Abstract
We present a simplified theory of the statistical behavior of a single mode laser ruled by two slow variables (class B lasers). By applying the center manifold theorem we introduce an improved adiabatic elimination procedure which reduces the description of class B lasers to two modified rate equations in an appropriate state space. The statistical dynamics is further reduced to a one dimensional Fokker-Planck equation in a parameter range corresponding to that where most experiments have been performed. The usefulness of this approach stems from the fact that a previously available theory is based on a two dimensional Fokker-Planck equation and limited to a narrower parameter range around threshold.
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To our knowledge, the only exception is represented by a paper of A. Fernández: Phys. Rev. A32, 3070 (1985), where a chemical instability is considered
The meaning of this factorization consists in attributing the time dependence exclusively to the slow variableW, whereas the fast one,q, thermalizes to its equilibrium set controlled byW. Also the reduction from the whole set of Maxwell-Bloch Eq. (2.1) to the 2-d system (2.8) could be formulated in terms of a factorization of probabilities
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Paoli, P., Politi, A. & Arecchi, F.T. Statistical dynamics of class-B lasers. Z. Physik B - Condensed Matter 71, 403–410 (1988). https://doi.org/10.1007/BF01312500
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DOI: https://doi.org/10.1007/BF01312500