Pressure Broadening Effects on the Output of a Gas Laser

Borenstein, Matthew; Györffy, B. L.; Lamb, Willis E.

doi:10.1103/physrev.169.340

Cited by 69 publications

(5 citation statements)

References 9 publications

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“…Ordinarily asymmetries in the output of simple gas lasers are attributed to collisions between the atoms. 3 ' 4 The lasers considered are assumed to be operated very near threshold, so that self-focusing is unimportant. 5 This treatment is based on one given elsewhere.…”

Section: Introductionmentioning

confidence: 99%

Gain and Dispersion Focusing in a High Gain Laser

Casperson

Yariv

1972

Appl. Opt.

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The transverse modes of a laser resonator containing a medium with a strong radial gain profile differ greatly from the modes of a similar resonator containing a low gain medium. Focusing and defocusing effects result from the gain profile and from the associated dispersion profile. The dispersion focusing causes an asymmetry in the power output as the laser is tuned across the gain line. The theory has been verified using a high gain 3.51-u xenon laser.

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Section: Introductionmentioning

confidence: 99%

Gain and Dispersion Focusing in a High Gain Laser

Casperson

Yariv

1972

Appl. Opt.

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“…8,10 With the last two assumptions, the relaxation of the components on the a T Q k basis of the density matrix for the atomic quantities {a stands for aa, 1357…”

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“…8,10 With the last two assumptions, the relaxation of the components on the a T Q k basis of the density matrix for the atomic quantities {a stands for aa, or bb and refers to the submatrices within each level) can be written 8 ' 4 [(d/rfO«P 0^) ]relax=-r^^ (l) where W u (v) is the Maxwellian velocity distribution; T a '{k) is the relaxation rate taking into account radiative decay, destruction by collisions, and velocity changes; and y a '(k) is the probability of survival of the quantity a T Q k after velocity changes by collisions or reabsorption of a photon. The usual relaxation rates, which can be measured by Hanle-effect experiments and which are insensitive to velocity changes, are given by r a (fe) = r a '(fe)-r a '(fe).…”

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Optical Pumping with a Multimode Laser Beam: Saturation Resonances by Magnetic Mode Crossing

Dumont¹

1972

Phys. Rev. Lett.

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The resonances of saturation which occur when the mode spacing is equal to the Zeeman splitting are theoretically studied for a mode spacing <, the natural width broadened by collisions. Two kinds of resonances occur. The first set, due to a population effect (crossing of holes), is not resolved and is unobservable. The second set, due to a Zeeman coherence effect, is well resolved since the widths of the resonances are of the order of the Hanle-effect width. These resonances are very sensitive to the relative phases of the modes.When a gas (Ne in our experiments) excited by a discharge is placed in a magnetic field and is submitted to a resonant laser beam (He-Ne laser) linearly a polarized, a resonance appears on the fluorescence lines emitted from one of the laser levels each time the Zeeman splitting is equal to the frequency difference between two modes. These resonances, first observed by Fork, Hargrove, and Pollack, 1 have been used to measure Landeg" factors. 2 However, some aspects concerning their widths and the influence of mode locking on their amplitudes were not clearly understood. For that reason we have performed a semiclassical calculation, in the formalism of irreducible tensors, up to the fourth order of perturbation in the laser electric field (as previously done to second order to study the Hanle effect 3 ).In this Letter we summarize the results in the case J a =0, J b~l (a, lower level; b, upper level). The details of the calculation and the discussion of the positions of resonances when both levels have a Zeeman structure will be published later. 4 The hypotheses are the following:(a) As our detection does not resolve the spectral shape of the fluorescence lines, and further-more as the detection is perpendicular to the laser beam, it is not necessary to take into account the frequency correlation between the laser and the fluorescent light. 5,6 The calculation of the atomic density matrix is sufficient to determine the fluorescence.(b) The perturbation development is performed according to the usual methods with the rotatingwave and the Doppler-limit approximations. 7,8 (c) We take into account spontaneous emission from the upper to the lower level.(d) Although we must write the equations separately for each atomic velocity along the laser axis, we assume that the relaxation is sufficiently isotropic to produce no coupling between different tensorial orders 9 and to give rise to relaxation rates independent of Q (we write the irreducible tensor as T Q k -9 k is the tensorial order and Q the component).(e) We take into account velocity changes due to collisions or trapping of fluorescence lines with the help of the strong-collision model. 8,10 With the last two assumptions, the relaxation of the components on the a T Q k basis of the density matrix for the atomic quantities {a stands for aa, 1357

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“…r is linear in pressure but depends on the ratio. It is significant that r 2 *r. Equation (5) assumes Ku»T and Ref. 4 includes corrections of order T/Ku and an asymmetry in A.…”

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Theory of Atomic Scattering in a He-Ne Laser

Stenholm¹

1971

Phys. Rev. Lett.

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The scattering theory of laser atoms developed by Berman and Lamb is found to have implications for the collision theory of a high-intensity laser. Assuming scattering in the lower laser state (2p A ) to dominate, one can fit the experiments on a 0.63~MHI He-Ne laser by Cordover and Bonczyk.This paper includes the work by Berman and Lamb 1 into the theory of collisions in a laser. 2 We paraphrase their discussion to see its implications: The pumping process injects atoms with the velocity distribution W(v). Their ensemble is described by the density matrix p(p, p') = 6(p~p')W^(p/m) in the plane-wave basis of the laser volume V.With (ft equal to the range of atomic interaction, we assign a volume 7 c »(ft 3 to each collision. The classical description can be retained when the field varies little over V c and in times r = V c 1/3 /v. The theory of Ref. 1 applies inside V c , and between the collisions the atoms are propagated as in Ref. 2. With (ft^10 " 9 m, X^l(T 6 m, and v^ 10 3 m/sec we take V c 1/3 = 10' 8 m, T=KT n sec, whereas field changes require y ab~l -10" 7 sec.An atom in state la) enters V c with the velocity p/m, and with Ref. 1 we assume different scattering in the two laser states. We take the upper state \a) to be unaffected 3 in V c and the state lb) to scatter with the elastic-scattering amplitude/(/>, 0). The dipole moment after scattering is

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Pressure Broadening Effects on the Output of a Gas Laser

Cited by 69 publications

References 9 publications

Gain and Dispersion Focusing in a High Gain Laser

Gain and Dispersion Focusing in a High Gain Laser

Optical Pumping with a Multimode Laser Beam: Saturation Resonances by Magnetic Mode Crossing

Theory of Atomic Scattering in a He-Ne Laser

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