Dissipation-induced instabilities in an optical cavity laser: a mechanical analog near the 1:1 resonance.
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.
Clerc
M G
MG
Control and Dynamical Systems, 107-81, Caltech, Pasadena, California 91125, USA.
Marsden
J E
JE