Studies On Transmission Of Optical Pulses In Variable Parameter Fiber Systems

Propagation of light pulses in optical fibers is widely considered because of their extensive applications to optical communication. As a new development, propagation of light pulses in variable parameter fiber systems is of particular interest. The problem can be described by the generalized nonlinear Schrodinger equation with variable coefficients, the generalized cubic-quintic nonlinear Schrodinger equation with variable coefficients, and the higher-order nonlinear Schrodinger equation with variable coefficients. On the other hand, it is of scientific significance and application prospect to study solutions of the nonlinear Schrodinger equations, since the equations are the most important models of modern nonlinear science. They appear not only in optical communication, but also in many branches of physics, such as nonlinear quantum field theory, magnetism, nonlinear optics and Bose-Einstein condensed matter et al.In the dissertation, based on the generalized nonlinear Schrodinger equation with variable coefficients, the generalized cubic-quintic nonlinear Schrodinger equation with variable coefficients, and the higher-order nonlinear Schrodinger equation with variable coefficients, by taking variable parameter fiber systems as application background, analytically and numerically, we investigate the transmission of picosecond optical pulses in variable parameter fiber systems, the transmission of chirped picosecond optical pulses in variable parameter fiber systems, the transmission of picosecond pulses with high optical intensities in variable parameter fiber systems, the transmission of femtosecond optical pulses in variable parameter fiber systems, and the propagation of light in nonlinear optical media with nonperiodic modulation. The results obtained here and the methods used here may be helpful to provide some theoretical bases for studying the stable transmission of optical pulses in real optical soliton control systems or inhomogeneous fiber systems. The main contents are as follows:(1) Based on the generalized nonlinear Schrodinger equation with variable coefficients, from the integrable point of view, by employing simple, straightforward Darboux transformation, we obtain an exact multi-soliton solution of the generalized nonlinear Schrodinger equation with variable coefficients. Because the solutions include arbitrary distributed functions, thus by choosing different form in them, one can explain or design the various soliton controls. That is, one can investigate the transmission of picosecond optical pulses in variable parameter fiber systems. As an example, by the solutions, we consider the transmission of picosecond soliton pulses in an exponential distributed fiber control system and in a periodic distributed amplification system. Furthermore, the interaction between two neighboring soliton pulses is investigated. The results reveal that the combined effects of controlling both the group velocity dispersion distribution and the nonlinearity distribution can restrict the interaction between the neighboring solitons. It is advantageous to increase the information bit rate in optical soliton communications. Also, with the aid of the numerical simulation, we analyze stability of the transmission with respect to the finite initial perturbations, such as white noise and weak background perturbation, and under nonintegrable condition. The results reveal that the transmission is stable, which provides some theoretical bases for further experimental confirmation. Finally, we present exact dark multi-soliton solutions of the generalized nonlinear Schrodinger equation with variable coefficients, and discuss the transmission. The results are useful not only in variable parameter optical soliton communication, but also in theoretical and experimental study of other physical problems.(2) Based on the generalized nonlinear Schrodinger equation with variable coefficients, by using an appropriate mapping, exact chirped multi-soliton solutions of the nonlinear Schrodinger equation with variable coefficients are found. As an example, we consider an exponential distributed fiber control system, and demonstrate the main character of exact solutions. It is found that chirped soliton pulses can all be nonlinearly compressed cleanly and efficiently in the exponential distributed fiber control system with no loss or gain, with the loss, or with the gain. Furthermore, under the same initial condition, compression of optical soliton in the optical fiber with the loss is the most dramatic. This is useful to the new design of pulse compression. In addition, we numerically analyze stability of the transmission under the finite initial perturbations and under nonintegrable condition. The results provide some theoretical bases for further experimental confirmation.(3) Based on the generalized cubic-quintic nonlinear Schrodinger equation with variable coefficients, under certain parametric conditions, we present exact bright and dark solitary wave solutions by ansatz method. These solutions are useful not only in the design of soliton control and management with high optical intensities, but also in the study of other problems, such as waveguides with saturable nonlinearity. As an example, by the solutions, the transmission of picosecond solitary wave pulses with high optical intensities in a periodic distributed amplification system is studied in detail. Then, we numerically analyze stability of the transmission with respect to the finite initial perturbations and parametric condition perturbations. The results reveal that the perturbations could not influence the main character of the transmission. Finally, we analyze the interaction between solitary waves in variable parameter fiber systems, such as hyperbolically decreasing dispersion fiber system. The results reveal that the combined effects of intentional controlling both the group velocity dispersion distribution, the nonlinearity distribution, and higher-order nonlinearity distribution can restrict the interaction between neighboring solitary waves to some extent. This provides some theoretical bases for extensive applications to optical transmission.(4) Furthermore, we investigate the transmission of femtosecond optical pulses in variable parameter fiber systems, starting from the higher-order nonlinear Schrodinger equation with variable coefficients under two sets of parametric conditions. The exact one-soliton solution is presented by the ansatz method for one set of parametric conditions. For the other, exact multi-soliton solutions are presented by employing the Darboux transformation. As an example, by the solutions, we study the transmission of femtosecond soliton pulses in a soliton control system, and we discuss the interaction of femtosecond soliton pulses. Stability of the transmission is also discussed by numerical simulation in detail. The results show that the soliton control system may relax the limitations to parametric conditions. And the transmission is stable. Finally, we discuss the transmission of dark femtosecond pulses in variable parameter fiber systems. The results are important to femtosecond soliton communication, and other branches of physics.(5) Finally, we consider the propagation of light in nonlinear optical media with nonperiodic modulation. The problem is governed by the generalized nonlinear Schrodinger equation with nonperiodic transverse modulation. We consider the equation and obtain exact solutions. By the solutions, we discuss a series of new optical nonlinear effects. For example, we could control arbitrarily the velocity of spatial solitary wave, namely, the output direction of light by adjusting the parameters. The results are useful to design optical devices and understand some interesting physical phenomenon in other branches of physics.