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

IEEE Journal of Quantum Electronics

On injection locking of homogeneously broadened lasers

M.M. Ibrahim

Published Mar 1, 1978• 15 citations
Publisher

Abstract

The dynamic rate equations are obtained from a semiclassical analysis for a homogeneously broadened laser operating in two modes with an externally injected signal. The time-dependent behavior of two competing modes can be described by three-coupled first-order nonlinear equations which relate the inversion density and the photon density of the two modes. Considerations regarding injection locking are presented.

DOI
10.1109/jqe.1978.1069757

Related papers

Semiclassical Theory of Injected Lasers with Arbitrary Stable and Unstable Resonators.

Steven M. Rinaldi

Abstract : A semiclassical analysis of injected lasers with stable and unstable resonators and arbitrary outcoupling fractions was performed. Homogeneously broadened lasers with Fabry-Perot and with positive branch, confocal unstable resonators were modeled. Both time-dependent and steady-state analyses of free-running and injected lasers were performed. Because of deficiencies in the standing wave semiclassical and the simple saturable gain models, a new semiclassical theory of homogeneously broadened lasers were developed. The theory is predicted upon the following assumptions: the atoms are two-level, a single longitudinal mode exists in the cavity, the transverse mode structure can be adequately modeled by the geometric optics mode, and the laser electric fields can be described by a pair of counterpropagating planar, cylindrical, or spherical traveling waves with different amplitudes. A general semiclassical theory was first developed, and then specialized to the Fabry-Perot and positive branch, confocal unstable resonator cases. Both the Maxwell-Bloch and rate equation approximation forms of the theory were derived. The general theory is sufficiently broad to allow the modeling of the geometric optics mode of any standing wave resonator configuration. The theory was shown to reduce to the simple saturable gain and standing wave semiclassical models in the appropriate limits. The analysis of the injected lasers were performed with the new semiclassical theory. Both time-dependent and steady-state analyses were performed.

•Dec 1, 1987•2 citations

Transient behaviour analysis of injection-locked lasers

Alireza Bahrampour, Mohammad Hossein Zandi

In this paper, we present a theory for analysing the transient behaviour of injection-locked lasers with monochromatic injection, wherein homogeneously broadened wide-band lasers with injection are analysed. In addition to boundary conditions, the initial distribution of the laser and the monochromatic injection signal fields are necessary for solving the governing equations. The Maxwell–Bloch equations are reduced to a system of ordinary differential equations with the initial conditions. In this paper, two approximation methods are introduced. These approximations are named the De-satellite signal approximation and the finite number satellite signal approximation, respectively. The finite number satellite signal approximation is used to study the transient behaviour of the satellite signal around the laser frequency in injection-locked lasers. The results are in good agreement with the data published by the previous studies on this topic.

Journal of Physics D Applied Physics•Jan 7, 2005•1 citation

Strong-signal laser operation. II. Specific cases

J. B. Hambenne, M. Sargent

The multimode strong-signal theory of the preceding paper is applied to a number of two- and three-mode cases. A two-mode stability analysis yields strong-signal counterparts to the third-order coupling parameter. Two-mode homogeneous-broadened operation leads to the discussion of population inversion gratings and associated Bragg scattering. Symmetry properties of the equations for the bidirectional ring are examined. Results for Doppler-broadened two-mode special cases and the three-mode locked unidirectional-ring operation are presented. The strong-signal results are compared to those of the third-order and rate-equation-approximation theories. For the bidirectional ring the historical third-order domain of relative excitation from 1.0 to 1.2 is divided into a valid third-order region and a less accurate region. The condition of bistable operation vs monostable operation is seen to be dependent on the relative excitation and the amount of homogeneous broadening. Two types of bistable operation are seen to exist, one where one mode is completely suppressed and another where both modes may have nonzero intensities.

Physical Review A•Feb 1, 1976•18 citations

Frequency locking of a laser by injected atomic coherence

Timothy Carty, M. Sargent

We consider a single-mode unidirectional ring laser containing a homogeneously broadened two-level medium whose atoms are injected in a coherent superposition of states. Provided that appropriate phase-matching conditions are met, the injected coherence contributes directly to the polarization of the medium and hence to the laser gain. We assume that the field is classical and perfectly phase matched with the injected coherence. We find that laser oscillation can occur below the usual laser threshold, and even in the absence of an inversion, with a frequency locked to the atomic line center. Mode locking is unstable for sufficiently strong relative excitation.

Optics Letters•Jan 1, 1990•3 citations

BISTABILITY IN A TWO-PHOTON LASER WITH INJECTED SIGNAL

Wang Yinghai, HU CHENG-SHENG, Wang Zhicheng +1 more

By means of the semiclassical method, we discuss the bistability in a two-photon laser with injected signal for the homogeneously broadened single mode ring cavity. It is demonstrated that in the resonant case one can find bistable states in a two-photon laser with injected signal. In the limit of "good cavity" and "bad cavity", we give a simple description of bistability leading to a predictions for the transient behavior of the output light and the hysteresis cycle by adiabatically eliminating the fast variables. It is found that the approach to the stationary state is monotonic in the low-branch and is oscillatory in the high-branch, and a critical slowing down occurs where the output field changes discontinuousiy.

Acta Physica Sinica•Jan 1, 1991•0 citations

Frequency locking of a laser by injected atomic coherence

Timothy Carty, Murray Sargent

We consider a single-mode unidirectional ring laser containing a homogeneously broadened two-level medium whose atoms are injected in a coherent superposition of states. Provided appropriate phase matching conditions are met, the injected coherence contributes directly to the polarization of the medium and hence to the laser gain. We suppose the field is classical and perfectly phase matched with the injected coherence. We find that laser oscillation can occur below the usual laser threshold and even in the absence of an inversion. In these cases the steady state laser frequency is locked to the atomic line center. As the excitation increases, the ability of the injected atomic coherence to lock the laser frequency decreases. Slightly above the usual laser threshold, the system unlocks and produces an output weakly modulated in time.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations
The dynamic rate equations are obtained from a semiclassical analysis for a homogeneously broadened laser operating in two modes with an externally injected signal. The time-dependent behavior of two competing modes can be described by three-coupled first-order nonlinear equations which relate the inversion density and the photon density of the two modes. Considerations regarding injection locking are presented.
Abstract : A semiclassical analysis of injected lasers with stable and unstable resonators and arbitrary outcoupling fractions was performed. Homogeneously broadened lasers with Fabry-Perot and with positive branch, confocal unstable resonators were modeled. Both time-dependent and steady-state analyses of free-running and injected lasers were performed. Because of deficiencies in the standing wave semiclassical and the simple saturable gain models, a new semiclassical theory of homogeneously broadened lasers were developed. The theory is predicted upon the following assumptions: the atoms are two-level, a single longitudinal mode exists in the cavity, the transverse mode structure can be adequately modeled by the geometric optics mode, and the laser electric fields can be described by a pair of counterpropagating planar, cylindrical, or spherical traveling waves with different amplitudes. A general semiclassical theory was first developed, and then specialized to the Fabry-Perot and positive branch, confocal unstable resonator cases. Both the Maxwell-Bloch and rate equation approximation forms of the theory were derived. The general theory is sufficiently broad to allow the modeling of the geometric optics mode of any standing wave resonator configuration. The theory was shown to reduce to the simple saturable gain and standing wave semiclassical models in the appropriate limits. The analysis of the injected lasers were performed with the new semiclassical theory. Both time-dependent and steady-state analyses were performed.
In this paper, we present a theory for analysing the transient behaviour of injection-locked lasers with monochromatic injection, wherein homogeneously broadened wide-band lasers with injection are analysed. In addition to boundary conditions, the initial distribution of the laser and the monochromatic injection signal fields are necessary for solving the governing equations. The Maxwell–Bloch equations are reduced to a system of ordinary differential equations with the initial conditions. In this paper, two approximation methods are introduced. These approximations are named the De-satellite signal approximation and the finite number satellite signal approximation, respectively. The finite number satellite signal approximation is used to study the transient behaviour of the satellite signal around the laser frequency in injection-locked lasers. The results are in good agreement with the data published by the previous studies on this topic.
The multimode strong-signal theory of the preceding paper is applied to a number of two- and three-mode cases. A two-mode stability analysis yields strong-signal counterparts to the third-order coupling parameter. Two-mode homogeneous-broadened operation leads to the discussion of population inversion gratings and associated Bragg scattering. Symmetry properties of the equations for the bidirectional ring are examined. Results for Doppler-broadened two-mode special cases and the three-mode locked unidirectional-ring operation are presented. The strong-signal results are compared to those of the third-order and rate-equation-approximation theories. For the bidirectional ring the historical third-order domain of relative excitation from 1.0 to 1.2 is divided into a valid third-order region and a less accurate region. The condition of bistable operation vs monostable operation is seen to be dependent on the relative excitation and the amount of homogeneous broadening. Two types of bistable operation are seen to exist, one where one mode is completely suppressed and another where both modes may have nonzero intensities.
We consider a single-mode unidirectional ring laser containing a homogeneously broadened two-level medium whose atoms are injected in a coherent superposition of states. Provided that appropriate phase-matching conditions are met, the injected coherence contributes directly to the polarization of the medium and hence to the laser gain. We assume that the field is classical and perfectly phase matched with the injected coherence. We find that laser oscillation can occur below the usual laser threshold, and even in the absence of an inversion, with a frequency locked to the atomic line center. Mode locking is unstable for sufficiently strong relative excitation.
By means of the semiclassical method, we discuss the bistability in a two-photon laser with injected signal for the homogeneously broadened single mode ring cavity. It is demonstrated that in the resonant case one can find bistable states in a two-photon laser with injected signal. In the limit of "good cavity" and "bad cavity", we give a simple description of bistability leading to a predictions for the transient behavior of the output light and the hysteresis cycle by adiabatically eliminating the fast variables. It is found that the approach to the stationary state is monotonic in the low-branch and is oscillatory in the high-branch, and a critical slowing down occurs where the output field changes discontinuousiy.
We consider a single-mode unidirectional ring laser containing a homogeneously broadened two-level medium whose atoms are injected in a coherent superposition of states. Provided appropriate phase matching conditions are met, the injected coherence contributes directly to the polarization of the medium and hence to the laser gain. We suppose the field is classical and perfectly phase matched with the injected coherence. We find that laser oscillation can occur below the usual laser threshold and even in the absence of an inversion. In these cases the steady state laser frequency is locked to the atomic line center. As the excitation increases, the ability of the injected atomic coherence to lock the laser frequency decreases. Slightly above the usual laser threshold, the system unlocks and produces an output weakly modulated in time.