|Abstract : Dissipative waves often called localized structures have been experimentally observed in many experimental devices involving nonlinear optical resonators pumped by a coherent laser field. They can be classified into two categories: (i) homoclinic: the intensity profile of light evolves towards either a periodic distribution originated from a symmetry breaking instability or to localized states. The later consists of bright or dark localized spots in one or more dimensions. They can be either randomly distributed, self-organized or independents. The bright dots may be considered as bits or pixels in a parallel processing of information, (ii) eteroclinic: the spatial distribution has localized solutions far from any symmetry breaking instability. In this case, localized structures result from interactions between switching fronts in bistable systems.
We aim to develop theoretical methods to understand: (i) the non-local coupling in space and/or time, (ii) the effect of delayed feedback on the stability of localized structures in optical systems: semiconductors, metamaterials, liquid crystals and photonic crystals fibers.
Given the universal nature of dissipative waves, we aim to apply the analytical and numerical methods we developed in the context of optical systems in other areas of research in nonlinear science. In this context, we plan to expand our work to other research area in plant ecology, in nonlinear chemistry, and in plasmas magnetically confined.