Anharmonic Oscillator Model for Dispersive Optical Bistability

R. Graham, Axel Schenzle

Annabella Selloni, A. Quattropani, P. Schwendimann +1 more

The response of a bistable optical system to a time-dependent driving field is studied in terms of a quartic anharmonic oscillator describing a non-linear medium. Dynamical lowering of the switching threshold is observed. The dispersive character of the model is confirmed.

Burke Ritchie, Charles M. Bowden

The dynamical solution of the driven classical anharmonic (AH) oscillator is obtained through a region of optical bistability. The dynamical solution is observed to switch from the lowest to highest steady-state (SS) root near a SS turning point with evidence of critical slowing down. The solution of a widely used multiple-photon version of the AH model is also obtained and is found to give qualitatively similar behavior. The average number of photons observed dramatically increases in the bistable region and exhibits damped oscillations.

H. Risken, Karl Vogel

J.S. Satchell, Sarben Sarkar

The non-linear polarisability model of dispersive optical bistability with periodic driving field is shown to have non-trivial limit cycle solutions in phase space. The model is quantised rigorously in the positive P representation. For a particular (but typical) limit cycle, the associated steady state probability distribution is shown to be compatible with a bivariate Gaussian. The inverse widths of the Gaussian are calculated as functions of position in both phase space and time.

Frederic A. Hopf, Sami A. Shakir