The emission characteristics of a vertical-cavity surface-emitting laser (VCSEL) coupled to an external cavity with a diffraction grating as a frequency-selective element are theoretically analyzed. We introduce envelope functions for the set of external-cavity modes based on the loci of modes with extremal gain or frequency in the proper parameter space. Replacing the set of discrete stationary solutions by these envelope functions, simple analytical expressions are derived for the existence of bistability between a lasing state strongly affected by the feedback and a state close to the solitary laser emission (in particular the nonlasing state) and for the frequency of the VCSEL in the grating-controlled regime. It is shown how the initial jump of the laser intensity during abrupt turn-on can be maximized. By a control of the feedback change, the width of the hysteresis loop can be increased significantly. The scheme under consideration can be useful in all-optical photonic switching applications.
- surface-emitting laser