Local and global bifurcations of optically-pumped three-level lasers
In recent years, experimental and theoretical studies of instability phenomena in active laser systems have been widely reported in the laser physics literature1. Many theoretical studies have considered the simplest physical configurations and therefore models comprising small systems of ordinary differential equations. In general, analysis of such models has concentrated on the equilibrium solutions and their bifurcations, with particular attention to the magnitudes of instability thresholds. This latter emphasis is largely a consequence of the high instability thresholds of the Haken-Lorenz two-level laser model2, which are widely considered to be physically unrealisable3. In fact, with the exception of the Haken-Lorenz model, which has been intensively studied because of its dual origin as a model of fluid flow4, the global bifurcation pictures of most laser models are unknown. Instead, laser physicists have focussed on dynamic features which are readily compared with experiments, such as properties of time series, power spectra, transitions to chaos and measures of chaotic attractor dimension. These observational descriptions of chaotic behaviour often appear partial and disjoint, whereas the direct study of model solutions and their global bifurcations can provide a clear and unfolded bifurcation diagram.
KeywordsHopf Bifurcation Bifurcation Diagram Homoclinic Orbit Strange Attractor Heteroclinic Orbit
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- J. Opt. Soc. Am. B2,1–272 (1985). J. Opt. Soc. Am. B5, 876 – 1215 (1988).Google Scholar
- H. Haken . Phys. Lett. 53A, 77 (1975).Google Scholar
- L.W. Casperson inLaser Physics. Eds: J.D. Harvey and D.F. Walls. Springer, Heidelberg, p. 88 (1986).Google Scholar
- C. Sparrow.The Lorenz Equations: Bifurcations, Chaos and Strange Attractors. Applied Mathematical Sciences 41, Springer-Verlag, New York (1982).Google Scholar