Localisation of light and spatial solitons
Spatial solitons represent optical beams propagating without changing their profile in nonlinear media. The natural process of diffraction which tends to spread the beam is counterbalanced by nonlinearity. Depending on the sign of the nonlinearity either bright or dark solitons can be formed.
Localisation of waves in media with nonlocal nonlinearity. These are nonlinear systems where the nonlinear response of the material in a particular spatial location is determined by the wave intensity in certain neighbourhood of this location. The nonlocality of nonlinearity has a profound effect on stability of plane waves and formation and stability of spatial optical solitons. Our recent activities are devoted to properties of solitons in nonlocal media in the presence of noise. We discovered that nonlocality has a beneficial effect of solutions ensuring their stable propagation even when they are subject to strong white noise perturbation in nonlinear periodic media.
Figure: Illustrating the effect of randomness of nonlinearity on soliton propagation in nonlocal media. Plots (a-d) illustrate the beneficial effect of nonlocality. The larger the degree of nonlocality σ the more stable is soliton propagation. For the reference plot (d) depicts propagation of ideal soliton in disorder-free medium.
Periodicity of the refractive index of the optical medium imposes restriction on the way the light may propagate. In particular, it leads to band-gap structure in the relation between longitudinal and transverse wave vectors of light waves. As a result, diffractional properties of beams are drastically affected, such that the sign of diffraction changes depending on whether the wave vector corresponds to the centre or edge of the transmission band. This also means one may observe nonlinear effects associated with self-focusing or defocusing in the same nonlinear medium. Consequently one may realize, for instance, formation of bright and dark solitons in the same sample of nonlinear material. In this project we are interested in interplay between nonlinearity and diffraction governed by the symmetry of index modulation on the formation of localised states and their stability.
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