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

Nonlinear intensity effects in a laser generating the three main standing waves

Fabien Bretenaker, A. Le Floch

Published Apr 1, 1991• 9 citations
Publisher

Abstract

The resonance condition is used to describe theoretically the three main kinds of standing waves with E\ensuremath{\perp}B (linear) and E?B (helicoidal and circular polarizations) that can be produced by the same laser and their nonlinear interaction with an atomic medium. It is shown that the saturation behavior of a single-mode gas laser is drastically modified by the nature of the operating standing wave. The predictions are checked experimentally with a laser from which each kind of standing wave can be generated with the same losses. The anisotropic structure of the saturation and in particular of the Lamb dip is isolated in each case. Very good agreement is observed between experiments and theory.

DOI
10.1103/physreva.43.3704

Related papers

Theoretical and Experimental Investigations of Saturation Effects in a Gas Laser

Maeda, Hisatoshi

Theoretical studies of standing and traveling wave lasers are presented. The spectral behavior of the amplified spontaneous emission (superradiance) in a pencil-shaped column is investigated theoretically and experimentally. Spectral narrowing followed by rebroadening has been observed as predicted by the theory. A geometrical representation of an interacting two-level atomic system has been developed and applied to an optical laser. A semi-classical model for a standing wave laser has been examined using the rotating wave approximation, and compared to the exact solution. Depth and width of the Lamb dip are determined theoretically and experimentally. The effect of radial profile of the laser field has been studied using the self-consistent-field approach, and the radius of the beam was measured at various positions from the window.

•Feb 12, 2018•0 citations

Bistability and tristability of single-mode gas lasers and lasers containing a saturable absorber

John C. Englund

When a tuned standing-wave gas laser operates on-resonance, neighboring frequencies experience gain in accordance with the Lamb dip. Bennett1 showed that it is possible for certain of these frequencies also to satisfy the phase-matching condition required by the dispersion relation. In such cases, gas lasers possess three possible steady states—one on-resonance state and two frequency-pushed ones. Bennett suggested that this effect could give rise to bistability and hysteresis in the frequency vs detuning characteristics.

•Jun 9, 1986•0 citations

Lamb-dip-like behavior in each spectral component of a spontaneously pulsing, single-mode, standing-wave gas laser

R. S. Gioggia, N. B. Abraham, Wulfhard K. Lange +2 more

The optical spectra corresponding to complex intensity pulsation patterns near line-center tuning of single-mode, standing-wave gas lasers contain some simple indicators of the origins of their complexity. Heterodyne measurements show that on detuning of the laser the power density in each component of the optical spectrum undergoes a Lamb-dip-like reduction as it passes through resonance with the zero-velocity atoms. These observations help to explain the sensitive dependence of the dynamics of standing-wave gas lasers on detuning within the Lamp dip and distortions of the Lamb-dip shapes when the lasers are unstable.

Journal of the Optical Society of America B•May 1, 1988•5 citations

Frequency tristability of single-mode, standing-wave gas lasers containing a saturable absorber

John C. Englund

The structure of the Lamb dip may permit a standing-wave gas laser containing a saturable absorber (LSA) to exhibit frequency tristability while oscillating in a single spatial mode. This is concluded from the steady-state and stability analyses of a plane-wave gas-laser model in which the atomic populations are taken as homogeneous. Conditions for this behavior are investigated, and it is concluded that very high pump excitations are needed, which is in contrast to previously reported predictions of frequency multistability for LSA’s containing homogeneously broadened media.

Journal of the Optical Society of America B•May 1, 1988•0 citations

Theory of Nonlinear Effects in a Gas Laser Amplifier. I. Weak Signals

A. Dienes

Using classical fields and the density-matrix formalism, we analyze the nonlinear characteristics of a gas laser amplifier subject to an axial magnetic field, operating with two optical-frequency signals of arbitrary polarization. Perturbational solutions, valid for relatively weak intensities, are obtained which describe the saturation interaction of the signals and the generation of combination tones. An arbitrary amount of Doppler broadening is considered throughout. The simple $J=1\ensuremath{\rightarrow}J=0$ model is found convenient to describe the physical processes taking place. In general, however, the interactions are found to depend on the $J$ values of the levels. We find that only saturation and no combination-tone generation occurs for two opposite circularly polarized signals, while both effects are, in general, present for two linearly or elliptically polarized fields. The limiting case of zero magnetic field is examined separately. It is also found that in many cases the medium is made effectively anisotropic by the nonlinear interactions. Applications to measurements of atomic parameters such as $J$ values, $g$ values, and lifetimes are discussed.

Physical Review•Oct 10, 1968•36 citations

On the theory of polarization effects in gas lasers

Daan Lenstra

Abstract Starting from a theory in which laser operation is described as the excitation of the natural modes of an open-resonator system, the case of a Fabry-Perot resonator with plane-parallel mirrors is treated. It is shown that, in the case of weakly anisotropic mirrors, the natural modes can be grouped in pairs, such that each pair corresponds to one scalar longitudinal mode. In that case, laser operation can and will be described in terms of these longitudinal modes, which then possess a vectorial field amplitude, in agreement with the usual formalism. The polarization preference in a single-mode gas laser operating on a transition between a singlet and a triplet state is investigated, taking into account differences in the relaxation constants for the various expectation values of atomic variables. A calculation of the effect on the relaxation constants due to interatomic collisions leads to the conclusion that theory and experiment are in good agreement with each other. Equations describing the time evolution of the polarization parameters of both modes in a two-mode operating gas laser are derived. It is found as a general rule that mode-mode interaction results in modes whose polarizations are mutually orthogonal. An exception to this rule is found in the case in which the single-mode preference is for circular polarization. The influence of two specific mirror anisotropies is discussed. The polarization behaviour of a single-mode gas laser in the presence of (partly) applied, transverse magnetic fields is extensively dealt with. It appears to be essential to distinguish between the case in which the magnetic field is applied only to a fraction of the active medium and the case in which the magnetic field is uniform in the entire medium. This distinction is shown to lead to a satisfactory theoretical description of a certain class of experiments. In the case of two other experiments, good agreement with the theory is obtained, by assuming the presence of mirror anisotropies of acceptable kind and size. Finally, the influence of small anisotropies on the degree of polarization of a single-mode gas laser is theoretically investigated, when the latter is polarized by means of a strong transverse magnetic field.

•Feb 1, 1979•0 citations
The resonance condition is used to describe theoretically the three main kinds of standing waves with E\ensuremath{\perp}B (linear) and E?B (helicoidal and circular polarizations) that can be produced by the same laser and their nonlinear interaction with an atomic medium. It is shown that the saturation behavior of a single-mode gas laser is drastically modified by the nature of the operating standing wave. The predictions are checked experimentally with a laser from which each kind of standing wave can be generated with the same losses. The anisotropic structure of the saturation and in particular of the Lamb dip is isolated in each case. Very good agreement is observed between experiments and theory.
Theoretical studies of standing and traveling wave lasers are presented. The spectral behavior of the amplified spontaneous emission (superradiance) in a pencil-shaped column is investigated theoretically and experimentally. Spectral narrowing followed by rebroadening has been observed as predicted by the theory. A geometrical representation of an interacting two-level atomic system has been developed and applied to an optical laser. A semi-classical model for a standing wave laser has been examined using the rotating wave approximation, and compared to the exact solution. Depth and width of the Lamb dip are determined theoretically and experimentally. The effect of radial profile of the laser field has been studied using the self-consistent-field approach, and the radius of the beam was measured at various positions from the window.
When a tuned standing-wave gas laser operates on-resonance, neighboring frequencies experience gain in accordance with the Lamb dip. Bennett1 showed that it is possible for certain of these frequencies also to satisfy the phase-matching condition required by the dispersion relation. In such cases, gas lasers possess three possible steady states—one on-resonance state and two frequency-pushed ones. Bennett suggested that this effect could give rise to bistability and hysteresis in the frequency vs detuning characteristics.
The optical spectra corresponding to complex intensity pulsation patterns near line-center tuning of single-mode, standing-wave gas lasers contain some simple indicators of the origins of their complexity. Heterodyne measurements show that on detuning of the laser the power density in each component of the optical spectrum undergoes a Lamb-dip-like reduction as it passes through resonance with the zero-velocity atoms. These observations help to explain the sensitive dependence of the dynamics of standing-wave gas lasers on detuning within the Lamp dip and distortions of the Lamb-dip shapes when the lasers are unstable.
The structure of the Lamb dip may permit a standing-wave gas laser containing a saturable absorber (LSA) to exhibit frequency tristability while oscillating in a single spatial mode. This is concluded from the steady-state and stability analyses of a plane-wave gas-laser model in which the atomic populations are taken as homogeneous. Conditions for this behavior are investigated, and it is concluded that very high pump excitations are needed, which is in contrast to previously reported predictions of frequency multistability for LSA’s containing homogeneously broadened media.
Using classical fields and the density-matrix formalism, we analyze the nonlinear characteristics of a gas laser amplifier subject to an axial magnetic field, operating with two optical-frequency signals of arbitrary polarization. Perturbational solutions, valid for relatively weak intensities, are obtained which describe the saturation interaction of the signals and the generation of combination tones. An arbitrary amount of Doppler broadening is considered throughout. The simple $J=1\ensuremath{\rightarrow}J=0$ model is found convenient to describe the physical processes taking place. In general, however, the interactions are found to depend on the JJJ values of the levels. We find that only saturation and no combination-tone generation occurs for two opposite circularly polarized signals, while both effects are, in general, present for two linearly or elliptically polarized fields. The limiting case of zero magnetic field is examined separately. It is also found that in many cases the medium is made effectively anisotropic by the nonlinear interactions. Applications to measurements of atomic parameters such as JJJ values, ggg values, and lifetimes are discussed.
Abstract Starting from a theory in which laser operation is described as the excitation of the natural modes of an open-resonator system, the case of a Fabry-Perot resonator with plane-parallel mirrors is treated. It is shown that, in the case of weakly anisotropic mirrors, the natural modes can be grouped in pairs, such that each pair corresponds to one scalar longitudinal mode. In that case, laser operation can and will be described in terms of these longitudinal modes, which then possess a vectorial field amplitude, in agreement with the usual formalism. The polarization preference in a single-mode gas laser operating on a transition between a singlet and a triplet state is investigated, taking into account differences in the relaxation constants for the various expectation values of atomic variables. A calculation of the effect on the relaxation constants due to interatomic collisions leads to the conclusion that theory and experiment are in good agreement with each other. Equations describing the time evolution of the polarization parameters of both modes in a two-mode operating gas laser are derived. It is found as a general rule that mode-mode interaction results in modes whose polarizations are mutually orthogonal. An exception to this rule is found in the case in which the single-mode preference is for circular polarization. The influence of two specific mirror anisotropies is discussed. The polarization behaviour of a single-mode gas laser in the presence of (partly) applied, transverse magnetic fields is extensively dealt with. It appears to be essential to distinguish between the case in which the magnetic field is applied only to a fraction of the active medium and the case in which the magnetic field is uniform in the entire medium. This distinction is shown to lead to a satisfactory theoretical description of a certain class of experiments. In the case of two other experiments, good agreement with the theory is obtained, by assuming the presence of mirror anisotropies of acceptable kind and size. Finally, the influence of small anisotropies on the degree of polarization of a single-mode gas laser is theoretically investigated, when the latter is polarized by means of a strong transverse magnetic field.