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Japanese Journal of Applied Physics

Nonlinear Level Crossing in the Standing-Wave Field

Kōichi Shimoda

Published Apr 1, 1972• 9 citations
Publisher

Abstract

The nonlinear susceptibility of a gas of molecules under level crossing in a single-mode laser field is calculated by an iteration procedure. The higher-order solutions up to the fourth order are explicitly given for arbitrary number of nearly degenerate levels. Contributions of the second-, third-, and fourth-order terms are discussed with particular emphasis on the third-order term. The third-order solution reveals the level-crossing effect in saturated absorption with the half-width almost twice as broad as the Lamb clip when the decay rates of the upper and the lower states are different to some extent. Finally the zero-field level-crossing experiment of methane at 3.39 µm by Luntz et al. is reexamined to result in the pressure broadening of its half-width to be 7.4 MHz/Torr.

DOI
10.1143/jjap.11.564

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Soviet Journal of Quantum Electronics•Nov 30, 1987•2 citations
The nonlinear susceptibility of a gas of molecules under level crossing in a single-mode laser field is calculated by an iteration procedure. The higher-order solutions up to the fourth order are explicitly given for arbitrary number of nearly degenerate levels. Contributions of the second-, third-, and fourth-order terms are discussed with particular emphasis on the third-order term. The third-order solution reveals the level-crossing effect in saturated absorption with the half-width almost twice as broad as the Lamb clip when the decay rates of the upper and the lower states are different to some extent. Finally the zero-field level-crossing experiment of methane at 3.39 µm by Luntz et al. is reexamined to result in the pressure broadening of its half-width to be 7.4 MHz/Torr.
The authors have investigated the zero-field level crossing lineshape in resonance absorption. A single-mode HeNe laser beam at 633 nm is applied to an external neon-gas absorption cell in a longitudinal magnetic field. They compare the measured lineshapes with theoretical predictions. Two superposed nonlinear Lorentzian-shaped resonances, known as the population effect of the 2p 4 -3s 2 transition and the Zeeman coherence effect of the lower 2p 4 level, appear on the background caused by the inhomogeneous broadening. Taking into account the background and the power broadening the authors obtain the linewidths at zero pressure gamma (2p 4 ,3s 2 )=(7.7+or-2.1) MHz and gamma (2p 4 )=(8.4+or-1.2) MHz. For the neon pressure broadening the authors get for pressures below 200 Pa (1.5 Torr) d gamma (2p 4 ,3s 2 )/dp=0.20+or-0.02 MHz Pa -1 and d(2p 4 )/dp=0.040+or-0.007 MHz Pa -1 . Their values are in acceptable agreement with the values obtained with other spectroscopic methods.
The semi-classical theory of a single-mode gas laser has been extended to include higher-order terms by a simpler method than previous ones. The present theory takes not only the lifetimes of the two states but also the effect of phase-perturbing collisions into consideration by using three phenomenological decay constants in the two-level system. Explicit expressions in the general case of nonlinear susceptibility of the laser medium or the saturable absorber are presented for the fifth and seventh orders, while the ninth-order expression is shown for a special case of a very long longitudinal relaxation time.
A generalized expression for electromagnetic polarization under level crossing in a single-mode gas laser is derived up to the third order in the field strength. This is made possible by the use of the probability integral of complex arguments to avoid the Doppler limit approximation. The level crossing effect is seen to appear in the third order, and its linewidth is shown to be asymmetric. It is also broader than the Lorentzian shape usually obtained under the Doppler limit. The dimensionless intensity parameter of the laser field is seen to lose its symmetry about the resonance value in the presence of level crossing. This is attributed to incoherence among different transitions. Further, the other terms like those describing the two-photon process in the third-order value are briefly discussed.
The field dependence of the susceptibility of a gas interacting with a standing wave is calculated near the center of a line for a field of arbitrary profile. An allowance is made for the effects of spatial modulation of the gas. Numerical calculations are reported for a field with a Gaussian profile allowing for degeneracy. These calculations can be checked directly against experimental results for a transition corresponding to a line at λ = 3.39 μ in CH4 , which should make it possible to determine accurately the dipole moment of the transition. The amplitude and half-width of a Lamb dip are calculated for a field of arbitrary profile on the basis of perturbation theory. The problem of approximation of a real Gaussian field with a model field characterized by an amplitude constant over a circular cross section is considered. The precision of model calculations is determined for weak and strong fields. Resonances in atomic beams are discussed under transit conditions. It is shown that in this case there is a slow atom effect, which is responsible for lines with a characteristic width that is a linear function of the homogeneous width of a transition when excited particles are detected on the basis of their fluorescence.