Nonlinear photonics of inhomogeneous media and surfaces

The project involves investigation of a number of topics in nonlinear photonics, as summarized below. Study of Anderson localization in optically induced photonic lattices with different kinds of disorder and defects. Investigation of surface solitons at the boundary of photonic lattices and Anderson localization effects at the surfaces. Investigation of localization and delocalization of narrow and wide beams in infinite, bounded and semi-bounded curved and straight waveguide arrays. Influence of single and counterpropagating beams, modes and shapes, widths, incidence positions and tilts, mutual coherence and distance, waveguide array (multi)periodicity, curving patterns, inclusion of defects and disorder, dimensionality, as well as media nonlinearity, on the laser light propagation in different inhomogeneous media. Supercontinuum light generation. Propagation of light in nonlinear inhomogeneous media, described by the generalized Helmholtz wave equation in the slowly varying envelope approximation. Study of nonlinear phenomena in parity–time symmetric models, with parity-time potentials in the presence of nonlinearity or lattice disorder. All investigations will cover systems with different dimensionality in the single beam or counterpropagating beam geometries. Finally, exact solution of multidimensional partial differential equations of interest in nonlinear photonics will be pursued, with an eye on the stability of such localized and extended solutions.