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Physical Review A

Laser instabilities in homogeneously broadened dense media

Michaël Fromager, Marc Brunel, François Sanchez

Published Apr 10, 2000• 8 citations
Publisher

Abstract

We investigate the laser equations in the mean-field limit for a homogeneously broadened two-level system, taking into account the local-field correction arising from dipole-dipole interactions. Our analysis concentrates on the dynamical properties of the laser versus the pumping parameter. The effect of detuning between atomic and cavity frequencies is also studied. We first show that the local-field correction reduces the range of the chaotic regime when the frequency detuning is set for minimum instability threshold operation. For a fixed local-field correction, we demonstrate that the symmetry of the dynamical scenario versus the frequency detuning is broken. In addition, we point out generalized bistability between the chaotic regime and the off state of the laser. This bistability results from the smallness of the basins of attraction of the off state.

DOI
10.1103/physreva.61.053804

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We investigate the laser equations in the mean-field limit for a homogeneously broadened two-level system, taking into account the local-field correction arising from dipole-dipole interactions. Our analysis concentrates on the dynamical properties of the laser versus the pumping parameter. The effect of detuning between atomic and cavity frequencies is also studied. We first show that the local-field correction reduces the range of the chaotic regime when the frequency detuning is set for minimum instability threshold operation. For a fixed local-field correction, we demonstrate that the symmetry of the dynamical scenario versus the frequency detuning is broken. In addition, we point out generalized bistability between the chaotic regime and the off state of the laser. This bistability results from the smallness of the basins of attraction of the off state.
We study numerically the effects of local-field corrections originating from near dipole—dipole interactions on the dynamics of a single mode, inhomogeneously broadened laser. Our analysis is based on a set of generalized Maxwell–Bloch equations in which the inhomogeneous nature of gain broadening is accounted for by introducing two new dynamical variables and a single parameter that governs the extent of inhomogeneous broadening. Our results show that local-field effects occurring in a dense gain medium reduce the range of continuous wave operation and lead to instabilities and chaos at much lower pumping levels.
We study the five semiclassical laser equations in the mean-field limit for the simple model of two-level atoms with homogeneous broadening in a single-mode unidirectional ring cavity, taking into account detuning between atomic and cavity frequencies. Our analysis concentrates on the properties of the laser at and beyond the second thresh-old in the bad-cavity case. We first show that the position of the second threshold depends on the excitation mechanism: When the pump parameter is increased either adiabatically or abruptly, two different thresholds occur. The sequence of periodic and chaotic solutions beyond the second threshold is then discussed as a function of the detuning and the pump parameter.
The influence of an additional relaxation channel of up-conversion type on the second threshold of a laser with a dense homogeneously broadened active medium is investigated in terms of a two-level model. Local-field effects caused by near dipole-dipole interactions are taken into account in this case. It is shown that the bad-cavity condition is not obligatory for chaotic behavior to appear in a laser system and that the second laser threshold can be substantially reduced by the up-conversion process.
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.