Properties Research Of Nonlinear Modes In PT-symmetric Lattices

Spatial soliton is a basic physical phenomenon of nonlinear optics.Its characteristic is that the shape and energy of the beam are kept constant during the transmission,which has important applications in all-optical communication and other fields.Since the introduction of the concept of PT-symmetry to nonlinear optics,it has attracted much attention from researchers both at domestic and abroad.It is proved that the solitons in the PT-symmetric potential show some unique properties,such as birefringence,power oscillation,etc.These features can not be achieved in traditional systems.Therefore,it is necessary to study the dynamic properties of optical solitons in PT-symmetric lattices in theory and experiment.In order to calculate soliton solutions,we use Finite-Difference method and Modified-Squared operate method;The propagation characteristics of the soliton by using Split-Step Fourier Methods analysis.This article includes the following core content:1.2D in-band solitons in PT-symmetric waveguide arraysWe address two types of two-dimensional(2D)localized solitons in Kerr media with an imprinted quasi-onedimensional lattice featuring a parity-time(PT)symmetry.Solitary waves originating from the edges of the Blochbands are stable in their entire existence domains.Purely nonlinear multipeaked states propagate stably in wide parameter windows.Both types of nonlinear waves exist in the finite bandgaps of the corresponding linear system and,cross-continuously,the Bloch band(continuous spectrum)sandwiched between(or neighboring)them.To the best of our knowledge,our findings thus provide the first example of embedded solitons in 2D PT periodic systems.2.PT-symmetric bright solitons in inhomogeneous defocusing nonlinearitiesWe address that various branches of bright solitons exist in a spatially inhomogeneous defocusing nonlinearity with an imprinted antisymmetric periodic gain-loss profile.The spectra of such systems with a purely imaginary potential never become complex and thus the parity-time symmetry is unbreakable.The mergence between pairs of soliton branches occurs at a critical gain-loss strength,above which no soliton solutions can be found.Intriguingly,which pair of soliton branches will merge together can be changed by varying the modulation frequency of gain and loss.Most branches of one-dimensional solitons are stable in wide parameter regions.Wealso provide the first example of two-dimensional bright solitons with unbreakable parity-time symmetry.