Cavity solitons are localized light peaks in the transverse section of nonlinear resonators. These structures are usually formed under a coexistence condition between a homogeneous background of radiation and a self- organized patterns resulting from a Turing type of instabilities. In this issue, most of studies have been realized ignoring the nonlocal eﬀects. Non-local eﬀects can play an important role in the formation of cavity solitons in optics, population dynamics and plant ecology. Depending on the choice of the nonlocal interaction function, the nonlocal coupling can be strong or weak. When the nonlocal coupling is strong, the interaction between fronts is controlled by the whole non-local interaction function. Recently it has shown that this type of nonlocal coupling strongly aﬀects the dynamics of fronts connecting two homogeneous steady states and leads to the stabilization of cavity solitons with a varying size plateau. Here, we consider a ring passive cavity filled with a Kerr medium like a liquid crystal or left-handed materials and driven by a coherent injected beam. We show that cavity solitons resulting for strong front interaction are stable in one and two-dimensional setting out of any type of Turing instability. Their spatial profile is characterized by a varying size plateau. Our results can apply to large class of spatially extended systems with strong nonlocal coupling.
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
Recent advances in the field of left-handed materials (LHM) have renewed the interest for the study of the propagation properties in these materials. In particular, many works have been devoted to the study of the Veselago plate, which constitutes the simplest linear system based on LHM. Recently, Zharov and co-workers introduced a description of the nonlinear properties of LHM. In particular, they suggested that LHM could be used as the basis of power limiters, all optical switches, etc. In this communication, we consider a Fabry-Perot cavity filled with two materials having refractive indexes of opposite signs, and driven by an external coherent field. Using the well-known mean-field approximation, we derive a partial differential equation describing the bidirectional propagation of light in this optical cavity. In the absence of reflection at the interface between the LHM and the RHM, our model is similar to the well-known LL-model. However, an important difference that appears when considering LHM is that the sign of the diffraction term can be reversed by varying the geometry. Besides the bistable behaviour of the homogeneous response curve of the system, our study reveals the existence of modulational instability. The wavelength of the spatial dissipative structure emerging from that instability can be tuned continuously by varying the diffraction coefficient.
Left-handed materials have attracted growing attention in recent years. Although many efforts have been concentrated on the study of linear devices filled with left-handed materials, it was only recently that the nonlinear optical properties and optical response of such materials have been described. However, no analytical description of light propagation in these media has been proposed. In this communication, we develop an analytical model describing the interaction of coherent electromagnetic radiation in structures containing both right- and left-handed materials with a Kerr type nonlinearity. We study the paraxial propagation of electromagnetic radiation in such structures. Using a multiple time and space scales analysis, we derive a system of two coupled nonlinear Schrödinger equations for the amplitudes of the fields, allowing for both forward and reflected waves to be present in the structure. Diffraction, group velocity dispersion and Kerr nonlinear effects are taken into account. Appropriate boundary conditions are derived. Finally, we point out the differences between propagation in right- and left-handed materials.