Study of lasers as nonlinear dynamical systems

The rate equations of a large class of lasers are considered. These equations represent the evolution of photon and carrier densities in the laser, where the laser output is proportional to the photon density. By applying techniques from the theory of dynamical systems to the rate equations, four important properties of the lasers are rigorously proved. These properties are: (1) for positive and bounded inputs, the laser outputs are bounded; (2) for positive constant inputs, the laser does not exhibit a limit cycle behavior; (3) for a positive constant input, the laser output settles at a positive steady-state value; (4) for positive constant inputs, the relaxation oscillations in the laser output can be attenuated if the coefficient of the spontaneous emission factor is increased.