Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: FAN FENG
Pages: [1] - [68]
Received Date: February 2, 2013
Submitted by:
The constant output power of a solid state laser is desired in many applications. Therefore, the property of the steady states of a laser is crucial. We consider a three-dimensional (3D) solid state laser model with several Gaussian modes. Discretized version, scalar version, and single-mode version of this model are shown. Using the scalar system, we achieve some stability property of the steady states by linearization techniques. We not only use the discretized system in numerical simulations, but also it to prove the uniqueness of the positive steady state of the single-mode system. Based on the results of the single-mode system, we obtain some theorems concerning the existence, nonexistence, nonuniqueness of the positive steady states of the multimode system. A prior-estimate of the steady state population inversion density and an inequality of the steady state output power are also given. Finally, we perform numerical simulations for the 3D laser model to confirm the analysis and to explore some of the dynamic scenarios.
steady states, solid state laser, 3D laser model.
