Analytical Studies On The Optical-Soliton Ultrashort Pulse With The Higher-Order Nonlinearity Effects

The generation of the short-time and high-power ultrashort pulses promotes the studies of the microcosm and ultrafast process in the such fields as physics, optics, chemistry and so on. In optical communications, ultrashort pulses can be used to improve the transmission bandwidth and enlarge the communication capacity. In par-ticular, the ultrashort pulses in the form of optical solitons [called as the optical-soliton ultrashort pulses (OSUPs)] can maintain the shapes and velocities during the propaga-tion because of the balance between the dispersion and nonlinearity effects. Therefore, this kind of ultrashort pulses can guarantee the quality of large-capacity and long-distance communication.Because the classical nonlinear Schrodinger (NLS) model appears inadequate for describing the subpicosecond and femtosecond ultrashort pulses in optical fibers, it is necessary to consider the modified NLS model with the higher-order effects (e.g., higher-order dispersion, self-steepening, and stimulated Raman scattering). In order to study the dynamics of OSUPs in different media, based on the modified NLS models this dissertation analyzes the generation conditions and interaction properties of different types of optical-soliton ultrashort pulses, and the effects of higher-order nonlinearities on the OSUPs. In addition, the modulation instability and ability of the OSUPs against initial perturbations under the effect of higher-order nonlinearity are discussed via the linear stability analysis and numerical methods, respectively. The work of this dissertation includes the following aspects:(1) Study on the dark-soliton and antidark-soliton ultrashort pulses in homogeneous monomode optical fibers. Based on the constant-coefficient derivative NLS model, the dark-and antidark-soliton ultrashort pulses are obtained in the normal group velocity dispersion (GVD) regime, and the related parametric conditions are also given for such two kinds of OSUPs. Analysis on the soliton interactions shows that dark and antidark solitons can interact with each other under the same background field. Breathers and double poles are firstly constructed in the normal GVD regime via the dark two-soliton solutions. The influence of parameters on their physical properties is also analyzed, which may provide some theoretical values for the experimental observations of breather and double pole ultrashort pulses in optical fibers.(2) Study on the OSUPs in the inhomogeneous monomode optical fibers. Based on the variable-coefficient derivative NLS model, the nonhomogeneous multi-soliton solitons are obtained under the integrable conditions which reduces the limitations of solving such model by introducing chirp factors in the previous studies. The compres-sion of OSUPs with the presence of exponentially-and linearly-decreasing dispersion profiles is realized, which provides some theoretical reference for the technique of ultra-short pulse compression in the dispersion-decreasing fibers. Through the asymptotic analysis of the two-soliton solutions, the explicit expressions of amplitudes, velocities and phases are given for the inhomogeneous solitons before and after the interactions. Then, one can modify the soliton interactions quantitatively.(3) Study on the vector-soliton ultrashort pulses in the birefringent optical fibers. Based on the coupled derivative NLS model, the parametric conditions are explicitly given for the generation of vector dark solions, vector antidark solitons and mixed-type vector solitons. Asymptotic analysis shows that the interactions between those three types of the vector solitons with two polarization components are always elastic, but the mixed-type vector solitons with two or more bright components admit the inelastic interactions along with energy exchange among the bright-soliton polarization components. Such energy-exchanging phenomenon between mixed-type vector solitons may provide some theoretic foundations for the realization of all-optical switch and information transfer via the collision of OSUPs. The numerical stability of OSUPs against the initial perturbations is also checked by means of the time-splitting spectral method.(4) Study on the vector-soliton-bound-state ultrashort pulses in the birefringent optical fibers. When the adjacent solitons have the same velocity, the bright-soliton bound states, dark-soliton bound states and antidark-soliton bound states are found to be formed under the effects of the higher-order nonlinearities. The soliton separa-tions in the bound states can be quasi-linearly adjusted by introducing the separating factors into the solutions. Through the analysis on the interactions between the bound state and bright soliton, it is found that the inelastic interaction can occur between the vector-bright-soliton bound state and vector-bright soliton along with the energy exchange. Therefore, the bright-soliton-bound-state ultrashort pulses may be used as the pump pulse to control the signal pulse.(5) Study on the soliton fission and fusion in the nonlinear resonant medium. Based on the resonant NLS model, the soliton resonance with the presence the quantum poten-tial is analyzed. Under different conditions, five types of interactions with intermediate. solitons are obtained:head-on interaction generating one large-amplitude intermediate-state soliton, head-on interaction generating one small-amplitude intermediate-state soliton, overtaking interaction generating one small-amplitude intermediate-state soli-ton, overtaking interaction generating one large-amplitude intermediate-state soliton and interaction generating four intermediate-state solitons. Note that the intermediate-state solitons result from the finite phase shifts during the interaction. Thus, the phe-nomena of soliton fission and fusion can be obtained when the phase shifts become infinite. These results may have potential applications in the supercontinuum gener-ation in the photonic crystal fibers and the black-hole experimental studies based on the ultrashort pulses.