Role Of Losses And Nonlinear Magnetic Susceptibility In The Modulational Instability In Nonlinear Metamaterials

Modulation instability is an important and universal phenomenon in nonlinear optics,from the discovery,has been the focus of attention of the scholars at home and abroad.Especially,the solitary waves caused by modulation instability can remain high stability during transmission,which makes solitary waves has been a hot topic in the field of optical communication.Metamaterials is a new type of artificial material;its unique electromagnetic response can make the permittivity and permeability become simultaneously negative,which makes it possible to demonstrate many unique electromagnetic properties.This paper is based on the special environment of metamaterials,to explore the transmission characteristics of modulation instability in metamaterials,to reveal the method of human-controlled modulation instability that takes place in metamaterials,to provide theoretical basis for application of metamaterials.The main results of this paper are summarized as follows:First of all,we based on the Drude model,introducing nonlinear electric susceptibility,nonlinear magnetic susceptibility and linear losses,rewrite the parameters in metamaterials.Then,on the basis of Maxwell's equations,we deduce the transmission model of lossy metamaterials,the parameters of the model are defined as nonlinear coefficient and nonlinear absorption coefficient.Secondly,we discuss the influence of nonlinear electric susceptibility,nonlinear magnetic susceptibility and linear losses on nonlinear coefficient and nonlinear absorption coefficient.We find that,on the part of contribution to nonlinear coefficient and nonlinear absorption coefficient,the nonlinear magnetic susceptibility can play a role with the nonlinear electric susceptibility of the same.However,when it is in the negative refraction region,the nonlinear magnetic susceptibility makes more contribution to nonlinear absorption coefficient.Also,the result shows us that the dielectric loss will reduce the value of nonlinear coefficient,but can contribute to the nonlinear absorption coefficient of growth.Thus,we conclude that,due to the design of metamaterials,we can control the basic parameters of metamaterials,which means to control the nonlinear phenomena and nonlinear absorption phenomena in the dielectric in the same time.Then,under the conventional nonlinear optical theory and our theoretical transmission model,we assume that nonlinear effects and nonlinear absorption effects exists only in the dielectric,deriving two modulation instability gain expressions based on the assumption and then,the modulation instability in positive refraction region and negative refraction region has also been well studied.The research results tell us that,firstly,because of the negative refraction in dielectric,the nonlinear magnetic susceptibility can replace the nonlinear electric susceptibility to make a contribution to modulation instability in negative refraction region.Even in self-defocusing region,modulation instability can also occur,which cannot be imaged in common dielectric.Secondly,through the contrast of the modulation instability under the two cases,we also find that nonlinear effects can increase the modulation instability gain and bandwidth,while the main effect of the nonlinear absorption is seen to be a decrease of the gain and bandwidth.In this paper,we adopt the latest confluent hypergeometric function to analyze the influence of the two kinds of coefficient on modulation instability gain and bandwidth,and also get the same conclusion.Thus,through controlling the nonlinear electric susceptibility and nonlinear magnetic susceptibility of the metamaterials,we can get the different modulation instability.Finally,the impact of loss of modulation instability in metamaterials has also been discussed.Along with the increase of the losses,the gain and bandwidth of modulation instability will decrease obviously.