Theoretical Investigation Of Optical Localized Wave And Transition In The Nonlinear Metamaterials

Recently,nonlinear localized waves on the plane-wave background has become a hot topic in many nonlinear physical systems.In the research field of traditional nonlinear optics,the fundamental theories and technologies have been mature during several years' development,scientists identified the significant application value of nonlinear localized waves.However,the correlative study on localized waves in nonlinear metamaterials has just started.Metamaterials are artificial structures that have peculiar properties which are absent in naturally occurring materials.And the special permittivity and permeability can be obtained through engineering the sizes and shapes of the microstructure.Metamaterials provides a new platform for propagation and evolution of nonlinear localized waves,the electromagnetic properties of Metamaterials offers us an alternative way to actively manipulate localized waves.In this thesis,we study optical localized waves on a plane-wave background in nonlinear metamaterials governed by the nonlinear Schr ¨odinger equation with self-steepening effect.By means of Darboux transformation,then we gain a generalized solution which describe many different localized waves,such as rogue wave,antidark-dark soliton pair,antidark soliton,and antidark soliton pair.Through the analysis of the solution,we find the transition between those structures are correlated with background amplitude a,background frequency q,nonlinear parameter g and self-steepening parameter S.To reveal generation mechanism and verify transition condition,modulation instability analysis method is introduced.In particular,our results illuminate the transition mechanism by establishing the exact correspondence between the transition and the modulation instability analysis.The propagation stability of the localized waves is confirmed numerically.Finally,the corresponding phase diagram is established in the both focusing and defocusing regime of metamaterials.These results will provide a theoretical reference on the excitation and management of different localized wave in metamaterials.