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

Spontaneous spatial pattern formation in wide gain section lasers

S.G. Wenden, Per Kristen Jakobsen, J. V. Moloney

Published Jan 1, 1991• 0 citations
Publisher

Abstract

Two-level and Raman lasers with wide-gain sections undergo spontaneous symmetry breaking beyond the first laser threshold resulting in an off-axis emission that, if stable, would correspond to a ring in the far field. The angle subtended by the emission to the laser axis depends on the laser detuning, polarization decay time, and size of the laser cross-section. Optical vortices, propagating fronts, and complex spatio–temporal patterns are predicted to emerge at the first and second thresholds. The intensity dependent detuning and pump laser transverse profile in the Raman laser offers a fascinating array of pattern forming possibilities involving coexisting dark and bright waves. When the polarization decays much faster than the cavity field and medium inversion, one usually adiabatically eliminates this variable from the Maxwell-Bloch equations. Inclusion of transverse effects in this limit, however, leads to spurious transverse instabilities that can be mistaken for numerical grid oscillations. Decoupling of the polarization variable from the electric field allows arbitrarily high transverse wavenumbers to grow.

DOI
10.1364/oam.1991.fn2

Related papers

Space-time dynamics of wide-gain-section lasers

Per Kristen Jakobsen, Jerome V. Moloney, Alan C. Newell +1 more

The space-time behavior of a wide-gain-section, single-longitudinal-mode laser is investigated. Analysis of the full Maxwell-Bloch model in one transverse spatial dimension identifies a traveling-wave solution beyond the first laser threshold, for positive detuning from resonance, which appears to be a globally attracting state of the laser. On the negative-detuning side we observe an initial bifurcation to a homogeneous plane-wave state. A second instability threshold can be identified by linearizing about the respective solutions for both positive and negative detuning. We also find that the standard approach to adiabatic elimination, whereby the polarization equation is adiabatically eliminated, can lead to a spurious high-transverse-wave-number instability in the reduced equations. The derivation of an adiabatically reduced set of equations to remove the instability on the positive-detuning side is a nontrivial matter.

Physical Review A•Jun 1, 1992•221 citations

Dynamic modes of wide-aperture laser systems above the second lasing threshold

Анчиков Дмитрий Александрович, Кренц Антон Анатольевич, Nonna E. Molevich +1 more

The processes of the formation of optical field structures in the transverse profile of wide-aperture laser radiation are studied within the model described by the system of Maxwell-Bloch equations. The main types of instabilities appearing above the second lasing threshold and corresponding mechanisms controlling the laser dynamics at negative frequency detuning are considered. The characteristic lasing modes and conditions of the spontaneous formation of transverse optical structures are determined.

Bulletin of the Lebedev Physics Institute•Aug 1, 2014•7 citations

Complex spatiotemporal dynamics in lasers

Jorge R. Tredicce, C. Green, E. J. D’Angelo +1 more

It is well known that transverse intensity profiles of lasers may show a nontrivial spatial structure. Usually, depending on the degree of symmetry, the spatial patterns have been associated with modes of a passive resonator or combinations of them which cause oscillations in the laser intensity (mode beating).1 It was recently shown2 that the fluctuations may be due, instead, to the nonlinear coupling between atoms and the field. Here we show that a spontaneous symmetry-breaking process is also at the origin of the formation of complex spatiotemporal dynamics in which oscillations at a single frequency, quasiperiodicity, and chaos may coexist within in the same spatial structure. We compare our experimental results with those obtained from bifurcation theory and numerical integration of the Maxwell–Bloch equations. The transition from a simple (Gaussian) profile to a complex (turbulent) profile is studied by means of the average intensity patterns, frequencies, and phases of the local intensity and cross-correlation functions.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Nonlinear transverse modes of large-aspect-ratio homogeneously broadened lasers: II. Pattern analysis near and beyond threshold

Joceline C. Lega, Per Kristen Jakobsen, Jerome V. Moloney +1 more

Complex order-parameter equation descriptions of pattern evolution in large-aspect-ratio two-level and Raman lasers are derived systematically as solvability conditions in a multiple-scales asymptotic expansion of the original Maxwell-Bloch laser equations in powers of a small parameter. These amplitude equations, although strictly valid near threshold for lasing, are shown to capture the essential features of pattern instability and evolution well beyond lasing threshold. A technical difficulty that can arise in the Raman laser, namely, subcriticality of the bifurcation near the critical wave number, is not addressed in the present paper and the order-parameter equations as derived are valid only when this situation does not arise. Analytical expressions for long-wavelength phase instabilities of the underlying traveling-wave pattern, which appears as the natural nonlinear lasing mode when the detuning of the laser from the gain peak is positive, are obtained from the coefficients of a Cross-Newell phase equation. Phase and amplitude instability boundaries, when computed via the original laser equations, the complex order-parameter equations and the phase equation, are shown to be consistent for all cases studied with the exception of the case when a subcritical bifurcation approaches the critical wave number ${\mathit{k}}_{\mathit{c}}$.

Physical Review A•May 1, 1994•58 citations

Stationary spatial patterns in passive optical systems: Two-level atoms

L. A. Lugiato, Claudio Oldano

We discuss a novel type of optical instability, which leads to the spontaneous formation of a stationary spatial structure, instead of to the onset of oscillations or pulsations. A passive system is contained in an optical cavity, to which we add two lateral mirrors. Under appropriate conditions, diffraction of radiation can induce the onset of a transverse-stripe structure in an initially uniform plane-wave field configuration. In this paper, we consider the case of a homogeneously broadened two-level system. The model on which our analysis is based is derived from the Maxwell-Bloch equations in the paraxial approximation, using the mean-field limit and assuming a large Fresnel number. We show that, with respect to the bistability parameter C, the threshold of the spatial instability coincides with the bistability threshold for absorptive, resonant optical bistability. The spatial instability requires, however, a detuned configuration and can arise both in the absence and presence of bistability. In the latter case, it can occur both in the lower and in the upper branch of the steady-state curve. The instability is caused by competition between different transverse modes, which realize a situation of spatial coexistence, different from the state of temporal coexistence which characterizes the spontaneous oscillations that arise from the previously known multimode instabilities. Finally, we discuss some points relevant for an experimental observation of this phenomenon.

Physical Review A•May 1, 1988•114 citations

Pattern formation in large-aspect-ratio single-mode inhomogeneously broadened lasers

E. Cabrera, Óscar G. Calderón, J. M. Guerra

Pattern formation in large-aspect-ratio single-mode inhomogeneously broadened lasers is studied by means of the integro-differential Maxwell-Bloch equations. As the inhomogeneous linewidth increases, the neutral stability curve shows a relaxation in the traveling wave selection allowing structures with different sizes to grow. We have performed numerical simulations with a simplified model based on a few discrete groups of atoms at different resonant frequencies to observe transverse dynamics above threshold for good and bad cavity configurations. We obtain, in general, that close to threshold the inhomogeneous broadening leads to a more complex pattern in comparison to the homogeneous broadening case. At higher pumpings, a stabilization in the number of spatial frequencies taking part in the transverse pattern is found. The influence of the laser aperture on temporal dynamics is also studied. It is shown how the typical self-pulsing regime present in single-mode inhomogeneously broadened lasers is destroyed for a wide enough aperture.

Physical Review A•Dec 14, 2004•7 citations
Two-level and Raman lasers with wide-gain sections undergo spontaneous symmetry breaking beyond the first laser threshold resulting in an off-axis emission that, if stable, would correspond to a ring in the far field. The angle subtended by the emission to the laser axis depends on the laser detuning, polarization decay time, and size of the laser cross-section. Optical vortices, propagating fronts, and complex spatio–temporal patterns are predicted to emerge at the first and second thresholds. The intensity dependent detuning and pump laser transverse profile in the Raman laser offers a fascinating array of pattern forming possibilities involving coexisting dark and bright waves. When the polarization decays much faster than the cavity field and medium inversion, one usually adiabatically eliminates this variable from the Maxwell-Bloch equations. Inclusion of transverse effects in this limit, however, leads to spurious transverse instabilities that can be mistaken for numerical grid oscillations. Decoupling of the polarization variable from the electric field allows arbitrarily high transverse wavenumbers to grow.
The space-time behavior of a wide-gain-section, single-longitudinal-mode laser is investigated. Analysis of the full Maxwell-Bloch model in one transverse spatial dimension identifies a traveling-wave solution beyond the first laser threshold, for positive detuning from resonance, which appears to be a globally attracting state of the laser. On the negative-detuning side we observe an initial bifurcation to a homogeneous plane-wave state. A second instability threshold can be identified by linearizing about the respective solutions for both positive and negative detuning. We also find that the standard approach to adiabatic elimination, whereby the polarization equation is adiabatically eliminated, can lead to a spurious high-transverse-wave-number instability in the reduced equations. The derivation of an adiabatically reduced set of equations to remove the instability on the positive-detuning side is a nontrivial matter.
The processes of the formation of optical field structures in the transverse profile of wide-aperture laser radiation are studied within the model described by the system of Maxwell-Bloch equations. The main types of instabilities appearing above the second lasing threshold and corresponding mechanisms controlling the laser dynamics at negative frequency detuning are considered. The characteristic lasing modes and conditions of the spontaneous formation of transverse optical structures are determined.
It is well known that transverse intensity profiles of lasers may show a nontrivial spatial structure. Usually, depending on the degree of symmetry, the spatial patterns have been associated with modes of a passive resonator or combinations of them which cause oscillations in the laser intensity (mode beating).1 It was recently shown2 that the fluctuations may be due, instead, to the nonlinear coupling between atoms and the field. Here we show that a spontaneous symmetry-breaking process is also at the origin of the formation of complex spatiotemporal dynamics in which oscillations at a single frequency, quasiperiodicity, and chaos may coexist within in the same spatial structure. We compare our experimental results with those obtained from bifurcation theory and numerical integration of the Maxwell–Bloch equations. The transition from a simple (Gaussian) profile to a complex (turbulent) profile is studied by means of the average intensity patterns, frequencies, and phases of the local intensity and cross-correlation functions.
Complex order-parameter equation descriptions of pattern evolution in large-aspect-ratio two-level and Raman lasers are derived systematically as solvability conditions in a multiple-scales asymptotic expansion of the original Maxwell-Bloch laser equations in powers of a small parameter. These amplitude equations, although strictly valid near threshold for lasing, are shown to capture the essential features of pattern instability and evolution well beyond lasing threshold. A technical difficulty that can arise in the Raman laser, namely, subcriticality of the bifurcation near the critical wave number, is not addressed in the present paper and the order-parameter equations as derived are valid only when this situation does not arise. Analytical expressions for long-wavelength phase instabilities of the underlying traveling-wave pattern, which appears as the natural nonlinear lasing mode when the detuning of the laser from the gain peak is positive, are obtained from the coefficients of a Cross-Newell phase equation. Phase and amplitude instability boundaries, when computed via the original laser equations, the complex order-parameter equations and the phase equation, are shown to be consistent for all cases studied with the exception of the case when a subcritical bifurcation approaches the critical wave number kc{\mathit{k}}_{\mathit{c}}kc​.
We discuss a novel type of optical instability, which leads to the spontaneous formation of a stationary spatial structure, instead of to the onset of oscillations or pulsations. A passive system is contained in an optical cavity, to which we add two lateral mirrors. Under appropriate conditions, diffraction of radiation can induce the onset of a transverse-stripe structure in an initially uniform plane-wave field configuration. In this paper, we consider the case of a homogeneously broadened two-level system. The model on which our analysis is based is derived from the Maxwell-Bloch equations in the paraxial approximation, using the mean-field limit and assuming a large Fresnel number. We show that, with respect to the bistability parameter C, the threshold of the spatial instability coincides with the bistability threshold for absorptive, resonant optical bistability. The spatial instability requires, however, a detuned configuration and can arise both in the absence and presence of bistability. In the latter case, it can occur both in the lower and in the upper branch of the steady-state curve. The instability is caused by competition between different transverse modes, which realize a situation of spatial coexistence, different from the state of temporal coexistence which characterizes the spontaneous oscillations that arise from the previously known multimode instabilities. Finally, we discuss some points relevant for an experimental observation of this phenomenon.
Pattern formation in large-aspect-ratio single-mode inhomogeneously broadened lasers is studied by means of the integro-differential Maxwell-Bloch equations. As the inhomogeneous linewidth increases, the neutral stability curve shows a relaxation in the traveling wave selection allowing structures with different sizes to grow. We have performed numerical simulations with a simplified model based on a few discrete groups of atoms at different resonant frequencies to observe transverse dynamics above threshold for good and bad cavity configurations. We obtain, in general, that close to threshold the inhomogeneous broadening leads to a more complex pattern in comparison to the homogeneous broadening case. At higher pumpings, a stabilization in the number of spatial frequencies taking part in the transverse pattern is found. The influence of the laser aperture on temporal dynamics is also studied. It is shown how the typical self-pulsing regime present in single-mode inhomogeneously broadened lasers is destroyed for a wide enough aperture.