nucleating dissipative solitons

I am very happy and proud to write that our recent work on excitable systems with delay was published in Nature Communications. Of course I am heavily biased but still, I believe this work is truly interesting in several ways. Of course there is the fact that we demonstrate storage of information in the phase of an optical beam (instead of power), and the fact that we can not only write, but also erase those phase bits. But the way we arrived to these results and the questions they raise are in my view more interesting than the answers they bring.

There has long been an interest in the analogy between spatially extended and delayed dynamical systems, and it has been very nicely formalized in some particular cases by G. Giacomelli and A. Politi in their 1996 paper about the Relationship between Delayed and Spatially Extended Dynamical Systems. Due to the large number of papers published about the topic, it is maybe surprising that so little work has been done on dissipative spatial structures in this context. We published recently with G. Giacomelli and F. Marino a first paper in this direction, in which we discussed the existence of localized states analogues in a delayed dynamical system. In that case, localized states emerged in the case of a bistable system with the addition of a delay term (plus some forcing in pseudo-space). In the present case, the nonlinear element is not bistable but instead it is excitable. Of course, that leads to localized states with very different properties, but it is nonetheless very striking that both of these phase space structures (which are known to be able to support localized states or waves in spatially extended systems) are able to support a kind of localized state in delay systems. In addition, in the present paper the model we use is simple enough that some analytics can be done and actually lead to a very nice spatially extended system featuring the nonlinearity of the sine-Gordon equation. Here is hoping that someone will step up to analyzing this in the case of the bistable case with pinned fronts ;).

A preprint of the paper is on our publications page: it is about Topological solitons as addressable phase bits in a driven laser.