Propagation Of Optical Dark Solitons In Metamaterials

Metamaterial,a new type of artificial material,is different from traditional materials due to its unique properties.After the structure of metamaterial is designed artificially,the dielectric constant and permeability of metamaterial can be changed,and the properties different from conventional materials can be obtained.The negative refractive index material with negative dielectric constant and negative permeability is the focus of our research.Metamaterials have many attractive applications,such as perfect lens,optical stealth technology and so on.Nowadays,some metamaterials can be produced in some ways,such as the use of very thin metal nanowire structure and periodic split ring resonator array structure.Metamaterials have attracted more and more scholars' attention.With the development of the research on metamaterials,more and more people are concerned about how to obtain stable optical pulses in metamaterials.The dispersion coefficient and nonlinear coefficient can be changed by modifying the structure of metamaterials,and the stable optical solitons can be obtained by adjusting the coefficient.This is one of the reasons for studying the propagation of optical solitons in metamaterials.The dark soliton has better anti-noise ability and stability than the bright soliton,and the amplitude attenuation and pulse broadening of the dark soliton are slower than the bright soliton,so the dark soliton may be a better choice in the future.The dispersion coefficient,nonlinear coefficient and self-steepness coefficient of metamaterials are correlated with the frequency of optical pulse,and there is a complex frequency dispersion relationship.At present,most of the researches on metamaterials assume very simple constants as the above coefficients,ignoring the complex dispersion relation,which reduces the reference value of the research work.Therefore,according to the dispersion relationship between the dispersion coefficient,nonlinear coefficient and self-steepness coefficient and the frequency of the optical pulse,we take the real values of these coefficients to study the dark soliton transmission.In this paper,we study the propagation of a single dark soliton and the interaction between fundamental-order dark solitons.Based on the nonlinear Schr(?)dinger equation and the lossless Drude model,the effects of nonlinearity,group velocity dispersion,third-order dispersion and self-steepening on dark soliton propagation under normal dispersion are studied by using the split-step Fourier method.By choosing the ratio of the group velocity dispersion length to the nonlinear length,the conditions for the stable propagation of dark solitons in metamaterials are obtained.A pair of solitons is closer to the real signal transmission than a single dark soliton.Therefore,we also study the interaction of a pair of fundamental-order dark solitons under the conditions of(1)same amplitude and same phase,(2)same amplitude and different phase and(3)different amplitude and same phase.It is observed whether the fundamental-order dark soliton pairs are also more stable than the fundamental-order bright soliton pairs,and that the fundamental-order dark soliton pairs exhibit different interaction characteristics under different conditions.Finally,a negative permeability material structure is designed to make the dark soliton stable long-distance transmission.The innovation of this paper is as follows:(1)The real and reliable parameters are obtained by Drude model.On this basis,the formation of single dark soliton in metamaterials medium,the balance between second-order dispersion and nonlinearity,and the influence of third-order dispersion are studied.The reason why dark soliton cannot be produced in anomalous dispersion region is analyzed,and the reason affecting the stability of dark soliton is discussed.(2)The interaction between solitons in soliton pairs closer to the real signal pulse sequence is studied.In the real Drude model,the effect of soliton spacing on the interaction between same-phase dark solitons with the same amplitude is discussed,and the interaction between different same-phase dark solitons with different amplitude and soliton spacing is discussed.And we analyze the performance of dark solitons with the same amplitude and different phases when the initial phase is different.(3)A design scheme of negative permeability material is proposed.The correlation curves of dispersion coefficient,nonlinear coefficient and self-steepness coefficient with normalized frequency " and square of normalized plasma frequency" ! " are drawn.According to the real part and imaginary part of " ! " which meet the conditions,determine the value range of ",finally through simulation,get a single dark soliton which can stably transmit for a long distance.