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Journal of the Optical Society of America B

Optical multistability in sodium: analysis of a theoretical model

Xiaoguang Wu

Published Jan 1, 1989• 2 citations
Publisher

Abstract

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.

DOI
10.1364/josab.6.000066

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The theory of the optical multistability by two-photon resonant interaction is investigated. The nonlinear medium inside a Fabry-Perot cavity is in two-photon resonance with the laser beam. The two-photon equation of state including dynamical Stark shift and relaxation parameters is obtained and studied under mean-field approximation. The equations for both Fabry-Perot cavity and ring cavity take basically the same form. The physics mechanisms resulting in optical multistability are also studied. It has been shown that the combined effects of Kerr switching and saturation absorption switching can lead to two-photon optical double-bistability, tristability as well as bistability. Furthermore, the criterion conditions under which double-bistability or tristability can occur are given and discussed. Finally, the phase-conjugated reflectivity by two-photon four-wave mixing is also shown to exhibit multistability as well as hysteresis.

Acta Physica Sinica•Jan 1, 1983•2 citations
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.
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.
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.
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.
Experiments were performed on a bistable system consisting of a low finesse cavity and sodium atoms as the nonlinear medium. The atoms were excited by a dye laser system tuned to the D lines. Both ring and Fabry-Perot configurations were employed, and steady-state as well as transient behaviour was investigated. Flat mirrors of approximately 93% reflectivity were used in all experiments. With sodium vapour as the medium, experiments were performed in steady state, and a marked difference was observed in the behaviour of the Fabry-Perot cavity as compared to the ring set-up. This discrepancy could be explained when the sodium transition was modelled as a three - level lambda -type system, where the Doppler width is of the same order of magnitude as the ground state splitting. In this case the atoms with a Doppler shift close to half the ground state splitting have a major influence on the macroscopic refractive index. Extensive computer simulations were performed using this three -level model, and good qualitative agreement between experiment and theory was obtained for both types of cavity. A vacuum system containing a multiple atomic beam apparatus was constructed in order to reduce the Doppler width. Both the ring and the Fabry-Perot configuration could be set up inside the vacuum chamber.. The steady-state experiments displayed bistability when the laser intensity, laser frequency or cavity frequency were cycled. At higher atomic densities the system showed instabilities and multiple switching.
The theory of the optical multistability by two-photon resonant interaction is investigated. The nonlinear medium inside a Fabry-Perot cavity is in two-photon resonance with the laser beam. The two-photon equation of state including dynamical Stark shift and relaxation parameters is obtained and studied under mean-field approximation. The equations for both Fabry-Perot cavity and ring cavity take basically the same form. The physics mechanisms resulting in optical multistability are also studied. It has been shown that the combined effects of Kerr switching and saturation absorption switching can lead to two-photon optical double-bistability, tristability as well as bistability. Furthermore, the criterion conditions under which double-bistability or tristability can occur are given and discussed. Finally, the phase-conjugated reflectivity by two-photon four-wave mixing is also shown to exhibit multistability as well as hysteresis.