phase kicks

A laser with injected signal (in some well defined parameter region) has been expected to behave as an excitable system for many years (actually since 1998, predicted in a nice paper by Coullet, Daboussy, Tredicce). Several observations of pulses in this parameter region have since then been realized, and those pulses have been interpreted as noise triggered excitable pulses. We fill a quite large gap with this recent paper, since we finally give a proof to the fifteen years old prediction: upon perturbation, well defined excitations may or may not be triggered depending on the strength of the perturbation.

"Excitability" is a property of many nonlinear systems and is by far not restricted to optics. Indeed the most paradigmatic example of an excitable system has been observed in biology with Hodgkin, Huxley and Katz's amazing measurement of the response of a neural cell to short electrical perturbations [1]. The excitable character of a system (independently of its biological, chemical, mechanical or optical nature) is therefore established by measuring the response of a system to external perturbations. If a perturbation is "small", the system will gently relax back to its stationary state. In this case, the transient leading the system back to its quiescent state of course depends on how far from its stable position the system was pushed. On the contrary for "large" perturbations, the relaxation trajectory becomes unique. Whenever the system is pushed far enough (far enough to be "excited"), it will go along a well defined orbit, which is perfectly deterministic and strongly attractive: this trajectory is therefore independent of the perturbation, provided the perturbation was sufficient to trigger the excitable response. The importance of the uniqueness of the trajectory (yet often neglected) becomes obvious if one considers the role of excitable pulses in the original example studied by Hodgkin and Huxley, which is of course the transmission of information along the axon. In fact, in a unidimensional excitable system, information can propagate via the motion of excitable pulses whose shape is not altered by the propagation. The perturbations leading to either of the responses are separated by an in principle well defined threshold, and any perturbation which overcomes this threshold will lead to this same excitable response.

In presence of noise or slow parameter fluctations the threshold may be a bit more difficult to identify, since identical perturbations may or may not trigger an excitable response if they are close to the ideal threshold [2]. But even in this case the excitable orbit itself does not depend on the perturbation. This is what we demonstrate in this paper: a sufficient perturbation can trigger all identical responses provided the kick is sufficient. We have applied two kinds of perturbations: optical (we perturb the phase of the injection beam), or electrical (a voltage pulse is applied to the diode, what is shown in the video above). Whatever the perturbation, the all or nothing response typical of excitable systems was observed, and we therefore finally know how to trigger excitable pulses in this system.

The paper has two main interests in my opinion. Due to the many papers discussing excitability in this system, the results were not unexpected. This may superficially appear as lowering the interest of the paper, but it is actually its first strength. It took fifteen years to finally have a measurement of the response of the system to well controlled external perturbations, now we have it. The second way this paper might have an impact is that excitable systems have long been envisioned as basis for the processing of information. No surprise: this is one of their key roles in biological systems. However, whatever the scheme one wants to envision, from simple pulse reshaping to complex networks of excitable optical cells, the fancy information processing scheme will remain useless whithout a way to input information to it, ie to trigger excitations. Now that we know how to trigger excitable pulses, there may be a possibility to enter information into any creative system based on one or more of these optical excitable elements (which happen to react within a few tens of picoseconds).

This paper also has an additional anecdotical interest. I had the pleasure a few years ago to collaborate with a good friend (Francesco Pedaci and his lab colleagues at that time) on the dynamics of a micrometer sized birefringent particle optically trapped and immersed in water. In that experiment, we observed that when the input polarization is rotated, the orientation of the birefringent crystal will follow that of the input polarization, but only up to a certain rotation frequency. Beyond this frequency, the particle will sometimes "phase slip" and miss one turn (actually: one half of a turn). This results in a pulse in the torque applied to the particle by the input beam, and we have demonstrated that when the birefringent particle is about to unlock, it behaves as an excitable system [2]. Now what is fascinating is that if one excepts the time scales, the measurements we performed at that time and the measurements reported in the present paper are essentially indistinguishable. Does that mean that the two systems are identical? No, of course, since the physical mechanisms which are involved (coherence of atomic populations under optical forcing in one case and transfer of angular momentum from light to matter in the other case) are so different that the two systems can't be considered the same. On the other hand one has to admit that this incredibly strong similarity exists and that it at least strongly suggests the existence of something in common in the nature of the two systems. What that common bit actually is is interesting. In any case, noting the similarity is essential: we have to look for novel and distinctive features in what we observe, otherwise there is no hope in going forwards, but we also have to build connections between different systems, since it allows one field of knowledge to benefit from many of the steps which were accomplished in other fields. That is what is happening here.

Anyway, congratulations to Margherita, Bruno and Michael who worked very well to produce the data we use in this paper.

The paper is on our publications page: it is about control of excitable pulses in an injection-locked semiconductor laser.

[1] The measurement was published by these three authors, while apparently only Hodgkin and Huxley worked on the modelling of the phenomenon in "A quantitative description of membrane current and its application to conduction and excitation in nerve" (1952)

[2] This was analyzed numerically and experimentally in a better controlled system: a birefringent crystal in an optical torque wrench