STUDY OF THE INSTABILITY OF BISTABLE INJECTION LASERS

The theory of instability for non-linear differential equations is applied to the rate equations of a bistable laser. It is found that there are three conditions have to be fulfilled in order to make the system stable. The first condition is automatically fulfilled for ordinary bistable lasers. The second and third conditions are related to self-pulsation and bistable characteristics of the laser respectively. It has been shown that if the third condition is not fulfilled in certain region, the linearized rate equation for small-signal will have a monotonously increasing solution in that region. This means that the light power output curve has a negative slope region, which would result in bistable character. On the other hand, if the second condition is not fulfilled, the linearized rate equation for small-signal will have enhanced oscillating solutions. This means that the laser will self-oscillate as long as the third condition is fulfilled in that region. Besides, it is also shown that both the self-pulsation and the bistable behaviours of the laser are closely related to the non-linearity of g(N) function, which is the necessary condition for having a linearized rate equation of third order.