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 Poincar? 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.