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Journal of Modern Optics

The role of coherent effects in mode bistability of a gas laser in inhomogeneous medium

Gabriela W acedil sik, Gerd Leuchs

Published Mar 20, 2001• 0 citations
Publisher
DOI
10.1080/09500340010004220

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The role of coherent effects in mode bistability of a gas laser in inhomogeneous medium

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We have studied microscopic effects leading to mode competition in an inhomogeneously broadened medium of a gas laser with a weakly anisotropic cavity. The polarization bistability observed in some lasers, which is believed to be caused by hole burning, we attribute to microscopic coherent effects induced by two light fields. Due to these effects one field can be coupled with another. Hole burning is found to be important, but not crucial. The exact solution of the equation of motion for field amplitudes is compared with the third order approximation of perturbation theory. The role of four wave mixing, important for bistability of axial modes in a homogeneously broadened medium, is discussed.

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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].

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Transient analysis of optical bistability in inhomogeneously pumped lasers

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•Jan 1, 1988•0 citations
We have studied microscopic effects leading to mode competition in an inhomogeneously broadened medium of a gas laser with a weakly anisotropic cavity. The polarization bistability observed in some lasers, which is believed to be caused by hole burning, we attribute to microscopic coherent effects induced by two light fields. Due to these effects one field can be coupled with another. Hole burning is found to be important, but not crucial. The exact solution of the equation of motion for field amplitudes is compared with the third order approximation of perturbation theory. The role of four wave mixing, important for bistability of axial modes in a homogeneously broadened medium, is discussed.
Population pulsations are fluctuations in the population difference (of a two level system) due to the presence of two or more coherent waves interfering in the medium. In this work, we show that population pulsations generated by three waves, a central wave and two mode-locked sidebands, are responsible for both the multiwavelength and the single-wavelength instabilities of single-mode lasers containing homogeneously-broadened media. The role of the population pulsations in establishing these instabilities, however, diminish as the central mode is detuned away from the atomic resonance frequency. For homogeneously-broadened lasers, we find two regions of single-wavelength instability. The first is at line center, for which population pulsations are solely responsible, and the second is off line center where the unsaturated medium provides the required gain and anomalous dispersion. For the case of inhomogeneously-broadened lasers, we show that population pulsations significantly increase the instability range over that predicted by Casperson for single-mode bad-cavity lasers. Both the unidirectional ring and the standing-wave cavities are treated. The Fourier expansion technique, used in this work, for treating three-frequency operation in saturation spectroscopy is shown to be equivalent (in appropriate limits) to the linear stability analysis in laser theory and optical bistability. We also show, in single-sideband saturation spectroscopy, that for long interaction lengths propagation effects can significantly influence the absorption and dispersion coefficients of the medium. Finally, we show that under certain conditions the pronounced splittind effects of the population pulsations develop into regions of intense absorption.
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].