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

Annual Meeting Optical Society of America

Good cavity laser instabilities

Paul Mandel, Ruo-Ding Li

Published Jan 1, 1989• 0 citations
Publisher

Abstract

In an attempt to explain the instability observed by Hillman et al.,1 we have analyzed the domain of parameters in which their dye laser operates. This leads to the consideration of an asymptotic limit for which the slowly varying envelope approximation no longer holds. As a result, the electric field equation must retain its second-order space and time derivatives. This opens new possibilities for the steady states and their stability properties, (i) Even in the case of perfect matching between atomic and cavity frequencies, the laser operating frequency is displaced from the cavity resonance, (ii) The single-mode stable steady state is not necessarily the mode whose frequency is nearest to the atomic transition, (iii) Instability of the steady state can occur without restriction on the laser cavity quality.

DOI
10.1364/oam.1989.fl2

Related papers

The generalized dynamic equation of optical bistability, and the laser and its stability analysis

Fa Ou, Yong Qiang Cai

A single-mode dynamic equation is obtained from the Maxwell equation with the slowly-varying amplitude approximation, and the boundary conditions of the cavity. Here the mean-field limit and the good-quality cavity case have been used. This equation is useful in describing the dynamic behavior of intrinsic optical bistable systems and/or lasers with injected signals for any kinds of materials, including two-level atoms. Furthermore, according to the linear stability analysis, a generalized instability criterion is derived.

Acta Physica Sinica•Jul 1, 1989•0 citations

Semiclassical dye-laser equations and the unidirectional single-frequency operation

Hong Chuan Fu, Hermann Haken

A semiclassical description for dye lasers is proposed, where the energy-level diagram of the dye molecule is assumed to consist of a continuous bandlike ground state and an excited singlet state. Unidirectional single-frequency (s.f.) operation is discussed. The linear-stability analysis for this operation reveals a very low threshold instability, which may appear generally in practical lasers. The ratio of the instability threshold to the lasing threshold may be of any value greater than 1, depending mainly on the bandwidth and the distribution of the dipole moments on the band, but it is independent of the cavity loss. This instability may account for that observed in recent experiments by Hillman, Krasinki, Boyd, and Stroud [Phys. Rev. Lett. 52, 1605 (1984)]. A general approach to analyzing the linear stability of the s.f. operation of the Maxwell-Bloch equations is also proposed, which states that only the eigenvalues of a 2\ifmmode\times\else\texttimes\fi{}2 matrix are relevant: one concerns the stability of the s.f. operation near the lasing threshold, the other determines the instability threshold of this operation.

Physical Review A•Nov 1, 1987•29 citations

Single- and two-mode models

Luigi A. Lugiato, Franco Prati, Massimo Brambilla

In the first section we discuss the stationary solutions for a laser with an injected signal, the active counterpart of the optical bistability analyzed in Chapter 11. Next, in Section 13.2 we consider another very interesting system, namely a laser with a saturable absorber, a free-running laser in which the optical cavity contains a passive medium in addition to the active medium. The single-mode model for this system can be constructed by combining the single-mode models for the free-running laser and for optical bistability. The discussion is then focussed on its stationary states. In Section 13.3 we return to the single-mode model for optical bistability and, by introducing an appropriate “cubic limit” on the parameters in play, we derive a cubic model for dispersive optical bistability with two-level atoms. The stationary equation for such a model formally coincides with that derived and discussed for a Kerr medium in Section 11.2. In the last section we start from the equations for a quadratic nonlinear medium in the degenerate configuration derived in Chapter 6 and combine them with the appropriate boundary conditions for the two field envelopes in play, assuming that the quadratic medium is contained in a ring cavity as happens in an optical parametric oscillator or in second-harmonic generation in a cavity. Next, by introducing the low-transmission limit and the single-mode limit we derive a two-mode model that describes the dynamics of a degenerate optical parametric oscillator or of second-harmonic generation in a cavity. Finally, for the case of a parametric oscillator we illustrate extensively the stationary solutions of the equations. A laser with an injected signal From a technical point of view, this system is interesting because of the possibility of stabilizing the frequency and the phase of separate lasers by taking advantage of the known affinity of nonlinear oscillators to lock onto a periodic forcing element. In 1972 Spencer and Lamb [125] predicted the possibility of bistable behavior in a laser with an injected signal before the surge of interest in optical bistability in the passive configuration.

Cambridge University Press eBooks•Feb 28, 2015•0 citations

THE GENERALIZED DYNAMICAL EQUATION OF OPTICAL BISTABILITY AND LASER AND ITS STABILITY ANALYSIS

Yunfeng Ai

A single-mode dynamical equation is obtained from the Maxwell equation with the slowly varying amplitude approximation and the boundary conditions of the cavity, here the mean field limir and the good quality cavity case have been used. This equation is useful in describing the dynamical behavior of intrinsic optical bistable systems and/or lasers with injected sig-nals for any kinds of materials including two-level atoms. Furthermore, according to the li--near stability analysis, a generalized instability criterion is derived.

Acta Physica Sinica•Jan 1, 1988•0 citations

Single-mode and multimode operation in inhomogeneously broadened lasers

Luigi A. Lugiato, Franco Prati, Massimo Brambilla

The instabilities in homogeneously broadened lasers, which we described in the previous chapter, have a paradigmatic importance because they arise in models which allow one to perform the linear-stability analysis in a simple analytic form. The treatment of the corresponding instabilities in the case of in homogeneously broadened lasers is substantially more complex in general. However, it is very interesting because, as we shall see, the instabilities arise in parametric domains that are much more accessible from the experimental viewpoint. A related issue is that of the possibility of multimodal emission in a laser. It is common knowledge that in order to attain multimode emission it is necessary to have a sort of in homogeneity in the gain medium, because in a completely homogeneous configuration all modes interact with all atoms, and the arising competition among modes implies that only one of them survives. There are basically two main kinds of in homogeneity, the first is of spatial nature and the other is of spectral nature. The first kind is realized in Fabry–Perot lasers, because different cavity modes interact with atoms at different spatial positions in the cavity thanks to the standing-wave configuration of the field and to the consequent phenomenon of spatial hole- burning (see Section 14.2 and Fig. 14.1). This circumstance is capable of weakening the mode–mode competition and allowing multimode operation. In unidirectional ring lasers, on the other hand, there is an “inhomogeneous” configuration in the case of inhomogeneous broadening, because different groups of atoms have different transition frequencies and therefore interact with different modes thanks to the spectral hole-burning (see Section 15.2 and Fig. 15.3). Again, this weakens the mode–mode competition and allows multimode operation. However, these are qualitative considerations, and the only reliable and quantitative method to determine the possibility of multimodal operation is the linear-stability analysis of the single-mode stationary solutions.

Cambridge University Press eBooks•Feb 28, 2015•0 citations

THE GENERALIZED DYNAMICAL EQUATION OF OPTICAL BISTABILITY AND LASER AND ITS STABILITY ANALYSIS

Fa Ou, Yong Qiang Cai, 华南工学院物理系

A single-mode dynamical equation is obtained from the Maxwell equation with the slowly varying amplitude approximation and the boundary conditions of the cavity, here the mean field limir and the good quality cavity case have been used. This equation is useful in describing the dynamical behavior of intrinsic optical bistable systems and/or lasers with injected sig-nals for any kinds of materials including two-level atoms. Furthermore, according to the li-near stability analysis, a generalized instability criterion is derived.

Acta Physica Sinica•Jan 1, 1988•0 citations
In an attempt to explain the instability observed by Hillman et al.,1 we have analyzed the domain of parameters in which their dye laser operates. This leads to the consideration of an asymptotic limit for which the slowly varying envelope approximation no longer holds. As a result, the electric field equation must retain its second-order space and time derivatives. This opens new possibilities for the steady states and their stability properties, (i) Even in the case of perfect matching between atomic and cavity frequencies, the laser operating frequency is displaced from the cavity resonance, (ii) The single-mode stable steady state is not necessarily the mode whose frequency is nearest to the atomic transition, (iii) Instability of the steady state can occur without restriction on the laser cavity quality.
A single-mode dynamic equation is obtained from the Maxwell equation with the slowly-varying amplitude approximation, and the boundary conditions of the cavity. Here the mean-field limit and the good-quality cavity case have been used. This equation is useful in describing the dynamic behavior of intrinsic optical bistable systems and/or lasers with injected signals for any kinds of materials, including two-level atoms. Furthermore, according to the linear stability analysis, a generalized instability criterion is derived.
A semiclassical description for dye lasers is proposed, where the energy-level diagram of the dye molecule is assumed to consist of a continuous bandlike ground state and an excited singlet state. Unidirectional single-frequency (s.f.) operation is discussed. The linear-stability analysis for this operation reveals a very low threshold instability, which may appear generally in practical lasers. The ratio of the instability threshold to the lasing threshold may be of any value greater than 1, depending mainly on the bandwidth and the distribution of the dipole moments on the band, but it is independent of the cavity loss. This instability may account for that observed in recent experiments by Hillman, Krasinki, Boyd, and Stroud [Phys. Rev. Lett. 52, 1605 (1984)]. A general approach to analyzing the linear stability of the s.f. operation of the Maxwell-Bloch equations is also proposed, which states that only the eigenvalues of a 2\ifmmode\times\else\texttimes\fi{}2 matrix are relevant: one concerns the stability of the s.f. operation near the lasing threshold, the other determines the instability threshold of this operation.
In the first section we discuss the stationary solutions for a laser with an injected signal, the active counterpart of the optical bistability analyzed in Chapter 11. Next, in Section 13.2 we consider another very interesting system, namely a laser with a saturable absorber, a free-running laser in which the optical cavity contains a passive medium in addition to the active medium. The single-mode model for this system can be constructed by combining the single-mode models for the free-running laser and for optical bistability. The discussion is then focussed on its stationary states. In Section 13.3 we return to the single-mode model for optical bistability and, by introducing an appropriate “cubic limit” on the parameters in play, we derive a cubic model for dispersive optical bistability with two-level atoms. The stationary equation for such a model formally coincides with that derived and discussed for a Kerr medium in Section 11.2. In the last section we start from the equations for a quadratic nonlinear medium in the degenerate configuration derived in Chapter 6 and combine them with the appropriate boundary conditions for the two field envelopes in play, assuming that the quadratic medium is contained in a ring cavity as happens in an optical parametric oscillator or in second-harmonic generation in a cavity. Next, by introducing the low-transmission limit and the single-mode limit we derive a two-mode model that describes the dynamics of a degenerate optical parametric oscillator or of second-harmonic generation in a cavity. Finally, for the case of a parametric oscillator we illustrate extensively the stationary solutions of the equations. A laser with an injected signal From a technical point of view, this system is interesting because of the possibility of stabilizing the frequency and the phase of separate lasers by taking advantage of the known affinity of nonlinear oscillators to lock onto a periodic forcing element. In 1972 Spencer and Lamb [125] predicted the possibility of bistable behavior in a laser with an injected signal before the surge of interest in optical bistability in the passive configuration.
A single-mode dynamical equation is obtained from the Maxwell equation with the slowly varying amplitude approximation and the boundary conditions of the cavity, here the mean field limir and the good quality cavity case have been used. This equation is useful in describing the dynamical behavior of intrinsic optical bistable systems and/or lasers with injected sig-nals for any kinds of materials including two-level atoms. Furthermore, according to the li--near stability analysis, a generalized instability criterion is derived.
The instabilities in homogeneously broadened lasers, which we described in the previous chapter, have a paradigmatic importance because they arise in models which allow one to perform the linear-stability analysis in a simple analytic form. The treatment of the corresponding instabilities in the case of in homogeneously broadened lasers is substantially more complex in general. However, it is very interesting because, as we shall see, the instabilities arise in parametric domains that are much more accessible from the experimental viewpoint. A related issue is that of the possibility of multimodal emission in a laser. It is common knowledge that in order to attain multimode emission it is necessary to have a sort of in homogeneity in the gain medium, because in a completely homogeneous configuration all modes interact with all atoms, and the arising competition among modes implies that only one of them survives. There are basically two main kinds of in homogeneity, the first is of spatial nature and the other is of spectral nature. The first kind is realized in Fabry–Perot lasers, because different cavity modes interact with atoms at different spatial positions in the cavity thanks to the standing-wave configuration of the field and to the consequent phenomenon of spatial hole- burning (see Section 14.2 and Fig. 14.1). This circumstance is capable of weakening the mode–mode competition and allowing multimode operation. In unidirectional ring lasers, on the other hand, there is an “inhomogeneous” configuration in the case of inhomogeneous broadening, because different groups of atoms have different transition frequencies and therefore interact with different modes thanks to the spectral hole-burning (see Section 15.2 and Fig. 15.3). Again, this weakens the mode–mode competition and allows multimode operation. However, these are qualitative considerations, and the only reliable and quantitative method to determine the possibility of multimodal operation is the linear-stability analysis of the single-mode stationary solutions.
A single-mode dynamical equation is obtained from the Maxwell equation with the slowly varying amplitude approximation and the boundary conditions of the cavity, here the mean field limir and the good quality cavity case have been used. This equation is useful in describing the dynamical behavior of intrinsic optical bistable systems and/or lasers with injected sig-nals for any kinds of materials including two-level atoms. Furthermore, according to the li-near stability analysis, a generalized instability criterion is derived.