We study the stability of optical bistable elements against holding-field noise by considering the specific case of a purely dispersive Kerr medium. For small devices, i.e., those for which the round-trip time is small compared to the material-response time, we show that operation of an optical switch with a holding-field intensity a few percent away from the switching value will not be subject to problems due to the noise in the holding laser. This is due to the extremely rapid increase of the average time between noise-induced switching events as the distance, in intensity, from the switching point increases. White noise or Ornstein-Uhlenbeck noise models are not sufficiently smooth for a correct description of this problem, and so we use a more elaborate colored-noise model to evaluate the diffusion constant in the Fokker-Planck equation for the nonlinear phase shift. The time between switching events is then obtained by solving a first-passage-time problem.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics