Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Magnetically induced optical self-pulsing in a nonlinear resonator

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

Published May 1, 1986• 76 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.33.3219

Related papers

Observation of Magnetically Induced Optical Self-Pulsing in a Fabry-Perot Resonator

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

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.

Physical Review Letters•May 23, 1983•36 citations

Light-shift-induced chaos in a nonlinear optical resonator

C. Boden, M. Dämmig, Fedor M. Mitschke

The interaction of spin-1/2 atoms in an optical resonator with a near-resonant cw light field and an external static magnetic field gives rise to self-sustained spin precession. This entails a modulation on the transmitted light at roughly the Larmor frequency. We show that under suitable conditions this oscillation can become irregular. A detailed analysis reveals a deterministically chaotic process. Dimensions, entropies, and Lyapunov exponents are determined; cross-checks demonstrate their mutual consistency. To describe the observed dynamics, a three-dimensional model is presented that resembles the well-known Bloch equations. Numerical simulations compare well with the experimental results. Of all the nonlinear terms in the model, the one describing the light shift can be singled out as responsible for the chaotic behavior. This allows an intuitive understanding of the onset of chaos as a result of the interaction between spin precession and light shift.

Physical Review A•May 1, 1992•8 citations

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

Wulfhard K. Lange, Fedor M. Mitschke, R. Deserno +1 more

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.

Journal of the Optical Society of America B•Jan 1, 1984•1 citation

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

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

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.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•0 citations

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 bistability with symmetry breaking

T. Yabuzaki, Taishi Okamoto, Masao Kitano +1 more

It is shown that a simple system without a cavity exhibits optical bistability with no hysteresis but with symmetry-breaking or pitchfork bifurcation. The optical system is composed of a cell containing atoms with spin in the ground state, a $\frac{\ensuremath{\lambda}}{8}$ plate and a mirror, and an incident light beam linearly polarized and nearly resonant with the atomic absorption line. The system has a positive-feedback loop for the rotation of polarization through competitive optical pumping by ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ circularly polarized components. When the intensity of the incident light exceeds a critical value, symmetry breaking occurs and its polarization is subject to rotation in the clockwise or anticlockwise sense. Correspondingly, atomic spin polarization is produced spontaneously in a direction parallel or antiparallel to the incident beam. This new type of optical bistability is found to be explained well in context with the cusp catastrophe, as well as the ordinary one with hysteresis. It is also found that, in the presence of a transverse magnetic field, self-sustained spin precession occurs, which results in the steady-state modulation of the light polarization at about the Larmor frequency. Experimental evidence of the symmetry breaking and pitchfork bifurcation is obtained by using sodium vapor.

Physical Review A•Apr 1, 1984•36 citations
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.
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.
The interaction of spin-1/2 atoms in an optical resonator with a near-resonant cw light field and an external static magnetic field gives rise to self-sustained spin precession. This entails a modulation on the transmitted light at roughly the Larmor frequency. We show that under suitable conditions this oscillation can become irregular. A detailed analysis reveals a deterministically chaotic process. Dimensions, entropies, and Lyapunov exponents are determined; cross-checks demonstrate their mutual consistency. To describe the observed dynamics, a three-dimensional model is presented that resembles the well-known Bloch equations. Numerical simulations compare well with the experimental results. Of all the nonlinear terms in the model, the one describing the light shift can be singled out as responsible for the chaotic behavior. This allows an intuitive understanding of the onset of chaos as a result of the interaction between spin precession and light shift.
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 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.
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.
It is shown that a simple system without a cavity exhibits optical bistability with no hysteresis but with symmetry-breaking or pitchfork bifurcation. The optical system is composed of a cell containing atoms with spin in the ground state, a $\frac{\ensuremath{\lambda}}{8}$ plate and a mirror, and an incident light beam linearly polarized and nearly resonant with the atomic absorption line. The system has a positive-feedback loop for the rotation of polarization through competitive optical pumping by ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ circularly polarized components. When the intensity of the incident light exceeds a critical value, symmetry breaking occurs and its polarization is subject to rotation in the clockwise or anticlockwise sense. Correspondingly, atomic spin polarization is produced spontaneously in a direction parallel or antiparallel to the incident beam. This new type of optical bistability is found to be explained well in context with the cusp catastrophe, as well as the ordinary one with hysteresis. It is also found that, in the presence of a transverse magnetic field, self-sustained spin precession occurs, which results in the steady-state modulation of the light polarization at about the Larmor frequency. Experimental evidence of the symmetry breaking and pitchfork bifurcation is obtained by using sodium vapor.