Synergetics pp 225-262 | Cite as

Physical Systems

  • Hermann Haken
Part of the Springer Series in Synergetics book series (SSSYN, volume 1)


The laser is nowadays one of the best understood many-body problems. It is a system far from thermal equilibrium and it allows us to study cooperative effects in great detail. We take as an example the solid-state laser which consists of a set of laser-active atoms embedded in a solid state matrix (cf. Fig. 1.9). As usual, we assume that the laser end faces act as mirrors serving two purposes: They select modes in axial direction and with discrete cavity frequencies. In our model we shall treat atoms with two energy levels. In thermal equilibrium the levels are occupied according to the Boltzmann distribution function. By exciting the atoms, we create an inverted population which may be described by a negative temperature. The excited atoms now start to emit light which is eventually absorbed by the surroundings, whose temperature is much smaller than ω/k B (where ω is the light frequency of the atomic transition and k B is Boltzmann’s constant) so that we may put this temperature ≈ 0. From a thermodynamic point of view the laser is a system (composed of the atoms and the field) which is coupled to reservoirs at different temperatures. Thus the laser is a system far from thermal equilibrium.


Rayleigh Number Electric Field Strength Saturable Absorber Ultrashort Laser Pulse Fluctuate Force 
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For related topics see

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Cooperative Effects in the Laser: Self-Organization and Phase Transition

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The Laser Equations in the Mode Picture

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The Order Parameter Concept

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The Single Mode Laser

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The Multimode Laser

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Hierarchy of Laser Instabilities and Ultrashort Laser Pulses

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Elastic Stability: Outline of Some Basic Ideas

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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

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