Bistability Of Delayed Optoelectronic Feedback Semiconductor Lasers

The nonlinear dynamics of semiconductor lasers(SLs) have been extensively studied due to their wide applications in laser physics, optical communications and other fields. Perturbed by optical injection, optical feedback or optoelectronic feedback(OEF), semiconductor lasers display plenty of nonlinear dynamics. Compared with optical injection and optical feedback, the semiconductor laser with delayed optoelectronic feedback has gain considerable attentions due to its advantages in insensitivity to optical phase variation and convenience to be electrically controlled. At present, in most theoretical and experimental research on SLs with OEF, when control parameters changed, the initial conditions of the systems are resetted each time, which means the feedback always begins from null when the delayed feedback time changed. Therefore, the connection among the output dynamics at different delay timeτis erased. However, in practical applications, it is familiar to meet the instances that delay time varies continuously, hence the influence of the continuous variation route of the delay time on the dynamics of a SL with OEF should be investigated.The theoretical model of SLs with OEF has been investigated in the article. In the process of solving the rate equations of delayed SLs with OEF, the delay time is presumed to vary from minimum to maxima with the working conditions of SLs keep changing without been erased. After the delay time reaches the maxima, it begins to reduce continuously. In the whole varying process, the initial conditions are only evaluated in the beginning of the simulation. This method is called the continuous time approach. The results of calculation show that using the continuous time approach method, it can be found that at a fixed delay time, for different varying route to reach this delay time, the different output dynamics of SL with OEF which corresponding to the bistability states may be observed. Furthermore, when the varying route of the delaytime is long enough, plenty of bistability states can be found, with their width increase gradually. In addition, the width of bistability states has relations to the feedback strength of OEF. With the increasing of system feedback strength, the width of bistability states adds in the mass. Compared the result between the positive and negative feedback, it appears that it's ealier to gain wider bistability states in positive OEF conditions. Moreover, by adding modulation signal, we find that the characteristics of the bistability states become more complex.