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Journal of Modern Optics

Space-time laser instabilities in homogeneously broadened dense media

D. Amroun, Marc Brunel, Hervé Leblond, François Sanchez

Published Jan 1, 2003• 1 citation
Publisher

Abstract

We investigate the space-time dynamics of a homogeneously broadened single-mode laser when local field correction (LFC) is taken into account. We demonstrate that the Maxwell—Bloch equations modified by LFC admit travelling-wave solutions, as when LFC is not taken into account. Their stability is discussed and compared to the case without LFC.

DOI
10.1080/0950034021000064771

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We investigate the space-time dynamics of a homogeneously broadened single-mode laser when local field correction (LFC) is taken into account. We demonstrate that the Maxwell—Bloch equations modified by LFC admit travelling-wave solutions, as when LFC is not taken into account. Their stability is discussed and compared to the case without LFC.
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 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.
The space-time behavior of a wide-gain-section, single-longitudinal-mode laser is investigated. Analysis of the full Maxwell-Bloch model in one transverse spatial dimension identifies a traveling-wave solution beyond the first laser threshold, for positive detuning from resonance, which appears to be a globally attracting state of the laser. On the negative-detuning side we observe an initial bifurcation to a homogeneous plane-wave state. A second instability threshold can be identified by linearizing about the respective solutions for both positive and negative detuning. We also find that the standard approach to adiabatic elimination, whereby the polarization equation is adiabatically eliminated, can lead to a spurious high-transverse-wave-number instability in the reduced equations. The derivation of an adiabatically reduced set of equations to remove the instability on the positive-detuning side is a nontrivial matter.
The dynamic behavior of a coherently pumped single-mode unidirectional ring laser with a homogeneously broadened three-level active medium is studied. Our formulation is based on a set often real equations of the plane-wave, mean-field Maxwell–Bloch type. The instability domain in the main control parameters space is determined. Our numerical study of these equations for a parameter range of the type explored in the recent experiments by Weiss Brock [ Phys. Rev. Lett.57, 2804 ( 1986)] reveals some similarities, but striking differences between our theoretical predictions and their experimental observations are also noted.
A set of strong-field Maxwell–Bloch equations is derived for a multimode, standing-wave, homogeneously broadened laser such as a dye laser, which obeys the atomic rate-equation limit. Numerical solutions show that the energy in the cavity oscillates between the field and the gain medium at multiples of the cavity mode spacing. By using these Maxwell–Bloch equations, intensity autocorrelation functions of a dye-laser system under varying conditions are calculated. We find that the numerical results qualitatively agree with recent experimental data.