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Topical Meeting on Optical Bistability (OB)

Critical Slowing Down and Magnetically-Induced Self-Pulsing in a Sodium-Filled Fabry-Perot Resonator

J. Mlynek, Fedor M. Mitschke, Wulfhard K. Lange

Published Jan 1, 1983• 0 citations

Abstract

We report on the observation of critical slowing down and of self-pulsing in a Fabry-Perot resonator (FP) filled with sodium atoms under conditions of transverse optical pumping /1/. The experimental set-up (see Fig.1) is similar to the one used in steady-state bistability studies reported before /2/. The dye laser, optically isolated from the FP by means of a Faraday rotator (FR) is detuned from the Na D1-line by 10 to 20 GHz. The sodium sample (N ≃ 1013 cm–3, buffer gas: argon, p=200 mbar) is placed in a near confocal Fabry-Perot (Beam waist: 1 20 μm) and can be subjected to a transverse magnetic field B. The intensity of the laser beam can be switched by means of an electro-optic modulator(EOM), thus providing input-steps of variable height (power:5 – 50 mW). A polarizer P1 is used to either circularly or linearly polarize the input beam. The right– and left circular polarization components of the resonator output beam can be separated by means of a λ/4-plate and a polarizing beam splitter P2. A pair of photodiodes PDi is used for detection.

DOI: 10.1364/obi.1983.fa6

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We report on the observation of critical slowing down and of self-pulsing in a Fabry-Perot resonator (FP) filled with sodium atoms under conditions of transverse optical pumping /1/. The experimental set-up (see Fig.1) is similar to the one used in steady-state bistability studies reported before /2/. The dye laser, optically isolated from the FP by means of a Faraday rotator (FR) is detuned from the Na D1-line by 10 to 20 GHz. The sodium sample (N ≃ 1013 cm–3, buffer gas: argon, p=200 mbar) is placed in a near confocal Fabry-Perot (Beam waist: 1 20 μm) and can be subjected to a transverse magnetic field B. The intensity of the laser beam can be switched by means of an electro-optic modulator(EOM), thus providing input-steps of variable height (power:5 – 50 mW). A polarizer P1 is used to either circularly or linearly polarize the input beam. The right– and left circular polarization components of the resonator output beam can be separated by means of a λ/4-plate and a polarizing beam splitter P2. A pair of photodiodes PDi is used for detection.

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

{\mathit{D}}_{1}

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.

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.

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.

Magnetically induced optical self-pulsing has been observed in a Fabry-Perot resonator containing sodium vapor. Experiments are performed on optically pumped Zeeman sub-levels of the Na ground state in the presence of a static transverse magnetic field

B

. When

B

exceeds a critical value

{B}_{\mathrm{cr}}

, self-sustained spin precession occurs, and the transmitted light is found to be modulated at about the Larmor frequency. The use of this tunable current-controlled oscillator in optical FM signal transmission is demonstrated.

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.