Dissipation-induced Instabilities in an Optical Cavity Laser: A Mechanical Analog Near the 1:1 Resonance

Clerc, M. G. and J. E. Marsden

Physical Review E, 64, 067603.

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.