Propagation Properties Of Spatial Solitons In PT-symmetric Optical Lattices

In this thesis, we mainly investigate the spatial optical solitons both in the-symmetric optical lattices with longitudinal barrier and in the-symmetric opticallattices with linear superlattices and modulated nonlinearity. According to the normalizednonlinear Schr dinger equation, using numerical methods such as the symmetric split-step Fourier method and etc., we analyze the propagation properties of spatial opticalsolitons in both-symmetric optical lattices. The contents of this thesis is as follows:In chapter1, we describe the history of the optical solitons briefly, and introduce theresearch background and current status of the spatial optical solitons in the-symmetric optical lattices. In the end, the main contents and the meaning of our researchare elaborated.In chapter2, the nonlinear Schr dinger equation is derived from Maxwell equations,and it is reduced to the normalized form. Then we introduce the plane wave expansionmethod to calculate the band structure of the optical lattices and give an introduction onsquared-operator method, modified squared-operator method, the analysis method oflinear stability and the symmetric split-step Fourier method.Chapter3focuses on the discussion of the tunneling effect of the spatial solitons atthe barrier and its propagation properties after passing through the barrier in the-symmetric optical lattices. We find that the propagation direction of solitons changes afterit passes through the potential barrier and we analyze the reason why the propagationdirection of the solitons changes from the view of the symmetry of lattice modulation, thetransverse refractive index modulation frequency and the refractive index modulationdepth. We can use this kind of direction deflection to steer solitons and it is of significantpotential scientific value for soliton steering, light switching and light routing.Chapter4is devoted to studying the spatial solitons in the-symmetric opticallattices with modulations both in linear and nonlinear part of the lattices. We investigatethe change of the band structure and the variation of the phase transition point of thelattice when altering the depth of superlattices. In the meantime, by using numericalmethods, we analyze how the existence, stability and propagation properties of the spatial optical solitons vary in the-symmetric optical lattices as the modulation depth ofnonlinearity increases. These properties may have potential applications in the opticalcommunications in the future.