Stability of CW solutions of semiconductor laser with large delay

In this paper the problem of existence and stability of continuous waves in a semiconductor laser model is studied. This model was proposed by Lang and Kobayashi and has the form of two differential equations with delay. The delay time is assumed to be large. We study the existence of continuous waves in the Lang–Kobayashi model. A special set $ I $ depending on all parameters of the problem is built. The condition of existence of continuous waves is that the “main parts” of solutions must be located on the set $ I $. Sufficient conditions of stability and instability of continuous waves are found for all sufficiently large values of delay. In the case of a zero linewidth enhancement factor the necessary and sufficient conditions of stability are found. Location of stability regions on the sets $ I $ is studied. It is proved that in the case of the zero linewidth enhancement factor the number of regions of stability on the set $ I $ is less than two. Necessary and sufficient conditions of existence of stability regions on the set $ I $ are found in this case.