Chaos in Laser Systems

  • Junji OhtsuboEmail author
Part of the Springer Series in Optical Sciences book series (SSOS, volume 111)


Starting from the Maxwell equation in a laser medium based on the model of two-level atoms, we derive the time-dependent Maxwell–Bloch equations for field, polarization of matter, and population inversion. Then, we prove that the three differential equations are the same as those of Lorenz chaos. Well above the laser threshold, the laser reaches an unstable point at certain pump level, which is called second laser threshold. However, only a few real lasers show chaotic dynamics with a second threshold and most other lasers do not have the second threshold, resulting in stable oscillations for the increase of the pump. Stable and unstable oscillations of lasers are related to the scales of the relaxation times for the laser variables. We discuss stability and instability of lasers based on the rate equations and present their classifications from the stability point of view.


Chaotic System Ring Resonator Population Inversion Chaotic Oscillation Relaxation Oscillation 
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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Shizuoka UniversityShizuokaJapan

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