Dynamics of FabryPerot resonators with suspended mirrors. I. Nonlinear coupled oscillators
Abstract
The dynamics of FabryPerot cavity with suspended mirrors is described. The suspended mirrors are nonlinear oscillators interacting with each other through the laser circulating in the cavity. The degrees of freedom decouple in normal coordinates, which are the position of the center of mass and the length of the cavity. We introduce two parameters and study how the dynamics changes with respect to these parameters. The first parameter specifies how strong the radiation pressure is. It determines whether the cavity is multistable or not. The second parameter is the control parameter, which determines location of the cavity equilibrium states. The equilibrium state shows hysteresis if the control parameter varies within a wide range. We analyze stability of the equilibrium states and identify the instability region. The instability is explained in terms of the effective potential: the stable states correspond to local minima of the effective potential and unstable states correspond to local maxima. The minima of the effective potential defines the resonant frequencies for the oscillations of the cavity length. We find the frequencies, and analyze how to tune them. Multistability of the cavity with a feedback control system is analyzed in terms of the servo potential. The results obtained in this paper are general and apply to all FabryPerot cavities with suspended mirrors.
 Publication:

arXiv eprints
 Pub Date:
 September 1998
 DOI:
 10.48550/arXiv.physics/9809038
 arXiv:
 arXiv:physics/9809038
 Bibcode:
 1998physics...9038R
 Keywords:

 Physics  Optics
 EPrint:
 LaTeX 2e, 39 pages, 14 figures