LOW PUMP LIMIT OF THE BIFURCATION TO PERIODIC INTENSITIES IN A SEMICONDUCTOR-LASER SUBJECT TO EXTERNAL OPTICAL FEEDBACK

The conditions for a bifurcation to periodic intensities (Hopf bifurca tion) for low values of the pump current are examined using singular p erturbation methods. We show that the frequency of the oscillations at the bifurcation point remains close to the relaxation oscillation fre quency of the solitary laser until the pump parameter is close to its effective threshold value. This part of our analysis adds substance to previous estimates of the frequency of the oscillations, which were g uided by experiments. In the second part of our analysis, we show that , very close to threshold, the frequency exhibits a sharp transition f rom the relaxation oscillation frequency to a frequency proportional t o the external cavity frequency (i.e., 2 pi/tau, where tau is the exte rnal round-trip time).