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Journal of the Optical Society of America B

Intrinsic oscillations in the polarization of light transmitted by a sodium-filled Fabry–Perot resonator

P. Salieri, Giovanni Giusfredi, S. Cecchi, F. T. Arecchi

Published May 1, 1988• 7 citations
Publisher

Abstract

We report on the static and dynamic behavior of the intensity and polarization of the light transmitted by a Fabry–Perot cavity filled with sodium vapor without a buffer gas. The light beam is resonant with the D1 transition, and the behavior can be traced back to the simultaneous presence of Zeeman pumping and hyperfine pumping in the sodium ground state, combined with velocity-selective hole-burning effects. Together with optical bistability, tristability, and pitchfork bifurcation, the system displays intrinsic oscillations in the absence of a magnetic field. We discuss the features of these phenomena, particularly the appearance of Hopf bifurcations, and the ways they are affected by the experimental control parameters. We also report evidence of period doubling and of more-complex dynamics in the presence of a magnetic field.

DOI
10.1364/josab.5.001166

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Abstract In experiments on a sodium-filled Fabry—Perot resonator optical bistability, tristability and critical slowing-down were observed, as well as magnetically induced self-pulsing (Phys. Rev. Lett. 50, 1660 (1983)). Our experimental results can be explained by the model of Kitano, Yabuzaki & Ogawa (Phys. Rev. A 24, 3156 (1981)) in a qualitative way. In a more detailed treatment we obtain modified equations of motion that make phase space three-dimensional. The results of a stability analysis and of numerical solutions of the equations of motion are compared to experimental observations. We discuss the limitations of the adiabatic elimination of the cavity and demonstrate that not only tristable but also bistable systems can evolve into oscillatory states under the action of a static magnetic field; though the range of allowed experimental parameters is more restricted.

Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences•Dec 18, 1984•1 citation
We report on the static and dynamic behavior of the intensity and polarization of the light transmitted by a Fabry–Perot cavity filled with sodium vapor without a buffer gas. The light beam is resonant with the D1 transition, and the behavior can be traced back to the simultaneous presence of Zeeman pumping and hyperfine pumping in the sodium ground state, combined with velocity-selective hole-burning effects. Together with optical bistability, tristability, and pitchfork bifurcation, the system displays intrinsic oscillations in the absence of a magnetic field. We discuss the features of these phenomena, particularly the appearance of Hopf bifurcations, and the ways they are affected by the experimental control parameters. We also report evidence of period doubling and of more-complex dynamics in the presence of a magnetic field.
We report on instabilities in the transmitted polarization of a laser beam crossing a planar Fabry-P\'erot resonator filled with sodium vapor, at a null magnetic field, when the input field is linearly polarized and tuned near the center of the D1 line. We have measured bifurcation diagrams in the input-power--cavity-detuning parameter space at various angles of incidence. The system shows monostability, bistability, and limit cycles in the transmitted polarization. Oscillations appear only when the angle of incidence is different from zero and the oscillation phase changes with the position on the transverse profile. The observed dynamics is explained by a simplified model which accounts for Zeeman and hyperfine pumpings, focusing and defocusing effects, and atomic motion. By means of this model, we have determined the codimensionality of the system within a theory of the dynamical systems.
Optical pumping between ground-state Zeeman sublevels recently has attracted much attention as a nonlinear mechanism in optical bistability and tristability, under both steady-state1 and transient conditions.2 If, in addition to optical feedback, the Zeeman-pumped atoms are subjected to a transverse static magnetic field, new phenomena are known to arise,2–5 the most prominent among them being the self-sustained spin precession.4,5 We report on new results and systematic studies on the various types of magnetically induced optical multistabilities in a sodium-filled Fabry-Perot resonator.
In previous experiments on the trasmission properties of a Fabry-Perot interferometer filled with Na vapor |1,2| a buffer gas was added to collisionally broaden the resonance, with velocity changing collisions inducing broad ground state pumping over the whole line. Here we consider the very different inhomogeneous regime (no buffer gas), where optical pumping takes place on single homogeneous velocity groups. We carefully control direction and strength of the magnetic field and examine the cavity transmission properties, both in intensity and polarization, in the temperature range 130 - 180 °C (0.5 - 9.2·1011 atoms/cm3), as the laser is tuned across the DI line.
We report the observation of transverse optical bistability (TOB) in a sodium-filled Fabry-P\'erot resonator, pumped by circularly polarized light, nearly resonant with the D1{\mathit{D}}_{1}D1​ line, in the presence of a buffer gas, for low vapor density. A sequence of circularly symmetric patterns, ascribable to superpositions of resonator modes, is obtained. The appearance of TOB can be explained in terms of a self-induced intensity-dependent lens formed in the medium by the interaction with the laser light. A simple model that considers the transverse diffusion of the atoms inside the cell provides predictions in good qualitative agreement with the observations.
Abstract In experiments on a sodium-filled Fabry—Perot resonator optical bistability, tristability and critical slowing-down were observed, as well as magnetically induced self-pulsing (Phys. Rev. Lett. 50, 1660 (1983)). Our experimental results can be explained by the model of Kitano, Yabuzaki & Ogawa (Phys. Rev. A 24, 3156 (1981)) in a qualitative way. In a more detailed treatment we obtain modified equations of motion that make phase space three-dimensional. The results of a stability analysis and of numerical solutions of the equations of motion are compared to experimental observations. We discuss the limitations of the adiabatic elimination of the cavity and demonstrate that not only tristable but also bistable systems can evolve into oscillatory states under the action of a static magnetic field; though the range of allowed experimental parameters is more restricted.