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Journal of the Optical Society of America B

Magnetically Induced Relaxation Oscillations in a Sodium-Filled Fabry–Perot Resonator

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

Published Jan 1, 1984• 1 citation
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Abstract

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.

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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.

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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.

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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.

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We describe a simple nonlinear optical device which transforms an ingoing cw light beam into a periodically modulated one. The mechanism of operation is due to a spin precession in the ground state of optically pumped atoms with a J=(1/2)\ensuremath{\rightarrow}J'=(1/2) transition in the presence of a static transverse magnetic field. With optical feedback from a resonator, this magnetically induced spin precession can be self-sustained and then can give rise to a self-pulsing of the transmitted light at roughly the Larmor frequency. A detailed theoretical description of the system is presented and stability criteria are considered. In contrast to earlier work, our calculations take into account the resonator round-trip time, an optical detuning from the atomic resonance, and absorptive losses within the resonator. New signal features are predicted: These include a complicated structure of the initial transient as well as a precipitation to a stationary state. Our theoretical model is confirmed by measurements which are performed by means of a Fabry-Perot resonator containing sodium vapor. The behavior of the device is studied for a wide range of experimental parameters; threshold powers for oscillation (\ensuremath{\gtrsim}5 mW) and the oscillation frequency and its tuning range (140 kHz--13 MHz) are investigated as well as the dynamics of the system following a step input of light.

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Self-sustained spin precession in an optical tristable system

Masao Kitano, T. Yabuzaki, T. Ogawa

The dynamical behavior of a Fabry-Perot cavity filled with atoms having Zeeman sub-levels in the ground state is investigated. Such a system is known to exhibit optical tristability, where the atomic spins are oriented parallel or antiparallel to the optical axis even for the linearly polarized incident light. It is found that, when a static magnetic field is applied transversely to the optical axis, self-sustained precession of the spin polarization occurs. Correspondingly, the ${\ensuremath{\sigma}}_{+}$ and ${\ensuremath{\sigma}}_{\ensuremath{-}}$ components of the transmitted light are modulated at about the Larmor frequency. We also show that the Bloch equation describing the motion of the spin polarization in the cavity can be reduced to van der Pol's equation.

Physical Review A•Dec 1, 1981•39 citations
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.
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 BBB. When BBB exceeds a critical value Bcr{B}_{\mathrm{cr}}Bcr​, 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 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.
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 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 describe a simple nonlinear optical device which transforms an ingoing cw light beam into a periodically modulated one. The mechanism of operation is due to a spin precession in the ground state of optically pumped atoms with a J=(1/2)\ensuremath{\rightarrow}J'=(1/2) transition in the presence of a static transverse magnetic field. With optical feedback from a resonator, this magnetically induced spin precession can be self-sustained and then can give rise to a self-pulsing of the transmitted light at roughly the Larmor frequency. A detailed theoretical description of the system is presented and stability criteria are considered. In contrast to earlier work, our calculations take into account the resonator round-trip time, an optical detuning from the atomic resonance, and absorptive losses within the resonator. New signal features are predicted: These include a complicated structure of the initial transient as well as a precipitation to a stationary state. Our theoretical model is confirmed by measurements which are performed by means of a Fabry-Perot resonator containing sodium vapor. The behavior of the device is studied for a wide range of experimental parameters; threshold powers for oscillation (\ensuremath{\gtrsim}5 mW) and the oscillation frequency and its tuning range (140 kHz--13 MHz) are investigated as well as the dynamics of the system following a step input of light.
The dynamical behavior of a Fabry-Perot cavity filled with atoms having Zeeman sub-levels in the ground state is investigated. Such a system is known to exhibit optical tristability, where the atomic spins are oriented parallel or antiparallel to the optical axis even for the linearly polarized incident light. It is found that, when a static magnetic field is applied transversely to the optical axis, self-sustained precession of the spin polarization occurs. Correspondingly, the ${\ensuremath{\sigma}}_{+}$ and ${\ensuremath{\sigma}}_{\ensuremath{-}}$ components of the transmitted light are modulated at about the Larmor frequency. We also show that the Bloch equation describing the motion of the spin polarization in the cavity can be reduced to van der Pol's equation.