Research On Spatial Optical Solitons In Optical Lattice

In this thesis, we mainly investigate spatial optical solitons in optical lattices. It’s of great significance to study optical soliton properties in both theoretical and practical aspects. Theoretically, studying of optical solitons can produce guidance for the research of solitons in other relative physical systems, and practically optical solitons have wide potential uses in optical logical device, beam control, all-optical communication network, optical routing, optical storage, and optical calculation, etc.Solitons in optical lattices have many properties which were not possessed by the solitons in the system without lattice. For instance, optical lattices exhibit band structure, and optical solitons can only exist in the gaps between bands; in different gaps, there exist different types of solitons, for example, in the first gap there exist vortex solitons; the fundamental solitons in lattices are more stable than those in the media without lattice.The numerical algorithms used in this thesis include:square operator iteration method (SOM), modified square operator iteration method (MSOM), plane wave expansion method, symmetric split-step Fourier method, fourth-order Runge-Kutta algorithm, etc.The properties of optical solitons in one-dimensional lattices, two-dimensional square lattices and two-dimensional triangle lattices were studied for non-dissipative system. To test the solitons’ stability, we added small random noise to the rigorous soliton solution, and simulated their propagation. Two cases were considered, i.e. the beam was incident along z direction with and without inclined angles. The results indicated that bright solitons could exist in optical lattices for both focusing and defocusing nonlinearities; fundamental solitons in the semi-infinite gap of the lattice were very stable; there exist massive amount of soliton solutions in both one and two-dimensional lattices; vortex solitons in the first gap of the lattice were all non-stable; discrete vortex solitons in the semi-infinite gap could propagate stably.In this thesis, solitons in one-dimensional parity-time (PT) lattices and two-dimensional localized gain-loss system were investigated for dissipative system. In fact, the numerical results would not be influenced by regarding dissipative system as generalized optical lattices.Our results show that when the defect is positive or zero, in the semi-infinite gap, the solitons are always stable, while in the first gap, the solitons are unstable in most of their existence region except for those near the edge of the second band; when the defect is negative, in the semi-infinite gap, other than those near the edge of the first band, most solitons are stable, but in the first gap, all solitons are unstable; stable vortex solitons were found in two-dimensional localized gain-loss system.