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Czechoslovak Journal of Physics

Statistical approach to bistable behaviour of a nonlinear system in a stationary field

A. Lukš, Jan Peřina, Vlasta Peřinová, M. Bertolotti, Concita Sibilia

Published Aug 1, 1984• 1 citation
Publisher
DOI
10.1007/bf01795859

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The quantum statistical properties of independent light beams are considered, forming interference fringes, which are in interaction with a particle (electron) beam treated as a two-level system. Using the master equation and the generalized Fokker-Planck equation techniques, the photocount statistics are derived and it is demonstrated that the whole, initially coherent, radiation field remains coherent for all times while single modes exhibit two-peak bistable behaviour, varying their photon statistics from Poisson statistics to some intermediate statistics for coherent and chaotic radiation.
Optical bistability is a phenomenon that arises in the transmission of light by an optical cavity filled with a medium which presents saturable absorption or nonlinear dispersion. From the theoretical viewpoint, optical bistability is a remarkable example of cooperative behaviour in an open system driven far from thermal equilibrium. From the practical viewpoint, optical bistability offers the possibility of realizing memory elements that may perhaps be used to construct an optical computer. We illustrate the basic physical principles of optical bistability at steady state, and the main features of the transient behaviour. The role and the effects of fluctuations (noise) are described in general. Particular attention is devoted to the situations in which the output of the system is not stationary in time, but oscillatory (self-pulsing behaviour), so that the system works as a converter of continuous wave light into pulsed. It is shown that, according to the values of the external parameters, the oscillations can be either periodic in time or completely aperiodic (optical turbulence). The state of the art in the problem of optical bistability is briefly discussed.