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

Polarization Effects in Zeeman Lasers with x−y -Type Loss Anisotropies

A. Le Floch, Roger Le Naour

Published Jul 1, 1971• 43 citations
Publisher

Abstract

It has already been reported that a laser subject to an axial magnetic field and having end mirrors which exhibit relatively high $x\ensuremath{-}y$-type loss anisotropy can be described by two theoretical methods. The first method uses self-consistent-field equations with distributed losses, whereas the second one is based on a resonance condition for a complete round-trip pass. The following study of a Zeeman laser with different $x\ensuremath{-}y$-type loss anisotropy at each mirror shows that the localization of the losses and the nonreciprocal character of the Farady rotation require a different formulation for each initial system. The rotation of the plane of polarization is different at each end of the laser, but it is shown that there always exists for central tuning a real or virtual average polarization vector which obeys Lamb's theory. The equivalence of the two methods is discussed.

DOI
10.1103/physreva.4.290

Related papers

Study of the Frequency-Locking Region of a Monomode Anisotropic Zeeman Laser

A. Le Floch, Guy Michel Stéphan

The experimental study of polarization in a Zeeman laser with strong $x\ensuremath{-}y$-type anisotropies makes evident the rotations of the electric field vector greater than the limiting value of $\frac{1}{4}\ensuremath{\pi}$ which is fixed by the self-consistent theory. The results are in agreement with the vectorial theory based on the resonance condition, which is necessary for the representation of such a type of quantum oscillator with nonreciprocal effects (including anisotropies). The self-consistent theory appears to provide a limit which becomes valid only for very weak anisotropies. Only the polarization of the so-called "Lamb's vector" can be described by the self-consistent theory and its rotation effectively attains $\frac{1}{4}\ensuremath{\pi}$ whatever the value of the anisotropy.

Physical Review A•Aug 1, 1972•14 citations

Coherence Effects in Gaseous Lasers with Axial Magnetic Fields. I. Theoretical

W. Culshaw, J. Kannelaud

The Lamb theory of the optical maser is applied to circularly polarized atomic transitions, and used to consider the beat frequencies and the coherence properties of such orthogonal fields when axial magnetic fields are applied to the gaseous laser. The beat frequency approaches zero in near-zero magnetic fields and synchronization can then occur between the right- and left-handed circularly polarized oscillations. For a resonator with no undue polarization constraint, such a strong coupling gives rise to a linearly polarized output, and to a rotation of the plane of polarization with increasing magnetic field. A self-consistent expression is derived for this rotation under steady-state conditions, and a maximum rotation of $\ifmmode\pm\else\textpm\fi{}\frac{1}{4}\ensuremath{\pi}$ with magnetic field is indicated before the synchronization breaks down and circularly polarized beat phenomena appear. The rotation with magnetic field depends on the laser intensity, on the anisotropy in the cavity losses, and on the position of the cavity resonance within the Doppler linewidth. Also, the angle of rotation is indeterminate unless such anisotropy is present. Other regions of such coherence can occur at higher magnetic fields, where the beat frequency again approaches zero. These depend on the detailed shape of the various dispersion curves of the laser medium. The results derived from the theory used are in general agreement with experimental observations on the 1.153-\ensuremath{\mu} He-Ne laser transition.

Physical Review•Jan 7, 1966•51 citations

Theory of a Zeeman ring laser: General formalism

David R. Hanson, Murray Sargent

A theory of a ring laser subject to a uniform, axial dc magnetic field is given in extension of the two-mirror standing-wave treatment by Sargent, Lamb, and Fork. The active medium consists of thermally moving atoms that have two electronic levels with arbitrary angular momenta. The electric field is treated classically for two circular polarizations of opposite sense in a cavity with any degree of cavity anisotropy. Losses due to backscattering are also included. In addition, the results of a generalized treatment are given which includes arbitrarily oriented magnetic field, a general state of electric field polarization, varying isotopic abundance, and hyperfine structure. The self-consistency requirement is used to obtain amplitude- and frequency-determining equations for multimode operation as functions of laser parameters. A general calculational technique, the "perturbation tree," is introduced in the calculation of the third-order component of the population matrix, greatly simplifying the algebra involved by allowing it to be abstracted in tabular form.

Physical Review A•Jan 1, 1974•23 citations

Polarization Properties of a Single-Mode Operating Gas Laser in a Small Axial Magnetic Field

W. van Haeringen

The polarization properties of a single-mode operating gas laser in a small axial magnetic field (field splitting\ensuremath{\ll}natural linewidth) with an initial cavity anisotropy are considered in detail. Expressions are given for the effects on the polarization parameters due to the active medium, the external field, and the initial anisotropy of the cavity. The cooperation of these three effects is discussed. Existing theories are in this respect shown to be either incomplete or inadequate. Specializations are made to several types of atomic transitions and cavity anisotropies. A group of low-field polarization phenomena observed on the He-Ne 1.153-\ensuremath{\mu} mode is theoretically discussed. In particular, it is shown that the observed polarization flip by tuning through the line center and the hysteresis effect, observed by Kannelaud and Culshaw, can be completely understood assuming a cavity whose main anisotropy is a linear phase anisotropy. At zero or very small magnetic field the theory predicts a preference for linear or circular polarization, depending on the type of atomic transition.

Physical Review•Jun 10, 1967•109 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

Theory of a Zeeman Laser. II

M. Sargent, Willis E. Lamb, R. L. Fork

The general theory of a Zeeman laser given in part I is used to analyze laser operation in axial and transverse magnetic fields. The analysis is illustrated by graphs of intensities and beat frequencies versus cavity detuning and magnetic field strength. Among the topics discussed are frequency-locking effects due to cavity anisotropy, the dependence of competition between polarization modes on magnetic field strength for various atomic angular momenta, and the measurement of atomic decay rates and $g$ values using a laser in a magnetic field.

Physical Review•Dec 10, 1967•87 citations
It has already been reported that a laser subject to an axial magnetic field and having end mirrors which exhibit relatively high x\ensuremath−yx\ensuremath{-}yx\ensuremath−y-type loss anisotropy can be described by two theoretical methods. The first method uses self-consistent-field equations with distributed losses, whereas the second one is based on a resonance condition for a complete round-trip pass. The following study of a Zeeman laser with different x\ensuremath−yx\ensuremath{-}yx\ensuremath−y-type loss anisotropy at each mirror shows that the localization of the losses and the nonreciprocal character of the Farady rotation require a different formulation for each initial system. The rotation of the plane of polarization is different at each end of the laser, but it is shown that there always exists for central tuning a real or virtual average polarization vector which obeys Lamb's theory. The equivalence of the two methods is discussed.
The experimental study of polarization in a Zeeman laser with strong $x\ensuremath{-}y$-type anisotropies makes evident the rotations of the electric field vector greater than the limiting value of $\frac{1}{4}\ensuremath{\pi}$ which is fixed by the self-consistent theory. The results are in agreement with the vectorial theory based on the resonance condition, which is necessary for the representation of such a type of quantum oscillator with nonreciprocal effects (including anisotropies). The self-consistent theory appears to provide a limit which becomes valid only for very weak anisotropies. Only the polarization of the so-called "Lamb's vector" can be described by the self-consistent theory and its rotation effectively attains $\frac{1}{4}\ensuremath{\pi}$ whatever the value of the anisotropy.
The Lamb theory of the optical maser is applied to circularly polarized atomic transitions, and used to consider the beat frequencies and the coherence properties of such orthogonal fields when axial magnetic fields are applied to the gaseous laser. The beat frequency approaches zero in near-zero magnetic fields and synchronization can then occur between the right- and left-handed circularly polarized oscillations. For a resonator with no undue polarization constraint, such a strong coupling gives rise to a linearly polarized output, and to a rotation of the plane of polarization with increasing magnetic field. A self-consistent expression is derived for this rotation under steady-state conditions, and a maximum rotation of $\ifmmode\pm\else\textpm\fi{}\frac{1}{4}\ensuremath{\pi}$ with magnetic field is indicated before the synchronization breaks down and circularly polarized beat phenomena appear. The rotation with magnetic field depends on the laser intensity, on the anisotropy in the cavity losses, and on the position of the cavity resonance within the Doppler linewidth. Also, the angle of rotation is indeterminate unless such anisotropy is present. Other regions of such coherence can occur at higher magnetic fields, where the beat frequency again approaches zero. These depend on the detailed shape of the various dispersion curves of the laser medium. The results derived from the theory used are in general agreement with experimental observations on the 1.153-\ensuremath{\mu} He-Ne laser transition.
A theory of a ring laser subject to a uniform, axial dc magnetic field is given in extension of the two-mirror standing-wave treatment by Sargent, Lamb, and Fork. The active medium consists of thermally moving atoms that have two electronic levels with arbitrary angular momenta. The electric field is treated classically for two circular polarizations of opposite sense in a cavity with any degree of cavity anisotropy. Losses due to backscattering are also included. In addition, the results of a generalized treatment are given which includes arbitrarily oriented magnetic field, a general state of electric field polarization, varying isotopic abundance, and hyperfine structure. The self-consistency requirement is used to obtain amplitude- and frequency-determining equations for multimode operation as functions of laser parameters. A general calculational technique, the "perturbation tree," is introduced in the calculation of the third-order component of the population matrix, greatly simplifying the algebra involved by allowing it to be abstracted in tabular form.
The polarization properties of a single-mode operating gas laser in a small axial magnetic field (field splitting\ensuremath{\ll}natural linewidth) with an initial cavity anisotropy are considered in detail. Expressions are given for the effects on the polarization parameters due to the active medium, the external field, and the initial anisotropy of the cavity. The cooperation of these three effects is discussed. Existing theories are in this respect shown to be either incomplete or inadequate. Specializations are made to several types of atomic transitions and cavity anisotropies. A group of low-field polarization phenomena observed on the He-Ne 1.153-\ensuremath{\mu} mode is theoretically discussed. In particular, it is shown that the observed polarization flip by tuning through the line center and the hysteresis effect, observed by Kannelaud and Culshaw, can be completely understood assuming a cavity whose main anisotropy is a linear phase anisotropy. At zero or very small magnetic field the theory predicts a preference for linear or circular polarization, depending on the type of atomic transition.
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.
The general theory of a Zeeman laser given in part I is used to analyze laser operation in axial and transverse magnetic fields. The analysis is illustrated by graphs of intensities and beat frequencies versus cavity detuning and magnetic field strength. Among the topics discussed are frequency-locking effects due to cavity anisotropy, the dependence of competition between polarization modes on magnetic field strength for various atomic angular momenta, and the measurement of atomic decay rates and ggg values using a laser in a magnetic field.