Modeling laser instabilities and chaos

Progress in the theoretical understanding and numerical modeling of chaotic lasers is summarized. The Maxwell-Bloch equations for a single-mode unidirectional laser are generalized to include Doppler broadening, off-line operations, and varying relaxation rates for the upper and lower levels of the laser transition. Different routes to chaos, e.g., bad cavities, period doubling, dual-frequencies and intermittency are examined numerically and all shown to lead to single-mode chaos. Field-correlation functions for chaotic lasers are reviewed, and the current difficulties with full correspondence between experiment and theory due to the unresolved statistical nature of chaos are emphasized. Some hope for success is voiced with the application of the field correlation functions for describing the strange attractor.