Study On Propagation Characteristics Of Temporal Optical Solitons Based On Nonlinear Schr(?)dinger Equation

Starting from different optical fibers and different models,this thesis studies the transmission of fractional temporal optical solitons and vector temporal optical solitons in optical fibers by using fractional mapping method,Hirota method,split-step Fourier method,pseudo-spectral method and deep learning method,which provides a theoretical basis to realize optical information transmission of ultra-high speed and large capacity.(1)A fractional nonlinear Schr(?)dinger equation with distributed coefficients is considered to describe the propagation of pi-second pulses in inhomogeneous fiber systems.However,soliton molecules based on the fractional nonlinear Schr(?)dinger equation are hardly reported although many fractional soliton structures have been studied.Analytical chirp-free and chirped non-travelling wave solutions and multi-soliton approximate solutions of this model are obtained by two analytical methods,including the variable-coefficient fractional mapping method and Hirota method.The form conditions of soliton molecules are given,and the dynamical characteristics and interactions between special fractional solitons,multi-solitons and soliton molecules are discussed in the periodic inhomogeneous fiber and the exponentially dispersion decreasing fiber.These results have theoretical guidance for the related experimental study in all-optical switches,optical amplifier and mode-locked lasers.(2)We use a modified physics-informed neural network to predict the dynamics of optical pulses including one-soliton,rogue wave,and two-soliton based on the coupled nonlinear Schr(?)dinger equation in birefringent fibers.The network includes multiple parallel structures to solve the coupled complex function partial differential equations.Meanwhile,we predict the elastic collision process of the mixed bright-dark soliton.Compared the exact solution with the predicted results,the modified physics-informed neural network method is proved to be effective for solving the coupled nonlinear Schr(?)dinger equation.This provides a reference for us to use deep learning methods to study the dynamic characteristics of solitons in optical fibers.In addition,this research has important theoretical value for soliton wavelength division multiplexing,multi-channel optical fiber networks and so on.(3)The energy conservation law is introduced into the loss function of the physics-informed neural network,and an energy-conservation deep learning method is constructed to study the coupled nonlinear Schr(?)dinger equation.Using the energy-conservation deep learning method,we analyze the formation mechanism of vector solitons in birefringent fibers,and predict the dynamic behaviors of vector solitons,including one-soliton,two-soliton interaction,soliton molecule,rogue wave,and nondegenerate soliton.The related physical processes such as the energy conversion and power conservation along the propagation of soliton are studied.Compared with the physics-informed neural network method,the energy-conservation deep learning has higher accuracy and good generalization ability for a variety of soliton pulse propagation scenarios in optical fiber.Therefore,the deep learning method based on the prior knowledge of energy conservation is an effective tool to promote the research of nonlinear optics.