Refractory times for excitable dual-state quantum dot laser neurons

Excitable photonic systems show promise for ultrafast analog computation, several orders of magnitude faster than biological neurons. Optically injected quantum dot lasers display several excitable mechanisms with dual-state quantum lasers recently emerging as true all-or-none excitable artificial neurons. For use in applications, deterministic triggering is necessary and this has previously been demonstrated in the literature. In this work we analyze the crucially important refractory time for this dual-state system, which defines the minimum time between distinct pulses in any train.

Figure 1

The secondary laser (SL) is a QD laser and the primary laser (PL) is a tunable laser source (TLS). The ${\mathrm{LiNbO}}_3$ phase modulators (MOD) are driven by a pulse generator (PG). A 50:50 power splitter sends a similar signal to each modulator. A variable electrical delay line (VDL) is added to adjust the time between two perturbations. A polarization controller (PC) is used to maximise coupling. The light emitted from the SL is sent into the circulator and then to a filter where the ES and GS light are separated and are sent directly to 12 GHz detectors connected to an oscilloscope (OSC). The red lines represent light at approximately 1300 nm close to the GS emission, the blue represents ES light only and the purple is both GS and ES. The black lines are high-speed electrical cables.

Figure 2

Anticlockwise perturbations are used in this figure. (a) The blue dots show the average time between two ES pulses after two perturbations were applied vs the time between two perturbations. Each data point is the average of 1000 sets of perturbations. The first perturbation is always successful. The absolute refractory time is 0.62 ns. The red dots show the efficiency of the second perturbation. (b) The blue dots show the normalized average times between two ES pulses after two perturbations were applied vs the time between perturbations. The average is of 1000 sets of perturbations. The red line shows the standard deviation of the times between two ES pulses. (c) The blue dots show the average peak intensity of the second ES pulse vs the time between perturbations. The red dots show the standard deviation of the peak intensities vs the time between perturbations.

Figure 3

The two small GS negative spikes at approximately 2 ns in each panel are the locations of the subthreshold clockwise perturbations. (a) Timetraces with perturbation separation of 0.66 ns: close to the absolute refractory time. The second pulse can have long escape times. (b) Perturbations separated by 0.85 ns. There is a narrow distribution for the second pulse. (c) Perturbations separated by 1.22 ns. There is a large distribution of delay times for the second pulse. (d) Perturbations separated by 1.6 ns. The second pulse has almost identical characteristics to the first.

Figure 4

Efficiency curves for the first clockwise perturbation (blue) and the second clockwise perturbation(red) given that the first perturbation has already triggered a pulse.

Figure 5

The blue curve shows the average normalized time between two ES pulses after two clockwise perturbations are applied. The red curve shows the standard deviation of the times between two ES pulses.

Figure 6

The blue line shows the efficiency of the first perturbation. It always excites a pulse for times greater than 1 ns. The red line shows the efficiency of the second perturbation. Between 0.56 ns and 0.90 ns two perturbations can produce three pulses with the associated efficiency curve plotted in yellow.

Figure 7

The blue curve shows the average normalized time between two ES pulses after two anti-clockwise perturbations are applied. The red curve shows the standard deviation of the times between two ES pulses.

Figure 8

Panel (a) shows a timetrace with two pulses arising from two perturbations. There is a 95% probability of three pulses occurring for this perturbation separation. Panel (b) shows a timetrace with three pulses arising from two perturbations. In panels (a) and (b) the time between the two perturbations is 0.72 ns.