Research On Optimum Numerical Simulation Methods Of Nonlinear Schrodinger Equations In Optical Fibers

The research on the optical fibers and nonlinear phenomena in the optical fibers are more and more attractive with the booming development of fiber optic communication systems. Since the equation of optical fibers is a nonlinear Schrodinger equation which does not generally lend itself to analytic solutions, a simulation approach is necessary for an understanding of the behavior of optical pulses propagated in a optical fibe. A plenty of numerical simulation methods have been proposed for this purpose. Most of them can fall into two categories:the pseudospectral and finite-difference methods. Pseudospectral methods are generally faster than the finite-difference methods to obtain the same accuracy. A conventional method is the split-step Fourier method that has been employed extensively for simulating the pulse-propagation problem in nonlinear dispersive fibers. The factors influencing the performance of the split step Fourier method result from two aspects: how to implement the split step Fourier method and select the step size. This paper proposed a novel method that involves the local error method with minimum area mismatch and the fourth-order Runge-Kutta method in the interaction picture. In summary, the major work in this dissertation is as follows:(1) Simply deduce and summarize the nonlinear Schrodinger equation (NLSE) and generalized nonlinear Schrodinger equation (GNLSE) which govern the propagation of optical signals in single-mode fibers. The NLSE is often used in such case that the Raman effect is ignored and is able to interpret most of the nonlinear phenomena in optical fibers. The GNLSE includes the Raman and higher-order nonlinear effect.(2) To demonstrate the validity and performance of various Split-Step Methods, they are con-trasted with Finite-Difference Methods, analyzed and proved by using mathematical methods. Var-ious conventional numerical calculation algorithms are in detail compared on their accuracies and simulation cost.Each method has unique features. The symmetric split step Fourier methods is a better method than others. Computational cost and simulation accuracy are the criterions used to assess numerical calculation methods.(3) A novel simulation method, the local error method with minimum area mismatch combined with the fourth-order Runge-Kutta method in the interaction picture, is proposed. The loss term is combined with the nonlinear term of the nonlinear Schrodinger equation, which is different from conventional split step Fourier methods. The nonlinear term is numerically simulated by using the fourth-order Runge-Kutta method in the interaction picture in frequency domain. Various step-size selection methods which each have their own advantages and disadvantages are studied. In the local error method with minimum area mismatch combined with the fourth-order Runge-Kutta method in the interaction picture, the step size distribution depends on the local error with minimum area mismatch which is determined by the steepest descent method. This method is a higher efficiency, accuracy, user- and system-independent method.(4) It is demonstrated that the local error with minimum area mismatch combined with the fourth-order Runge-Kutta method is the best efficiency method in all of the methods discussed in this dissertation by simulating the femtosecond soliton, supercontinuum generation and an eight-channel wavelength division multiplexing system. By numerically calculating Wavelength Division Multiplexing systems that only involve the Kerr and third-order dispersion effects, and comparing the novel method proposed by this dissertation with the Uncertainty Principle Method, Local Error Method, Nonlinear Phase Rotation Method, Walk-off Method, it is verified that the novel method presented by this dissertation is the most efficient and user- and system-independent algorithm.