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Physical Review A

Self-oscillations of the mirrorlike sodium vapor driven by counterpropagating light beams

Martine Le Berre, Elisabeth Ressayre, Andree A. Tallet

Published Jun 1, 1991• 24 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.43.6345

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Annual Meeting Optical Society of America•Jan 1, 1986•0 citations
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.
The instability threshold characteristics are investigated for two different optical devices, the ring cavity and the feedback mirror, with passive weakly absorbing two-level atoms cell. The linear stability analysis of the ring cavity predicts emission of several conical shells, depending on the optical arrangement and the buffer gas pressure. In the case of pure vapor, each conical shell has its own frequency. All the cones display the same frequency in the case of large buffer gas pressure. The feedback mirror device displays very different instability characteristics, with only one frequency emitted along a unique cone, in agreement with the experiment. The self-oscillation is shown to be controlled by the reflectivity properties of the cell, which behaves at threshold as a mixture of ordinary mirror and phase conjugate mirror
We present here instabilities observed in the transverse profile of a continuous-wave light beam that crosses a sample of sodium vapor twice by means of a feedback mirror. The wave front and the intensity of the beam are spatially modulated by the intensity-dependent dispersive and absorptive action of the vapor. Experimental evidence indicates that the vapor acts as a phase-conjugate mirror, thus providing an active cavity when it is coupled with the feedback mirror. The instabilities develop as a consequence of sideband generation at the resonant modes of this cavity. The transverse-mode profiles of these sidebands are analyzed experimentally.
Spatiotemporal instabilities of a single-feedback-mirror device are investigated with the help of the linear stability analysis of the stationary regime for a saturable medium that has a complex nonlinear susceptibility; the outcome is compared with experimental results. The first striking result of the analysis is the occurrence of an oscillation with a period nearly twice the round-trip time, regardless of its value with respect to the atomic linewidth for given physical situations, when only longitudinal grating effects are considered. This result cannot be interpreted as a pure phase-conjugate resonator operation, which is expected to occur only when transverse grating effects are included. When such effects are included, the second striking feature is the prediction of the spontaneous breaking of the revolution symmetry; symmetry is broken by rotating light spots, with an instability threshold that depends on the number of spots; this prediction agrees with experiment.
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.
We have previously shown that counterpropagating waves in a Kerrlike medium exhibit spontaneous oscillations above a certain threshold intensity. The period of these oscillations was related to the medium length and to its response time. These oscillations were explained as results of parametric gain and feedback supplied by the grating formed through the nonlinear interaction. In this paper we extend the theory to a two-level medium. The complexity of the parametric interaction in this medium provides a reach spectrum of behaviors. The power exchange due to this interaction, between waves of different frequencies, is usually maximized when the frequency difference is the Rabi frequency. However, another maximum, which is smaller in magnitude, occurs in certain limits when the frequency difference is T1. Our derivation is based on performing a linear stability analysis to the steady-state solutions of the Maxwell-Bloch equations. We assumed a small signal absorption and large detuning from resonance. The solutions were studied in the limit of pure radiative broadening (T2 = T1) and rapid collisional dephasing (T2 ≪ T1). It is found that for most cases Rabi frequency self-oscillations are dominant. However, for T2 ≪ T1 and for large interaction length, we found slower oscillations, with a period of T1. We show that the results can be understood by the gain feedback model. We also discuss the effect of inhomogeneous broadening and present experimental parameters required for observation of T1 oscillations.