Research On Composite Waves In PT Symmetric Nonlocal Nonlinear Coupled System

Beam interference patterned surface has important applications in light reflection,light diffusion and light absorption etc.How to produce diverse and high-precision optical patterns and how to produce these patterns simply and efficiently has been a key problem in the field of micro and nano machining.Based on the interference of composite waves in Pt-symmetric nonlocal nonlinear coupled systems,the formation and regulation of various beam interference patterns are studied theoretically.Because the interaction between the two components of the composite beams leads to complex and interesting properties,a series of rich interference patterns are obtained in this thesis.The interference patterns can be applied to optical etching,optical printing and fine machining,and can be used as theoretical support for simple and effective preparation of patterned surfaces.In this thesis,based on the coupled PT symmetric nonlocal nonlinear Schr?dinger equation,we introduced a general linear transformation and constructed the composite wave solutions of the nonlocal nonlinear coupled system.Based on these composite wave solutions,we studied the interference phenomena of Airy and Gaussian beam in nonlocal nonlinear coupled systems and the rich transmission characteristics of various nonlinear composite waves,such as bright-dark,bright-bright,dark-dark composite waves,rogue wave-rogue wave and soliton wave-breather etc.The specific research content of this thesis is as follows:1.Based on the coupled nonlocal PT symmetric system,by introducing a general linear transformation the coupled nonlocal system can be decoupled into two linear diffraction equations under the balance of nonlinear effects.Through the Fourier transform,the Airy and Gaussian solutions of the two linear equations are obtained.Based on these exact solutions and the introduced linear transformation,we studied the interference of Gaussian beam string,two Gaussian beams with the same or opposite chirp,Airy beams with the same or opposite self-acceleration,Gaussian beam and Airy beam.The rich interference patterns of Gaussian beam and Airy beam in coupled nonlocal PT symmetric system can be applied to optical etching or optical printing.2.Based on the PT symmetric nonlocal nonlinear system with nonlocal cross-phase modulation,self-phase modulation,and four-wave mixing,by introducing a linear transformation with the information of amplitude-phase modulation,the coupled system can be decoupled into two PT symmetric nonlocal nonlinear Schr?dinger equations(n NLSE)under certain constraints.By using the exact soliton solutions of the PT symmetric n NLSE and the introduced linear transformation,we studied the amplitude-phase modulation characteristics of the composite waves and the evolution of the composite bright-dark,bright-bright and dark-dark waves,which are difficult to realize in local systems.The results in the chapter provide a theoretical basis for the interaction between bright and dark solitons in nonlocal systems.3.Based on the linear transformation with amplitude-phase modulation information obtained in the previous chapter and the exact solutions of the nonlocal nonlinear equations with self-induced PT symmetric potential,such as breather solution,rogue wave and periodic soliton solution etc.,the rich evolution patterns of complex waves composed of rogue wave-rogue wave,dark soliton-Ma-breathers,bright/dark solitons-periodic solitons,and soliton lattice-soliton lattice are studied.These special composite waves exhibit various evolution patterns,such as triangle,rectangle,square and hexagon etc.It is worth mentioning that,due to the arbitrariness of linear transformation parameters and the diversity of exact solutions,there are an infinite number of composite wave solutions in nonlocal nonlinear coupled systems in theory.This research has enriched the theory of beam transmission in nonlocal systems.