【摘要】 本文介绍一种分析激光器稳定性特性的线性化方程方法。由Poincar啨非线性理论 ,首先将非线性速率方程在阈值处线性化 ,再由线性方程的系数矩阵的特征量给出四种稳定性类型更多还原

【Abstract】 A method of analyzing the laser stability based on the linearized equation is presented.The operating state of a laser can usually be described through the rate equations of photons and population inversion, these equations are a set of nonlinear equations.Therefore,laser is indeed nonlinear device.The stady state solution of the rate equations gives the threshold condition.The steady state solution is merely an equilibrated point of the nonlinear equations,the laser could not work in the case of steady state.Steady state solution being stable or unstable is so called the stability problem of laser. Based on the Poincaré nonlinear theory,to study the stability of the steady point of a system,the time evolution of the system experienced perturbation near the steady point must be examined.The method of the analysis is that the rate equations are firstly expanded as a Taylor series and the nonlinear terms are ignored ,then the linear equations are obtained.This linear system has the same properties as the nonlinear system under small perturbation.Therefore,the linear equations can be used instead of the nonlinear equations for analyzing the system stability. The type of the steady state of the linear equations can be determined by the invariant of the coefficients matrix,i.e.,the trace,determinant and discriminant of the matrix.Particularly,the knowledge can be obtained that the type of the stability could be changed above the threshold.Furthermore,if the time variation of the process parameters are taken into accout,the knowledge can also be obtained that the laser chaos can certainly occur.更多还原