Sub-diffraction-limited localized structures: influence of linear non-local interactions

Cavity solitons are controllable two-dimensional transverse Localized Structures (LS) in dissipative optical cavities. Such LS have been suggested for use in optical data storage and information processing. Typically diffraction constrains the size of these light spots to be of the order of the square root of the diffraction coefficient of the system. Due to recent advances in the development of metamaterials, the diffraction strength in a cavity could be controlled by adding a left-handed material layer in a Fabry-Perot resonator together with a traditional nonlinear material. This system thus potentially allows for LS beyond the size limit imposed by natural diffraction. However, when the diffraction strength becomes smaller, the non-local response of the left-handed metamaterial starts to dominate the nonlinear spatiotemporal dynamics. Considering a typical linear non-local response, we develop a mean-field model describing the spatiotemporal evolution of LS. First. the influence of this non-local response on the minimal attainable width of the LS is studied [Gelens et al., Phys. Rev. A 75, 063812 (2007)]. Secondly we elaborate on the different possible mechanisms that can destabilize the LS. leading to stable oscillations, expanding patterns, or making the LS disappear. Furthermore, we also show multiple routes towards excitability present in the system. We demonstrate that these different regions admitting stationary, oscillating or excitable LS unfold from two Takens-Bogdanov codimension-2 points [Gelens et al., Phys. Rev. A 77 (2008)].