Fig. 1. Experimental setup with an external cavity for the OF via a mirror. NPBS, nonpolarizing beam splitter; MCT, mercury–cadmium–telluride detector; OSCI, fast oscilloscope; AWG, arbitrary waveform generator; LDD, laser diode driver.

Fig. 2. Experimental time traces of the QCL output when external OF is applied to the QCL and with a sine modulation of the continuous bias of: (a) 1.8 MHz, (b) 2 MHz, and (c) 2.2 MHz; all of the traces were retrieved for a continuous bias of 430 mA and a modulation amplitude of 120 mA, but only the one in the middle exhibits dropouts with a magnified amplitude, which is, however, not enough to categorize them as extreme events.

Fig. 3. (a) Experimental time trace with extreme events and associated thresholds for the two criteria. The dashed red line represents the threshold corresponding to criterion C1 (H=0.665) and the dashed green line represents the threshold corresponding to criterion C2 (H=0.749). Events with their maximum above these dashed lines are considered as extreme. (b) Histogram of the time intervals between extreme events in the case where the C1 criterion is applied to the time trace.

Fig. 4. Histogram of the retrieved maximal intensity and the related threshold for the C1 criterion. Red bars display the extreme events of the time trace displayed in Fig. 3.

Fig. 5. (a) Time series centered on the maximum of local bursts and superposition of 37 extreme events. The corresponding averaged output power is displayed with a purple solid line and the threshold corresponding to an abnormality of 2 is displayed with a dash-dot line. (b) Same data plot but for 13 extreme events surging above an abnormality index of 2.4. In the left panel, the trough preceding the optical burst, as well as the oscillations following the extreme event, is underlined.

Fig. 6. (a) Experimental time traces of the QCL when OF and a sine wave modulation with a period of 10μs and an amplitude of 4 mA are applied. The dashed red line represents the C1 criterion and the dashed green line represents the C2 criterion. (b) Close-up on extreme events and the low-amplitude sine modulation, revealing that extreme events can only occur on top of the periodic modulation.

Fig. 7. (a) Experimental time traces of the QCL when OF and an asymmetric square wave modulation with a period of 10μs, an amplitude of 4 mA, and a duty cycle of 20% are applied. The dashed red line represents the threshold corresponding to criterion C1, and the dashed green line represents the threshold corresponding to criterion C2. (b) Close-up on four extreme events and the low-amplitude square modulation, the golden arrow represents the amplitude discrepancy between the extreme pulses and the square wave modulation. Extreme events are synchronized with the pulse up of the perturbation.

Fig. 8. (a) Histogram of the time intervals between extreme events in the case where C1 criterion is applied to the time trace of Fig. 6; (b) histogram of the time intervals between extreme events in the case where C1 criterion is applied to the time trace of Fig. 7.

Fig. 9. (a) Time series centered on the maximum of local bursts and superposition of 17 extreme events in the case of the sine perturbation. The corresponding averaged output power is displayed with a purple solid line, and the threshold corresponding to an abnormality index of 2 is displayed with a dash-dot line. (b) Same data plot but for 48 extreme events in the case of the pulse-up perturbation. In the first case, the amplitude of the spikes is not constant, and they are all within a time window of 0.02μs. In the second case, the spikes have a consistent amplitude but a strong jitter occurs, with a burst width between 0.3 and 1μs.