Propagation Danamics Of High-Order Solitons In PT Symmetric Lattices

Various families of solitons supported by periodic harmonic optical lattices are under intensive study these days, attributed to their novel physics as well as potential applications, such as information processing and signal routing. Lattice solitons has been substantially enriched and advanced by research and develop in nonlinear optics and material science. After the notion of PT symmetric potential was first mentioned, it is intensively considered in diverse areas of physics rapidly, for the reason that light propagate in the PT periodic potential exhibit uniquely properties, such as double refractive and power oscillation. The study of dynamics of PT lattice solitons are of great important both in theory and in practice.This thesis is focusing on the properties of solitons, including the existence, stabil-ity and simulation of propagation dynamics, in the nonlinear optical systems imprinted linear-nonlinear PT optical lattices. The thesis includes mainly as following parts:1. Multi-stable solitons in PT symmetric optical latticeWe address the existence and stability properties of optical solitons in a compet-ing cubic-quintic medium with an imprinted complex lattice featuring a parity-time symmetry. Various families of solitons with even and odd geometrical symmetries are found in both semi-infinite and the first finite gaps. Linear stability analysis corrobo-rated by direct propagation simulations reveal that solitons with different symmetries and different number of humps can propagate stably at the same propagation constants simultaneously, i.e.. multi-stable solitons can exist in this scheme. Interestingly enough, both even and odd solitons belonging to different branches can be stable in the first gap. which indicates that the imaginary part of complex lattice plays an important role for the stabilization of solitons. This is in sharp contrast to the stability of solitons in a cubic-quintic medium modulated by a conventional real lattice.2. Multi-peaked gap solitons in PT symmetric optical latticesWe report the existence and stability properties of multi-peaked solitons in a defo-cusing Kerr medium with an imprinted complex optical lattice featuring a parity-time (PT) symmetry. Various families of soliton solutions with a different number of peaks are found in the first finite gap of the lattice. Linear stability analysis corroborated by direct propagation simulations reveals that multi-peaked gap solitons can propagate stably in a wide range, provided that their propagation constant exceeds a critical value. Our findings demonstrate, for the first time, the existence of stable multi-peaked gap solitons in a PT symmetric lattice.3. Stabilization of multipole-mode solitons in mixed linear-nonlinear lattices with a PT symmetryWe report the evolution of higher-order nonlinear states in a focusing cubic medium, where both the linear refractive index and the nonlinearity are spatially modulated by a complex optical lattice exhibiting a parity-time (PT) symmetry. We reveal that in-troduction of out-of-phase nonlinearity modulation makes possible the stabilization of higher-order solitons with number of poles larger than7, which are highly unstable in linear PT lattices. Under appropriate conditions, multipole-mode solitons with out-of-phase components in the neighboring lattice sites are completely stable provided that their power or propagation constant exceeds a critical value. Thus, our findings sug-gest an effective way for the realization of stable multipole-mode solitons in periodic potentials with gain-loss components.