Analytic Study On Transmission Properties Of Optical Solitons

Optical solitons are formed thanks to the perfect equilibrium between the linear and nonlinear effects in media. Temporal optical solitons (Spatial optical solitons) arise from the balance between the optical pulse broadening caused by dispersion (diffraction) and compression caused by self-focusing (self-phase modulation).Optical soliton is the self-trapped electromagnetic wave propagating in nonlinear media that maintain its width, amplitude and transverse velocity. Just for these unique properties make optical solitons as the most ideal carriers of information, are widely applied to the long distance optical communication and ultra-fast signal processing systems. Optical soliton communications have many advantages that the traditional optical fiber communications don’t have, such as the high information capacity, long transmission distance, high transmission rate, low bit error rate, good confidentiality and strong anti-interference ability and so on.In nonlinear fiber optics, the nonlinear Schrodinger equation (NLSE) describes the propagation of an optical pulse in the nonlinear media. The effort to seek analytical solutions to the NLSE, especially the soliton solutions, has an important significance for the study of optical solitons. This thesis mainly focuses on the transmission properties of optical solitons in the various nonlinear media. The specific research contents and the results obtained are as follows:1. Analytic study on temporal optical solitons in the Kerr-law fibersWith the aid of the self-similarity transformation and Jacobian elliptic equation expansion method, the cubic nonlinear Schrodinger equation (CNLSE) with inter-modal dispersion (IMD), detuning, time-and space-modulated external potentials, and dissipation, describes the dynamics of the propagation of an optical pulse in the Kerr-law multi-mode fiber, has been solved analytically. Jacobian elliptic periodic solutions, singular solutions, bright soliton and dark soliton are obtained; the CNLSE with detuning, IMD, external potential, fiber dissipation, self-steepening and third order dispersion (TOD), describes the dynamics of the propagation of ultra-short optical pulses (in the femtosecond regime) through gas-filled hollow-core photonic crystal fiber (HC-PCF), has been solved analytically by employing the Backlund transformation and Hirota’s direct method. The optical one-soliton solutions are derived, and the influence of correlation coefficients on the transmission properties of optical solitonsso liton width, amplitude, and phase) are analyzed.2. Analytic study on temporal optical solitons in the parabolic-law fibersBy using the sub-equation expansion method, the cubic-quintic nonlinear Schrodinger equation (CQNLSE) with inter-modal dispersion (IMD), detuning, time-and space-modulated external potentials, and dissipation, describes the dynamics of the propagation of an optical pulse in the parabolic-law multi-mode fiber, the CQNLSE with TOD, fourth order dispersion (FOD) and self-steepening, describes the dynamics of the propagation of a light pulse (T0≤100fs) in the higher-order dispersion parabolic-law fiber, the CQNLSE with Raman effect and self-steepening, describes the dynamics of the propagation of ultra-short optical pulses in the parabolic-law dispersion flattened fiber (DFF), and the time-modulated CQNLSE with external potential and Raman effect, describes the dynamics of the propagation of a light pulse (T0>100fs) in the time-modulated parabolic-law DFF, the three-dimensional (3D) time-modulated weakly nonlocal CQNLSE, describes the dynamics of the propagation of an optical pulse in the time-modulated weakly nonlocal nonlinear parabolic-law fiber, have been solved analytically. Exact solutions to these equations are constructed, which include the soliton solutions.3. Analytic study on temporal optical solitons in the spatially inhomogeneous dual-power law fibersBy employing the Lie group method, the NLSE with space-modulated GVD and non-Kerr law nonlinearity, describes the dynamics of the propagation of an optical pulse in the spatially inhomogeneous non-Kerr law fibers, has been solved analytically. Analytical soliton solutions are got. Four laws of nonlinearity that are Kerr law, parabolic law, power law and dual-power law are considered.4. Analytic study on spatial optical solitons in the media with various types of competing nonlinearitiesBased on the the integrable theory, the one-dimensional (ID) weakly nonlocal CQNLSE, describes the dynamics of the propagation of a light pulse in the media with competing weakly nonlocal nonlinearity and second order polynomial-law nonlinearity, has been solved analytically. Analytical bright and singular soliton solutions are got; Based on the the integrable theory, the one-dimensional (ID) weakly nonlocal cubic-quintic-septic nonlinear Schrodinger equation (CQSNLSE), describes the dynamics of the propagation of an optical pulse in the media with competing weakly nonlocal nonlinearity and third order polynomial-law nonlinearity, has been solved analytically. Explicit bright and singular soliton solutions are got; The nonlinear Schrodinger equation with competing nonlocal nonlinearities and local quintic nonlinearity, describes a light pulse propagating in the media with competing nonlocal self-defocusing nonlinearity, nonlocal self-focusing nonlinearity and local quintic nonlinearity, has been solved analytically by using the variational principle. The influence of competing parameters on the dark soliton properties (soliton width and transverse velocity) are discussed.