Exploring Propagation Dynamics Of Disordered Lattices Solitons

When light propagation in nonlinear media, the diffraction effects and the induced nonlinear effects may achieve a balance. The light wave are shape-preserved and with-out any distortions during propagation, it is called a spatial soliton. Spatical solitons can play a considerable role in all-optical communication, optical switch, and all-optical photonic device. In1958, Anderson predicted the Anderson localization, Following this work, many efforts have been devoted to exploring the wave dynamics in various fields involving disordered configurations. For the reason of many different of fami-lies of solitons in disordered lattices, research the dynamics of solitons in disordered lattices are of great signifyca-nces both in theory and in practice.This thesis is focusing on propagation dynamic of spatial solitons in disordered lat-tices described by nonlinear schrodinger equation. We solve the equation use iteration method, linear-stability analysis the the stationary solutions, propagation simulations in a plit-step Fourier algorithm and a pseudospectral method. It includes mainly as following two parts:1. Higher-order solitons in amplitude-disordered waveguide arraysWe investigate the existence and stability of different families of spatial solitons in optical waveguide arrays whose amplitudes obey a disordered distri-bution. The com-petition between focusing nonlinearity and linearly disordered refractive index mod-ulation results in the formation of spatial localized nonlinear states. Solitons origi-nating from Anderson modes with few nodes are robust during propagation. While multi-peaked solitons with in-phase neighboring components are completely unstable, multipolemode solitons whose neighboring components are out-of-phase can propagate stably in wide parameter regions provided that their power exceeds a critical value. Our findings, thus, provide the first example of stable higher-order nonlinear states in disor-dered systems.2. Disordered surface gap solitonsWe address the existence of surface gap solitons at the interface between a uni-form medium and a disordered optical lattice with a defocusing Kerr nonlinearity. Gap solitons resonating with Anderson modes feature unique properties of both surface waves and disordered lattices. Bifurcations of solitons with in-phase main peaks in the nearest-to-interface lattice channels are discussed. Resonant interactions broaden the surface gap solitons and result in the formation of multibranch nonlinear modes with different number of peaks. Linear stability analysis results demonstrate that solitons at the edges of disordered lattices are completely stable or suffer a weak oscillatory in-stability. Thus, we put forward an effective way for the realization of shape-preserving self-localized nonlinear bound states with many peaks.