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

Telecommunications and Radio Engineering

Saturation of Stationary Inversion States in a Three-Level Traveling-Wave Quantum Amplifier with Bistable Resonator Pumping

D. N. Makovetskii

Published Jan 1, 2003• 1 citation
Publisher

Abstract

The inversion states of a saturated three-level traveling-wave quantum paramagnetic amplifier have been investigated under conditions of bistable resonator pumping. The equations of motion for the vectorial order parameter have been obtained using adiabatic elimination of fast variables. These equations are a generalization of the scalar two-level Drummond model for the case of a three-level quantum active system. Isolated branches of the constant of inversion have been found from stationary solutions of equations for the vectorial order parameter. A analysis of bifurcations in the saturated quantum amplifier with bistable pumping has been represented with full details.

DOI
10.1615/telecomradeng.v59.i7-9.100

Related papers

Saturation of Stationary Inversion States in a Three-Level Traveling-Wave Quantum Amplifier with Bistable Resonator Pumping

D. N. Makovetskii

The inversion states of a saturated traveling-wave three-level quantum paramagnetic amplifier have been investigated under conditions of bistable resonator pumping. The equations of motion for the vectorial order parameter have been obtained using adiabatic elimination of fast variables. The exact solutions for stationary inversion states have been found from these equations. For high-quality pump resonators, the isolated and the semi-isolated branches of the inversion ratio have been revealed in stationary solutions. The existence of the semi-isolated branches means a possibility of collapse of the inversion state under influence of a saturating signal. Revival of inversion is possible in this case only by the hard excitation of the pump system. This nonlinear phenomenon is of a qualitatively another nature than one described by us in arXiv:0901.0449v1 [nlin.AO], and may be observed at moderate Q-factor of pump resonator.

arXiv:0911.2124•Nov 11, 2009•1 citation

Bistability and Transient Processes in a Three-Level Phaser System Saturated by a Standing Pumping Field and a Signal Traveling Wave

D. N. Makovetskii

Nonstationary processes in a three-level active paramagnetic phaser system have been investigated in case of the inversion state branching (bistability) which takes place below the threshold of self-excitation of the phonon generation. It has been shown that the nature of the branching of inversion states and transient processes in such a system depends significantly not only on a hypersound signal intensity, that was determined before, but also on a signal modulation frequency. Narrow nonlinear resonances and a critical slowing-down of transient processes have been found at simultaneous saturation of a spin-system by a standing electromagnetic pumping field and a hypersound-signal traveling wave.

Telecommunications and Radio Engineering•Jan 1, 2005•0 citations

Branching of stationary inversion states in a cavity-pumped paramagnetic maser amplifier

D. N. Makovetskii, Alexander A. Lavrinovich, N. T. Cherpak

The nonlinear dynamics in a paramagnetic maser amplifier is investigated experimentally and theoretically under conditions such that the active medium exerts a sufficiently strong feedback influence on the pump field to induce population inversion of the spin levels. Branching of the inversion ratio due to the onset of bistability in the nonlinear microwave cavity of the pump at a frequency of 150 GHz is observed experimentally. Conditions are determined for the possible excitation of new nonlinear resonances when the spin system is inverted by a standing-wave field, and the stability of the resulting stationary nonequilibrium states of the paramagnet is analyzed.

Technical Physics•May 1, 1999•2 citations

Stationary, harmonic, and pulsed operations of an optically bistable laser with saturable absorber. I

Paul Mandel, Thomas Erneux

We study the semiclassical equations for a laser with a saturable absorber in the mean-field limit, assuming homogeneously broadened two-level atoms, for a set of parameters where the system displays optical bistability and time-periodic solutions. In the first part the bifurcation diagram for stationary and periodic solutions is obtained by numerical integration. Two different classes of stable periodic solutions arise: small-amplitude solutions and passive $Q$ switching. We observe hysteresis domains involving up to three solutions (stationary and/or periodic). We also discuss the validity of some standard approximations and show that even in the absence of detuning the phases play an important role. We also discuss the influence of the initial conditions whose symmetry properties induce important modifications of the bifurcation diagram. In the second part we introduce an alternative adiabatic elimination scheme which allows us to construct the small-amplitude periodic solutions over nearly their whole range of existence. We then study these solutions near the Hopf bifurcation from which they emerge and derive analytic conditions for their stability. When they are stable, $\stackrel{\mathrm{\ifmmode\acute\else\textasciiacute\fi{}}}{\mathrm{w}}$e also give the conditions under which a secondary Hopf bifurcation will occur, leading to quasiperiodic solutions.

Physical Review A•Oct 1, 1984•55 citations

Four-wave mixing in resonantly amplifying media in the inversion saturation regime

Yu F Kir'yanov, Кочемасов Геннадий Григорьевич, S M Martynova +1 more

The two-level approximation is used to make a theoretical analysis of four-wave mixing in the active medium of a laser whose radiation wavefront is to be reversed. Explicit allowance is made for changes in the amplitudes of the pump waves as a result of their amplification during propagation in the active medium. Both the completely degenerate case, when the frequencies of all four waves are the same, and the case of a small detuning of the signal wave frequency relative to the pump waves are considered. For the completely degenerate case a system of reduced equations allowing for saturation of the inversion was solved by computer using an iterative method. It was found that, under optimum conditions in the saturation regime, the power of the wave reflected from a four-wave mixer may be higher than that of the signal wave.

Soviet Journal of Quantum Electronics•Aug 31, 1981•4 citations

Lasers with three-level absorbers

Govind Prasad Agrawal

Output characteristics of a traveling-wave monomode laser with an intracavity three-level absorber are investigated. The laser frequency is assumed to be symmetrically detuned from the two ground-state sublevels for a $\ensuremath{\Lambda}$-type transition scheme. It is shown that bistability and hysteresis in the laser output, characteristics of a first-order phase transition, may arise much before the absorber saturates. For this reason, bistability may be observed even if the gain medium saturates faster than the absorber, in contrast with the case of a two-level saturable absorber. The physical mechanism for bistable behavior is coherent population trapping which accumulates all absorbing atoms in the ground-state sublevels with a sharp decrease in absorption.

Physical Review A•Sep 1, 1981•10 citations
The inversion states of a saturated three-level traveling-wave quantum paramagnetic amplifier have been investigated under conditions of bistable resonator pumping. The equations of motion for the vectorial order parameter have been obtained using adiabatic elimination of fast variables. These equations are a generalization of the scalar two-level Drummond model for the case of a three-level quantum active system. Isolated branches of the constant of inversion have been found from stationary solutions of equations for the vectorial order parameter. A analysis of bifurcations in the saturated quantum amplifier with bistable pumping has been represented with full details.
The inversion states of a saturated traveling-wave three-level quantum paramagnetic amplifier have been investigated under conditions of bistable resonator pumping. The equations of motion for the vectorial order parameter have been obtained using adiabatic elimination of fast variables. The exact solutions for stationary inversion states have been found from these equations. For high-quality pump resonators, the isolated and the semi-isolated branches of the inversion ratio have been revealed in stationary solutions. The existence of the semi-isolated branches means a possibility of collapse of the inversion state under influence of a saturating signal. Revival of inversion is possible in this case only by the hard excitation of the pump system. This nonlinear phenomenon is of a qualitatively another nature than one described by us in arXiv:0901.0449v1 [nlin.AO], and may be observed at moderate Q-factor of pump resonator.
Nonstationary processes in a three-level active paramagnetic phaser system have been investigated in case of the inversion state branching (bistability) which takes place below the threshold of self-excitation of the phonon generation. It has been shown that the nature of the branching of inversion states and transient processes in such a system depends significantly not only on a hypersound signal intensity, that was determined before, but also on a signal modulation frequency. Narrow nonlinear resonances and a critical slowing-down of transient processes have been found at simultaneous saturation of a spin-system by a standing electromagnetic pumping field and a hypersound-signal traveling wave.
The nonlinear dynamics in a paramagnetic maser amplifier is investigated experimentally and theoretically under conditions such that the active medium exerts a sufficiently strong feedback influence on the pump field to induce population inversion of the spin levels. Branching of the inversion ratio due to the onset of bistability in the nonlinear microwave cavity of the pump at a frequency of 150 GHz is observed experimentally. Conditions are determined for the possible excitation of new nonlinear resonances when the spin system is inverted by a standing-wave field, and the stability of the resulting stationary nonequilibrium states of the paramagnet is analyzed.
We study the semiclassical equations for a laser with a saturable absorber in the mean-field limit, assuming homogeneously broadened two-level atoms, for a set of parameters where the system displays optical bistability and time-periodic solutions. In the first part the bifurcation diagram for stationary and periodic solutions is obtained by numerical integration. Two different classes of stable periodic solutions arise: small-amplitude solutions and passive QQQ switching. We observe hysteresis domains involving up to three solutions (stationary and/or periodic). We also discuss the validity of some standard approximations and show that even in the absence of detuning the phases play an important role. We also discuss the influence of the initial conditions whose symmetry properties induce important modifications of the bifurcation diagram. In the second part we introduce an alternative adiabatic elimination scheme which allows us to construct the small-amplitude periodic solutions over nearly their whole range of existence. We then study these solutions near the Hopf bifurcation from which they emerge and derive analytic conditions for their stability. When they are stable, $\stackrel{\mathrm{\ifmmode\acute\else\textasciiacute\fi{}}}{\mathrm{w}}$e also give the conditions under which a secondary Hopf bifurcation will occur, leading to quasiperiodic solutions.
The two-level approximation is used to make a theoretical analysis of four-wave mixing in the active medium of a laser whose radiation wavefront is to be reversed. Explicit allowance is made for changes in the amplitudes of the pump waves as a result of their amplification during propagation in the active medium. Both the completely degenerate case, when the frequencies of all four waves are the same, and the case of a small detuning of the signal wave frequency relative to the pump waves are considered. For the completely degenerate case a system of reduced equations allowing for saturation of the inversion was solved by computer using an iterative method. It was found that, under optimum conditions in the saturation regime, the power of the wave reflected from a four-wave mixer may be higher than that of the signal wave.
Output characteristics of a traveling-wave monomode laser with an intracavity three-level absorber are investigated. The laser frequency is assumed to be symmetrically detuned from the two ground-state sublevels for a $\ensuremath{\Lambda}$-type transition scheme. It is shown that bistability and hysteresis in the laser output, characteristics of a first-order phase transition, may arise much before the absorber saturates. For this reason, bistability may be observed even if the gain medium saturates faster than the absorber, in contrast with the case of a two-level saturable absorber. The physical mechanism for bistable behavior is coherent population trapping which accumulates all absorbing atoms in the ground-state sublevels with a sharp decrease in absorption.