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

Transmission Properties Of A Sodium-Filled Fabry-Perot

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

Published Oct 14, 1986• 0 citations
Publisher

Abstract

We report on systematic studies of the static and dynamic behavior of intensity and polarization of the light transmitted by a sodium-filled Fabry-Perot cavity. The device displays a rich variety of phenomena, including optical bistability, tristability, pitchfork bifurcation, as well as intrinsic oscillations. 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.

DOI
10.1117/12.938849

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We report on systematic studies of the static and dynamic behavior of intensity and polarization of the light transmitted by a sodium-filled Fabry-Perot cavity. The device displays a rich variety of phenomena, including optical bistability, tristability, pitchfork bifurcation, as well as intrinsic oscillations. 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.
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.
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.
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.
We study a theoretical model that describes an optically pumped Fabry–Perot cavity filled with sodium vapor as a nonlinear absorptive medium. The nonlinear medium is subjected to a static magnetic field. A difference of population is built up between Zeeman sublevels of the ground state when the pump exceeds a threshold. This gives rise to a nonsymmetrical absorption of the two circularly polarized components of the incident light. The emphasis of this paper is on the derivation of analytic results. We show that the system can exhibit a self-pulsing behavior and that in a suitable domain of parameters the system has two or more steady states. This is known as optical bistability or optical multistability.
It is predicted with use of a simplified model that a Fabry-Perot cavity filled with atoms with Zeeman sublevels in the ground state should exhibit optical tristability via optical pumping. For linearly polarized incident light, three stable states appear in the polarization of the transmitted light; ${\ensuremath{\sigma}}_{+}$ dominant, ${\ensuremath{\sigma}}_{\ensuremath{-}}$ dominant, and linear polarizations. This optical tristability is discussed in the context of a butterfly catastrophe.
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.