The First-Order-Like Phase Transition Induced By Colored Noise In A Laser System

The influence of noise color on the first-order-like phase transition (FOLT) in several kinds of laser systems is investigated in this paper.Firstly, decoupling theory is applied to analyze multiplicative colored noise in a single mode laser system. Steady state intensity distribution function with colored noise is obtained. The first-order-like phase transition driven by multiplicative colored noise is studied and compared with the case of multiplicative white noise. It is shown that the noise correlation time has great effects on the parameter plane of the first-order-like transition .The steady state intensity distributions in a laser system change greatly with noise correlation time T .Secondly, functional derivation is employed to analyze the two-dimensional colored noise in the third order laser model with dispersive medium. The stationary intensity distribution is derived. The variation of the most probable intensity with pump parameterand noise intensity correlation time is investigated. With the shifted 1/N expansion, theinstantaneous solution of the laser model, i.e., the change of eigenvalues with the pump parameter is obtained. It is shown that the pump parameter and intensity noise correlation time are the major factors of the first-order-like transition. Angular noise correlation time has great influence on the linewidth in the power spectrum .Thirdly, a unified colored-noise approximation is applied to calculate the steady state distributions of the dispersive optical bistability when the fluctuations in the amplitude and phase of the incident field are considered as colored noise. The steady state distributions are obtained. The conditions that the first-order-like phase transition is induced by noise color in either the intensity or phase fluctuations are investigated and compared. When only the intensity fluctuation is included in the incident light with different parameters of incident intensity and phase, the parameter plane of the FOLT shows interesting behavior with the changes of colored noise correlation time and multiplicative noise intensity. It isshown that the noise color and multiplicative noise intensity can greatly affect the FOLT in the laser system. If only the phase fluctuation is included in the incident light, the correlation time can also affect the parameter plane of the FOLT. Comparison of the FOLT induced by colored noise in intensity and phase fluctuations shows that the number of the extremum in the steady state distribution is changed from one to two, and then to three successively for colored noise intensity fluctuation. While for colored phase fluctuation, the number of extremum in the steady state distribution is changed from one to three directly. It is very clear that colored noise induced FOLT in dispersive bistable system shows very interesting phenomenon.