Long-term spatiotemporal dynamics of solid-state lasers and vertical-cavity surface-emitting lasers

The number of Maxwell-Bloch equations describing the spatiotemporal evolution of solid-state and semiconductor-based lasers can be reduced when the temporal scales of the fields and atomic variables are very different. We demonstrate the existence of slow (center) manifolds for models of solid-state lasers (such as Nd:YAG) and vertical-cavity surface-emitting lasers and determine reduced equations in the presence of both diffraction and carrier diffusion. Two separate methods of obtaining the reduced equations are presented. Excellent agreement between the reduced models and the original equations is obtained when the slow manifolds are expanded in a perturbative series. Since stiffness is removed, the computational time for the long-term spatiotemporal dynamics of these devices can be strongly reduced, typically by 2 orders of magnitude.