reflectivity matrices. The probe gain when two identical pumps counterpropagate through a two-level system is demonstrated to be very different from the gain for a probe in a one-way device, and typically peaked near a frequency twice the one-way Rabi frequency, while multiwave mixing displays a generalized mirror behavior of the atomic cell. The multimode instability in a Fabry-P'erot interferometer is also discussed and shown to be mainly a result of counterpropagating probe coupling while the coupling between copropagating probe and idler is negligible.
The dynamical behavior of counterpropagating light waves interacting with a nonlinear medium is studied numerically. It is found that the wave and the medium form a system that becomes unstable under certain conditions and exhibits self-oscillation. Because the interacting medium is modeled by an ensemble of two-level systems, we recognize the self-oscillation frequency as the Rabi-frequency of the constituent systems. The physical mechanisms responsible for this self-oscillation are the gain and the distributed feedback of the combined lightwave-medium system. When the environment changes, in particular when the intensity is increased, this system becomes more unstable and we find that the oscillation exhibits more complex behavior, including quasi-periodic motion and chaos. We analyze the output fields by using Fourier spectra, phase portraits, and autocorrelation functions. In the chaotic regime, the Lyapunov exponents and dimensions are also calculated. A physical interpretation of the quasiperiodic motion is given by an exact calculation of the absorption spectrum of our two-level medium. The negative absorption (gain) peaks are found at the frequencies of the quasi-periodic motions, thus implying that the gain of the combined light-medium system is responsible at least in part for the observed complex behavior. In addition, we investigate the stability of the propagating plane wave when a transverse wave is added to the system as a perturbation. Instabilities are analyzed by linearizing the nonlinear equations which model the lightwave-medium system. The results show that the instability is highly-correlated with the four-wave mixing phase conjugation.
We have developed a theory for nondegenerate oscillations in optical resonators containing an intracavity phase-conjugate element. The phase-conjugate element consists of a nonlinear transparent medium that is pumped externally by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation of an input beam of slightly different frequency occurs because of nondegenerate four-wave mixing. The theory takes into account linear absorption (or gain) in the medium and is applied to study the threshold behavior of phase-conjugate oscillators. For the special case of no conventional mirrors, the phase-conjugate oscillator reduces to an ordinary phase-conjugate mirror, and our general formulation yields the results of previous studies. Our analysis shows that the parametric gain required for oscillation increases (or decreases) as a result of linear absorption (or gain) in the medium, and oscillation can occur at a frequency different from that of the pump beams in the presence of large linear gain (or loss). The effects of linear absorption (or gain) on the filter operation are also examined.
Two counterpropagating waves in a Kerr medium were shown to exhibit instabilities, which lead to self-oscillations, bifurcations, and chaos.1 These instabilities, as well as self-oscillation phenomena in bistable systems, can be explained by a gain-feedback mechanism.2 Fields at frequencies adjacent to the input pump-wave frequency can be amplified through four-wave-mixing interactions. If feedback is supplied, sidebands at these frequencies can be excited and beat with the pump wave to yield an oscillating output. In a counterpropagating-beam configuration, the feedback is distributed, and it originates from the grating that is formed by the interfering beams.
Absolute instabilities of counterpropagating pump beams in a dispersive Kerr medium, placed inside a Fabry–Perot cavity, are analytically studied by use of the analysis and the results of part I [J. Opt. Soc. B14, 607 (1998)]. Our approach allows characterization of such a complicated nonlinear system in terms of a doubly resonant optical parametric oscillator. We consider the growth of modulation-instability sidebands associated with each pump beam when weak probe signals are injected through one of the mirrors of the Fabry–Perot cavity. The results are used to obtain the threshold condition for the onset of the absolute instability and the growth rate for the unstable sidebands in the above-threshold regime. As expected, the well-known Ikeda instability is recovered at low modulation frequencies. The effects of the group-velocity dispersion are found to become quite important at high modulation frequencies. Although the absolute instability dominates in the anomalous-dispersion regime, it exists even in the normal-dispersion regime of the nonlinear medium. Below the instability threshold, our analysis provides analytic expressions for the probe transmittivity and the reflectivity of the phase-conjugated signal that is generated through a four-wave-mixing process.
The threshold characteristics of the static and periodic instability of the single feedback mirror device are investigated for a homogeneously broadened two-level medium as a function of the input intensity, the detuning, the buffer-gas pressure, the atomic concentration, and the round-trip time d, and compared with experimental results. For a large range of parameters that agrees with the experiment, the self-oscillation process is shown to be mainly induced by the longitudinal grating, which ensures a large instability domain, and controlled by the buffer-gas pressure, which must be low enough in order that the threshold period of the oscillation is constant on a doughnutlike transverse profile and nearly equal to 2d. This oscillation, called the 2d oscillation, is neither a result of pure phase-conjugate-mirror operation of the atomic medium nor a result of a Rabi sideband gain process. It is shown to take place through a mixture of phase-conjugate-mirror and ordinary mirror operations, which are both allowed by the specific optical arrangement of the device.