Abstract:

The Maxwell-Bloch (Arecchi-Bonifacio) equations represent the most appropriate model to describe longitudinal laser instabilities, starting from the coherent emission of light above the standard laser threshold to the multimode behavior emerging above the socalled second laser threshold. I show that under reasonable approximations, this spatio-temporal model, consisting of one partial differential equation and two ordinary differential equations, can be reduced to a model with delayed feedback, where the spatial dependence is entirely removed. Furthermore, in the limit of a very fast relaxation of atomic polarization, I show that the resulting dynamics can be well approximated by a Hamiltonian model of Klein-Gordon type, a relationship which explains the difficulty encountered while trying to eliminate adiabatically atomic polarization.