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

Inhomogeneity effects in a gas laser

Guy Michel Stéphan, Manfred Trümper

Published Oct 1, 1983• 48 citations
Publisher

Abstract

We show that in a gas laser the inhomogeneity in the distribution of amplifying atoms and the transverse Gaussian distribution of the saturating electromagnetic field give rise to different lens effects which are generally opposite to each other and influence the line shapes in different ways, shifting the Lamb dip either to the blue or to the red. For those laser phenomena which increase one or the other of the lens effects, the role of a diaphragm is of particular importance, since it determines the spatial distribution of the resonant field. We present here a new method for studying the resonant diffracted field in a laser. Also, we give a unified description of the various inhomogeneities. Doing away with the usual method of mean-field approximation, we numerically calculate, for a diaphragmed, monomode weak-gain gas laser, the intensity, variation of the beam diameter, and the radius of curvature as functions of the frequency.

DOI
10.1103/physreva.28.2344

Related papers

Theory of a gas laser with a Gaussian field profile

Hisatoshi Maeda, Kōichi Shimoda

A theory for a gas laser with a Gaussian radial field distribution is considered. Rotating wave approximation is adopted to calculate the atomic polarization of the two−level system. An asymmetry of the shape of the Lamb dip and a shift of its center frequency are numerically obtained in the self−consistent laser field.

Journal of Applied Physics•Mar 1, 1975•21 citations

Nonperturbative theory of inhomogeneous effects in gas lasers

Susan M. Scott

The self-consistent field approximation (SCFA)[1]-[4] is used to calculate the steady-state mode energies and frequency shifts for a gas laser. The SCFA is a statistical approximation which was shown[3] to be accurate for small values of a parameter (\gamma^{2}N), which is always small for gas lasers. The SCFA is simpler and more convenient for studying the complicated dynamical effects that occur in gas lasers than the more recent[5]-[8] quantum theoretical models. It does not, of course, give any new description of the laser photon statistics, since the approximation treats the field as a pure coherent state[9] and is, therefore, equivalent to the semiclassical theory. The main results of this paper are to show how dynamical effects can be calculated nonperturbatively for arbitrary values of the field strength, and to analyze the different roles played by different kinds of inhomogeneous effects in gas lasers. These inhomogeneous effects are due to the dependence of the atomic inversion density on the atomic positions and velocities. Some numerical results are given which show that the nonperturbative theory can explain some effects not previously explained by perturbation theories. [1], [2].

IEEE Journal of Quantum Electronics•May 1, 1968•4 citations

Theory of a High-Intensity Gas Laser

B. J. Feldman, Michael S. Feld

This paper presents a semiclassical theory of a single-mode gas laser valid for essentially arbitrary values of field intensity. The theory is formulated in terms of an ensemble-averaged form of the density-matrix equations of motion involving a single set of coordinates. The polarization and the population-inversion density are expanded in spatial Fourier components. One obtains a set of coupled difference equations in the Fourier coefficients ${y}_{n}$, which may be solved subject to appropriate boundary conditions on ${y}_{n}$ for large $n$. The solutions may be expressed in terms of continued fractions in the general case, and in closed form in important special cases. Quantities of interest are evaluated by computer. The steady-state laser intensity and frequency are obtained from the coupled electromagnetic field equations as functions of the cavity parameters and the linear gain of the amplifying medium. At moderate values of field intensity, the velocity distribution of the space-averaged population inversion density exhibits a fine structure for low-velocity atoms superimposed on the usual broader depletion. This structure is a manifestation of the coherent ringing of the amplifying medium. The results are compared with those obtained in the rate-equation approximation, and with the recent work of Stenholm and Lamb. Discrepancies with the latter paper are explained.

Physical Review A•May 1, 1970•144 citations

Magnetic field and pressure effects in a saturated gas laser amplifier

Robert T. Menzies

Theoretical and experimental studies of a gas laser amplifier are presented, assuming the amplifier is operating with a saturating optical frequency signal. The analysis is primarily concerned with the effects of the gas pressure and the presence of an axial magnetic field on the characteristics of the amplifying medium. Semiclassical radiation theory is used, along with a density matrix description of the atomic medium which relates the motion of single atoms to the macroscopic observables. A two-level description of the atom, using phenomenological source rates and decay rates, forms the basis of our analysis of the gas laser medium. Pressure effects are taken into account to a large extent through suitable choices of decay rate parameters. Two methods for calculating the induced polarization of the atomic medium are used. The first method utilizes a perturbation expansion which is valid for signal intensities which barely reach saturation strength, and it is quite general in applicability. The second method is valid for arbitrarily strong signals, but it yields tractable solutions only for zero magnetic field or for axial magnetic fields large enough such that the Zeeman splitting is much larger than the power broadened homogeneous linewidth of the laser transition. The effects of pressure broadening of the homogeneous spectral linewidth are included in both the weak-signal and strong-signal theories; however the effects of Zeeman sublevel-mixing collisions are taken into account only in the weak-signal theory. The behavior of a He-Ne gas laser amplifier in the presence of an axial magnetic field has been studied experimentally by measuring gain and Faraday rotation of linearly polarized resonant laser signals for various values of input signal intensity, and by measuring nonlinearity - induced anisotropy for elliptically polarized resonant laser signals of various input intensities. Two high-gain transitions in the 3.39-μ region were used for study: a J = 1 to J = 2 (3s2 → 3p4) transition and a J = 1 to J = 1 (3s2 → 3p2) transition. The input signals were tuned to the centers of their respective resonant gain lines. The experimental results agree quite well with corresponding theoretical expressions which have been developed to include the nonlinear effects of saturation strength signals. The experimental results clearly show saturation of Faraday rotation, and for the J = 1 t o J = 1 transition a Faraday rotation reversal and a traveling wave gain dip are seen for small values of axial magnetic field. The nonlinearity induced anisotropy shows a marked dependence on the gas pressure in the amplifier tube for the J = 1 to J = 2 transition; this dependence agrees with the predictions of the general perturbational or weak signal theory when allowances are made for the effects of Zeeman sublevel-mixing collisions. The results provide a method for measuring the upper (neon 3s2) level quadrupole moment decay rate, the dipole moment decay rates for the 3s2 → 3p4 and 3s2 → 3p2 transitions, and the effects of various types of collision processes on these decay rates.

•Aug 12, 2015•1 citation

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

Theory of a Single-Mode Gas Laser

Howard Greenstein

A gas laser oscillating steadily in a single mode is described theoretically using the "generalized Bloch equations" as the point of departure. The nonlinear susceptibility is calculated without utilizing perturbation techniques, so that the theory retains validity for laser fields of arbitrary intensity. Expressions are presented for (1) the "gain profile" which exhibits the phenomenon of dual "hole burning," (2) the powertuning characteristics, including the conditions for the appearance of the central tuning dip, and (3) the frequency of oscillation, in which are displayed the effects of mode pulling and pushing. Emphasis is on a strongly inhomogeneous line and a high-$Q$ cavity, although some more general results are included as well. For excitations only slightly above threshold, a comparison is made with the Lamb single-mode theory, and in all cases agreement is found.

Physical Review•Nov 10, 1968•35 citations
We show that in a gas laser the inhomogeneity in the distribution of amplifying atoms and the transverse Gaussian distribution of the saturating electromagnetic field give rise to different lens effects which are generally opposite to each other and influence the line shapes in different ways, shifting the Lamb dip either to the blue or to the red. For those laser phenomena which increase one or the other of the lens effects, the role of a diaphragm is of particular importance, since it determines the spatial distribution of the resonant field. We present here a new method for studying the resonant diffracted field in a laser. Also, we give a unified description of the various inhomogeneities. Doing away with the usual method of mean-field approximation, we numerically calculate, for a diaphragmed, monomode weak-gain gas laser, the intensity, variation of the beam diameter, and the radius of curvature as functions of the frequency.
The self-consistent field approximation (SCFA)[1]-[4] is used to calculate the steady-state mode energies and frequency shifts for a gas laser. The SCFA is a statistical approximation which was shown[3] to be accurate for small values of a parameter (\gamma^{2}N), which is always small for gas lasers. The SCFA is simpler and more convenient for studying the complicated dynamical effects that occur in gas lasers than the more recent[5]-[8] quantum theoretical models. It does not, of course, give any new description of the laser photon statistics, since the approximation treats the field as a pure coherent state[9] and is, therefore, equivalent to the semiclassical theory. The main results of this paper are to show how dynamical effects can be calculated nonperturbatively for arbitrary values of the field strength, and to analyze the different roles played by different kinds of inhomogeneous effects in gas lasers. These inhomogeneous effects are due to the dependence of the atomic inversion density on the atomic positions and velocities. Some numerical results are given which show that the nonperturbative theory can explain some effects not previously explained by perturbation theories. [1], [2].
This paper presents a semiclassical theory of a single-mode gas laser valid for essentially arbitrary values of field intensity. The theory is formulated in terms of an ensemble-averaged form of the density-matrix equations of motion involving a single set of coordinates. The polarization and the population-inversion density are expanded in spatial Fourier components. One obtains a set of coupled difference equations in the Fourier coefficients yn{y}_{n}yn​, which may be solved subject to appropriate boundary conditions on yn{y}_{n}yn​ for large nnn. The solutions may be expressed in terms of continued fractions in the general case, and in closed form in important special cases. Quantities of interest are evaluated by computer. The steady-state laser intensity and frequency are obtained from the coupled electromagnetic field equations as functions of the cavity parameters and the linear gain of the amplifying medium. At moderate values of field intensity, the velocity distribution of the space-averaged population inversion density exhibits a fine structure for low-velocity atoms superimposed on the usual broader depletion. This structure is a manifestation of the coherent ringing of the amplifying medium. The results are compared with those obtained in the rate-equation approximation, and with the recent work of Stenholm and Lamb. Discrepancies with the latter paper are explained.
Theoretical and experimental studies of a gas laser amplifier are presented, assuming the amplifier is operating with a saturating optical frequency signal. The analysis is primarily concerned with the effects of the gas pressure and the presence of an axial magnetic field on the characteristics of the amplifying medium. Semiclassical radiation theory is used, along with a density matrix description of the atomic medium which relates the motion of single atoms to the macroscopic observables. A two-level description of the atom, using phenomenological source rates and decay rates, forms the basis of our analysis of the gas laser medium. Pressure effects are taken into account to a large extent through suitable choices of decay rate parameters. Two methods for calculating the induced polarization of the atomic medium are used. The first method utilizes a perturbation expansion which is valid for signal intensities which barely reach saturation strength, and it is quite general in applicability. The second method is valid for arbitrarily strong signals, but it yields tractable solutions only for zero magnetic field or for axial magnetic fields large enough such that the Zeeman splitting is much larger than the power broadened homogeneous linewidth of the laser transition. The effects of pressure broadening of the homogeneous spectral linewidth are included in both the weak-signal and strong-signal theories; however the effects of Zeeman sublevel-mixing collisions are taken into account only in the weak-signal theory. The behavior of a He-Ne gas laser amplifier in the presence of an axial magnetic field has been studied experimentally by measuring gain and Faraday rotation of linearly polarized resonant laser signals for various values of input signal intensity, and by measuring nonlinearity - induced anisotropy for elliptically polarized resonant laser signals of various input intensities. Two high-gain transitions in the 3.39-μ region were used for study: a J = 1 to J = 2 (3s2 → 3p4) transition and a J = 1 to J = 1 (3s2 → 3p2) transition. The input signals were tuned to the centers of their respective resonant gain lines. The experimental results agree quite well with corresponding theoretical expressions which have been developed to include the nonlinear effects of saturation strength signals. The experimental results clearly show saturation of Faraday rotation, and for the J = 1 t o J = 1 transition a Faraday rotation reversal and a traveling wave gain dip are seen for small values of axial magnetic field. The nonlinearity induced anisotropy shows a marked dependence on the gas pressure in the amplifier tube for the J = 1 to J = 2 transition; this dependence agrees with the predictions of the general perturbational or weak signal theory when allowances are made for the effects of Zeeman sublevel-mixing collisions. The results provide a method for measuring the upper (neon 3s2) level quadrupole moment decay rate, the dipole moment decay rates for the 3s2 → 3p4 and 3s2 → 3p2 transitions, and the effects of various types of collision processes on these decay rates.
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.
A gas laser oscillating steadily in a single mode is described theoretically using the "generalized Bloch equations" as the point of departure. The nonlinear susceptibility is calculated without utilizing perturbation techniques, so that the theory retains validity for laser fields of arbitrary intensity. Expressions are presented for (1) the "gain profile" which exhibits the phenomenon of dual "hole burning," (2) the powertuning characteristics, including the conditions for the appearance of the central tuning dip, and (3) the frequency of oscillation, in which are displayed the effects of mode pulling and pushing. Emphasis is on a strongly inhomogeneous line and a high-QQQ cavity, although some more general results are included as well. For excitations only slightly above threshold, a comparison is made with the Lamb single-mode theory, and in all cases agreement is found.