Properties Of Solitons In PT Symmetric System

The formation of spatial solitons can be explained by the lens effect:The trans-mission of the beam in space will be diffracted in the transverse direction. When the strong light and the nonlinear medium interact, the refractive index of the medium will change, so that the optical depth becomes larger, a similar lens is formed, which makes the beam focus. When the diffraction and nonlinear self focusing effect is balanced, so that the beam is no longer horizontal, forming a self trapped beam in the transmission process to maintain the same amplitude and energy. The study of spatial optical solitons is rapidly applied to various physical domains. Once the concept of PT symmetry put forward, this subject has attracted great attention. Initially, our interest mainly concen-trated in the systems of non-Hermitian quantum mechanics, and then new applications have been found in optics. Meanwhile, optics can provide a fertile ground for PT, where the concepts can be realized and demonstrated experimentally.Evolution of beam is thus governed by the dimensionless nonlinear schrodinger equation, then we use Newton iterative method, pseudospectral method and finite dif-ference method. This article mainly pay close attention to the solution, the existence area, stability and propagation behavior of solitons in PT symmetric optical systems. The thesis includes mainly as the following parts:1. Diffraction management and soliton dynamics in frequency-chirped PT sym-metric latticesWe address two closely related problems:diffraction management and soliton dy- namics in parity-time PT symmetric lattices with a quadratic frequency modulation. The normal, anomalous, or zero diffraction is possible for narrow.beams with a broad band of spatial frequencies. The frequency band of nondiffraction beams can be en-larged by increasing the chirp rate of lattices. Counter-intuitively, the gain-loss com-ponent plays the same role as the real part of lattice on the suppression of diffraction, which leads to an effective reduction of critical lattice depth for nondiffraction beams. Additionally, we reveal the existence of a novel type of bright solitons in defocusing Kerr media modulated by chirped PT lattices. We also demonstrate that lattice chirp can be utilized to suppress the instability of solitons. Our results expand the concept of PT symmetry in both linear and nonlinear regimes, and may find interesting optical applications2. Gap solitons in PT-symmetric lattices with a lower refractive-index coreWe address the existence and stability properties of families of gap solitons in a lower refractive-index core, sandwiched between two optical lattices with a parity-time PT symmetry imprinted in a defocusing medium. The scale of flat-topped complex solitons can be controlled arbitrarily by varying the embedded index core. Multipeaked solitons are found to exhibit equal peak values in the region of the index core, and they have no analog in other lattice-modulated or bulk media.We demonstrate that, in sharp contrast to solitons in regular PT lattices, flat-topped and multipeaked solitons are ei-ther stable or suffer a negligibly weak instability, even when the gain-loss coefficient approaches the PT-symmetry-breaking point. Our results, thus, build a bridge be-tween the PT defect solitons in a narrow index core and the PT kink pairs in a broad index core. We also suggest an effective way for the observation of surface solitons in PT-symmetric lattices...