Equalization of pulse timings in an excitable microlaser system with delay

Abstract

An excitable semiconductor micropillar laser with delayed optical feedback is able to regenerate pulses by the excitable response of the laser. It has been shown that almost any pulse sequence can, in principle, be excited and regenerated by this system over short periods of time. We show experimentally and numerically that this is not true anymore in the long term: rather, the system settles down to a stable periodic orbit with equalized timing between pulses. Several such attracting periodic regimes with different numbers of equalized pulse timing may coexist and we study how they can be accessed with single external optical pulses of sufficient strength that need to be timed appropriately. Since the observed timing equalization and switching characteristics are generated by excitability in combination with delayed feedback, our results will be of relevance beyond the particular case of photonics, especially in neuroscience.

Robust spike timing in an excitable cell with delayed feedback

“…Notably, the striking similarity between the theoretical predictions and experimental data was not produced by fitting a specific mathematical model to the chosen cell type, but was reflective of general properties of excitability that are present in most neurons, as well as other cell types [ 4 – 8 ]. The parallels of our results with those observed in laser systems [ 18 , 20 ] further highlight the ubiquitous nature of the regeneration of activity in excitable systems with delay. Our experimental setup showcases that a living mammalian system, represented by an excitable cell, is a feasible platform for studying this phenomenon in a neural context.…”

“…non-equispaced in time) approximately conserved across many subsequent delay intervals. Nevertheless, the effect of the weak convergence to the stable solution ( figure 1 e ) is evident: ultimately, the neuron settles to the stable solution with two equally spaced spikes in a similar manner to that observed in laser systems [ 20 ].…”

“…As such, our framework provides flexibility to explore such avenues. Secondly, while the repetitive activity of the kind we discuss here may be fragile in certain experimental systems, recent work in laser physics found sufficiently large parameter ranges over which different multiple pulse rhythms due to excitability and delayed feedback can be found stably over very large timescales [ 20 , 41 ]. This suggests that these dynamics may be quite robust in practice also when the excitable element is a cell of suitable type.…”

“…The presence of rich dynamics, including coexistence between different types of dynamic behaviour in nonlinear systems with delays [15][16][17], has sparked significant interest in investigating the interplay between excitability and delay in a variety of systems. A prominent example of such a system involves semiconductor micro-cavity lasers [18][19][20]; in an analogous fashion to neural systems, the number of emission pulses per delay period in the laser system is thought to be reflective of its ability to store information. In particular, it has been suggested that this property could be used in the construction of bioinspired 'neuromorphic' photonic resonators that process information through light pulses alone [21,22].…”

Pulse-timing symmetry breaking in an excitable optical system with delay

“…Multistability has been shown to be of particular interest for all-optical processing capabilities, e.g. associative memories [14][15][16].…”