We will investigate, experimentally and theoretically, the dynamics of nonlinear optical waves at mesoscopic scales, ranging from several wavelengths (~10 microns) down to the sub-wavelength regime (~0.2 microns). Our studies will cover a variety of optical settings: from various kinds of periodic systems (photonic lattices) with and without disorder, to bulk materials and nano-suspensions. Under proper conditions, light propagating nonlinearly in these systems can display complex nonlinear dynamics, giving rise to a variety of fascinating phenomena. Perhaps the most intriguing are associated with the suspensions containing dielectric nano-spheres, upon which light acts, by virtue of the gradient force, to modify the local density of spheres, thereby varying the effective refractive index. We will use light to alter the properties of the fluid (e.g. surface-tension, viscosity), which, in turn, will affect the pattern of optical wave in space and time. We will study nonlinear optics coupled directly to nonlinear fluid dynamics. Our preliminary results demonstrate optically-induced convection and optically-driven waves in the fluid. In the same system, we will explore sub-wavelength optical spatial solitons. Our preliminary experimental results clearly show very narrow solitons, narrower than imaging optics can resolve. In another effort, we will explore arrays of sub-wavelength waveguides with a sharp index contrast, and will study a variety of nonlinear phenomena unique to such structures. Other efforts include linear and nonlinear wave phenomena in photonic lattices, such as Anderson localization of lightt, the optical realization of the famous Hofstadter butterfly, waves in honeycomb lattices exhibiting unique features arising from symmetry (diabolic points, Berry phase effects, backscattering, etc.), Anderson localization in quasi-crystals and in honeycomb structures, transport of solitons in random potentials, and more.
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