title: Dissipation-induced instabilities in an optical cavity laser: a mechanical analog near the 1:1 resonance.
abstract: The 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms has been studied. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allows one to show that an optical cavity with small pumping is unstable when one takes into account the dissipative effects. The Maxwell-Bloch equations are the asymptotic normal form that describe this instability when energy is injected through forcing at zero frequency. A simple mechanical system close to the 1:1 resonance has been displayed, which is a mechanical analog of the laser.
authors.affiliation: Control and Dynamical Systems, 107-81, Caltech, Pasadena, California 91125, USA.
authors.forename: M G
authors.initials: MG
authors.lastname: Clerc
authors.forename: J E
authors.initials: JE
authors.lastname: Marsden