Effects Of Different Kinds Of Colored Noises On The Nonlinear Optical System

Two different kinds of approximate theories for analyzing colored noise are employed in the nonlinear system. Then effects of the colored nature of the noise on the statistical properties of the laser system, the stochastic resonance of bistable system, and the steady-state probability current of quasi-periodic system are investigated.Firstly, a two-dimensional decoupling theory is developed when colored noise is included in a nonlinear dynamical system. By a functional analysis, the colored noise is transformed to an effective noise that includes the noise correlation time, the mean dynamical variable, and the original noise strength. When the two-dimensional decoupling theory is applied to single-mode and two-mode dye laser system, the mean(I), variance λ2 (0), and effective eigenvalue λeff of laser intensity are calculated.Excellent agreement between theoretical analysis, numerical simulations, and experimental measurements are obtained. When the value of noise correlation time r ischanged, the variance λ2 (0) and effective eigenvalue λeff as a function of the meanlaser intensity (I) are calculated. It is shown that the increase of noise correlation timeT can reduce the fluctuations in the laser intensity. When the two-dimensional decoupling theory is applied to a single-mode laser system, it is shown that there is relatively large fluctuation in the phase when the laser undergoes from thermal light to coherent light. It is shown that increasing the noise correlation time T can also reduce the fluctuation in the phase of the laser light. It is clear that the colored nature of the noise can reduce the fluctuation in the laser system.The dynamical property of a one-dimensional nonlinear system is investigated when the coupling between multiplicative and additive noise terms is colored noise. Theeffective eigenvalue λeff and the intensity correlation time Tc of the system are derived for different noise correlation time T . It is shown that the increase of noisecorrelation time can reduce the fluctuation in the system near threshold when the noise coupling coefficient λ is positive. When the coupling λ is negative, the increase of noise sorrelation time r can enhance the fluctuation near threshold.The phenomenon of noise-induced transport of Brownian particles in periodic and quasi-periodic systems with coupling between multiplicative colored noise and additive white noises is investigated. By the method of unified colored noise approximation and the transformation of noise terms in Langevin equation, the corresponding Fokker-Planck equation is obtained. The steady state probability current is derived according to the conservation law of probability. The steady state probability current is calculated for different values of colored noise correlation time in different periods. It is found that the noise color can suppresses the noise-induce transport of Brownian particles both in periodic and in quasi-periodic systems.Secondly, combining the unified colored noise approximation and the functional analysis, the steady state distribution function is derived when both multiplicative colored noise and additive white noise are included in a bistable system with colored coupling between two kinds of noise. Through the two-state theory, the expression of signal-to-noise ratio (SNR) is obtained. The phenomenon of stochastic resonance is investigated.When there is a weak periodic signal is included in a bistable system, the effects of noise on the stochastic resonance in the system is investigated if both multiplicative and additive noise are white noise while the coupling between the two noise terms is colored noise. It is found that the signal-to-noise ratio (SNR) of the system is affected not only by the coupling coefficient λ between two noise terms, but also by the noise correlation time T . The stochastic resonance appears as the value of the coupling coefficient λ between two noise terms is increased. When the noise correlation time T is increased, the SNR is changed f...