Study On The Propagation Properties Of Gap Solitons In Optical Lattices

Soliton, as a fundamental physical phenomenon in nature, has many special propertiesand broad application prospects. With the development of computing technology and theimprovement of experiment condition, spatial soliton has gradually become a hot topic inlaser physics. The gap soliton studied in this thesis is a type of spatial soliton, and mainlyexist in the optical lattices which have Bloch band structure. The study result of this thesismay improve the fundamental theory of physics, and promote the development of relatedsubjects. Besides, our results also can provide theory guides for the application of gapsolitons.In this thesis, we focus on the existence and stability of gap solitons in two-dimensionalreal optical lattices and Parity-Time symmetric optical lattices based on Kerr nonlinear opticalmedia. We find that, in real optical lattices with focusing Kerr nonlinearity, in negative defectthe defect solitons exist in the semi-infinite gap and the first gap, and can be stably propagate;In positive defect the defect solitons only stably exist in the semi-infinite gap. While in thedefocusing Kerr media, when the defect is positive, the defect solitons can stably exist in boththe semi-infinite gap and the first gap; But in negative defect, the defect solitons only stablyexist in the semi-infinite gap. In the Parity-Time symmetric lattices, the existence of gapsolitons were similar to the real lattices, but the stabilities were very different. In Parity-Timesymmetric lattices, the solitons with high power are usually unstable.At last, we study the defect gap solitons in real linear periodic optical lattices withparity-time-symmetric nonlinear potentials. We find in this theoretical model, when theimaginary part of the Parity-Time symmetric potential is small, the gap solitons will stablyexist in a wide region both in positive defect and negative defect. However, when theimaginary part of the Parity-Time symmetric potential increasing, the defect gap solitons inthe high power region(s) will become not stable.Some conclusion of this thesis can be extend to higher-dimensional solitons. The solitonsstudy method and the numerical methods in this thesis also are generalized, and can be usedto study the related theoretical models.