Control of excitable pulses in an injection-locked semiconductor laser

In spite of numerous theoretical and experimental reports of excitability in lasers with injected signal based on the locking-unlocking transition, the response of the system to controlled external perturbations (which is at the basis of the definition of excitable systems) has not been experimentally studied yet. In the following, we analyze the response of an injection-locked semiconductor laser to different external perturbations. We demonstrate the existence of a perturbation threshold beyond which the response of the system is independent of the strength of the stimulation and, thus, demonstrate its excitable character. We show that optically perturbing such an excitable system via the control of the phase of the injection beam can be useful for optical pulse generation.

Figure 1

Schematic of experimental setup. O.I., optical isolator; P.M., phase modulator; $\lambda /\left(2\right|4)$, (half|quarter)-wave plate; Pol., polarizer; PBS, polarizing beam splitter; F.P., Fabry-Perot interferometer.

Figure 2

Optical spectra of the injected VCSEL as a function of the bias current. The VCSEL is locked to the forcing between 2.04 and 1.94 mA. Outside of this region, the injection level being very weak, the spectra contains mostly the master laser frequency (horizontal line), the VCSEL frequency (thick oblique lines), and a small four-wave mixing peak. The color scale is logarithmic.

Figure 3

Perturbation efficiency depending on the amplitude of the phase jump. Low-amplitude phase jumps do not trigger any visible response (bottom inset, ${52}^{\circ }$), while above a certain threshold (${55}^{\circ }$) nearly all perturbations are successful. In this case, all the responses are essentially identical (top inset, ${66}^{\circ }$; second inset, ${55}^{\circ }$; third inset, ${52}^{\circ }$). The time traces were acquired with a 12.5-GHz bandwidth, 100 GS/s sampling rate real-time oscilloscope. The DC component of the signal is removed by an AC-coupled amplifier. VCSEL bias current 1.026 mA, injected power 42 $\mu$W.

Figure 4

Top panel: Response to phase jumps of the injection beam depending on the phase jump height. In all cases the phase jump duration is of 100 ps. On the top trace, no response is observed. On the bottom trace, nearly all perturbations successfully trigger a response. The middle trace is the intermediate case in which either types of response can be observed. The pulses are applied at a 50-MHz repetition rate, dead time between measurements has been cut off. Bottom panels: normalized response amplitude as function of the phase jump and standard deviation of the response amplitude. VCSEL bias current 1.935 mA, injected power 30 $\mu$W.

Figure 5

Perturbation efficiency depending on the height of the voltage pulse applied to the VCSEL. The time traces in the insets have been acquired at a 20-GS/s sampling rate with 6-GHz analog bandwidth oscilloscope. The amplitude of the excitable response is about 10% of the DC signal. The DC component has been removed. The bias current is 1.6 mA; the injected power is 93 $\mu$W.