Time Delays In Bistable And Single-mode Laser Systems

The effects of noise and time delays on nonlinear systems are investigated. The steady state properties of a noise-driven bistable system are analyzed when different kinds of time delays are included in the system. The time-delayed feedback is used to control the fluctuations in the steady state of a single-mode laser system. The dynamical properties of a single-mode laser are discussed when there are two different kinds of time delays.Firstly, the theory of probability density approximation is developed when there are two different types of time delays existed in the deterministic and fluctuating forces respectively in a noise-driven bistable system. The approximate Fokker-Planck equation, the analytical results of the stationary probability distribution and the variance are derived. It is shown that the time delay in the deterministic force can suppress the fluctuations in the system. While the time delay in the random force can enhance the fluctuations in the system. Numerical simulations are in good agreement with the approximate theoretical results, especially when the time delay is small.Secondly, the method of time-delayed feedback is used to control the fluctuations in the steady state of a single-mode laser. Using the small time delay approximation, the analytical expressions of the stationary probability distribution function, normalized variance and skewness of the system are obtained. It is found that the time-delayed feedback can effectively suppress the fluctuations of the single- mode laser system.Thirdly, the dynamical properties of a single-mode laser are investigated when there are two different types of time delays existed in the deterministic and fluctuating forces respectively. The theory of probability density approximation is employed. The approximate Fokker-Planck equation, the intensity correlation time and the effective eigenvalue are derived. It is shown that the time delay in the deterministic force can enhance the intensity fluctuation when the laser is operated below threshold. When the laser is operated above threshold, the time delay in the deterministic force can suppress the fluctuation in the laser intensity. The effect of the time delay in the random force on the fluctuation in the laser intensity is much weaker than that in the deterministic force.