Study On Spatial Soliton In One - Dimensional Photonic Lattice

Spatial solitons exhibit unique properties, such as having fixed space shape, steady energy, etc. When spatial solitons propagate in nonlinear media, the nonlinear effects of the medium material and the diffraction effects produced by the solitons may achieve a balance. Thus, spatial solitons can play a considerablely important role in creating reconfigurable all-optical circuits where is guided and controlled by light itself. And the exploration and research of the properties of optical solitons have a powerful means. This thesis is focusing on the analysis and simulation of propagation dynamics of spatial solitons. In our calculation, we use Plane-Wave Expansion method, Modified Squared-Operator Iteration method, Split-Step Fourier methods, Fourier Collocation method, etc. The thesis mainly includes defect solitons supported by optical lattices in biased centrosymmetric photorefractive crystals, Solitons in focusing and defocusing optical lattices and Solitons in chirped photonic lattices.Firstly, defect modes (defect solitons) are studied in optical lattices in biased centrosymmetric photorefractive crystals based on photorefractive nonlinear wave propagation equations, analyzed the stabilities in photonic lattices with numerical simulation methods. These defect modes exist in different bandgaps due to the change of the defect strength. For a positive defect, defect modes exist in each bandgap. The strongest confinement of defect modes appears in the semi-infinite bandgap when the positive defect strength is fixed. For a negative defect, defect modes exist in each bandgap except the semi-infinite bandgap. When the negative defect strength is fixed, the strongest confinement of defect modes appears in the first bandgap, and the strong negative defects do not favor the creation of defect modes in the first bandgap. For a given bandgap, the strongest confinement of defect modes appears when the negative defect strength is equal to a certain value.Secondly, a detailed analysis of the properties and dynamical stability of different families of one-dimensional lattice solitons is studied in both focusing and defocusing saturable optical medium with harmonic transverse modulation of linear refractive index. Stability analysis reveals the existence of stability regions for even solitons that broaden with increase of degree of saturation of nonlinear response. Stable multi-soliton structures can be built from an arbitrary number of lowest order odd solitons with appropriately engineered phases.Finally, optical solitons in chirped optical lattices whose amplitude or frequency changes in the transverse direction are studied. Soliton propagation in such lattices can be accompanied by the progressive self-bending of the soliton trajectory, and we show that the soliton bending rate and output position can be controlled by varying the lattice depth, the chirp amplitude, and the frequency modulation rate.