Stability in a general coupled laser array

For the first time we have presented a method to investigate the stability of quiescent state in a coupled laser array. By introducing tiny perturbation, stability of quiescent state can be known by investigating eigenvalues of coefficient matrix of the corresponding linear differential equations. Only when real parts of the eigenvalues were all negative or zero, the corresponding quiescent state is stable. Two tapes of coupled laser array with loop and linear topological structure were studied respectively. It was found that there were innumerable quiescent states and they could be divided into several types based on phase relation. Some types were stable and others were unstable. Topological structure affects the stability of quiescent state in a coupled laser array.