How to have narrow-stripe semiconductor lasers self-pulsate

The rate equations of narrow-stripe semiconductor lasers are considered. These equations represent the dynamics of the photon number and the electron densities in the active and absorbing regions. Having the rate equations, (i) it is shown that the laser is the bounded-input bounded-state (BIBS) and the bounded-input bounded-output (BIBO) stable; (ii) the amplitudes of step inputs are determined for which all equilibrium points of the laser are unstable. The boundedness of the laser output and the instability of its equilibrium points imply that the laser can have a periodic, a quasi-periodic, or a chaotic output. When the output is periodic, the laser is self-pulsating, which is the desirable behavior of the laser. Moreover, a procedure is given to determine the values of laser parameters for which the laser self-pulsates