Abstract

Over the last years, there has been steadily growing interest in nonlinear systems in which the nonlinear coupling can induce phenomena such as a Hopf bifurcation, bistable behavior or chaos¹⁾. Here our focus will be on nonlinear, noisy optical systems which either undergo a continuous Hopf bifurcation or exhibit bistability. The control parameters may also be subject to fluctuations. Using the standard assumption that those fluctuations evolve on an entirely different time scale, one usually approximates the noise by white (Gaussian) fluctuations. Typical examples are the treatments of the single mode laser²⁾ or a dye laser³⁾ at threshold. Above threshold, the whole matter can complicate considerably. In particular, it has been realized recently, that finite noise correlation effects, e.g. in pump laser fluctuations⁴⁾ or in noisy external driving laser fields, can play a crucial role. Because optical systems exhibiting bistability^5,6) are particular sensitive to the details of the noise properties; as is manifested by the exponential suppression of probability of the locally unstable state, those systems are quite suitable to put to a critical test various different theories and approximations.

© 1985 Optical Society of America