XPM-paired Solitons And Modulation Instability In Metamaterials

Light belongs to the family of electromagnetic wave.It is the ultimate means for sending information.Usually,we describe the properties of light with the electric field and the magnetic field components.However,in one sense,light just has "one hand",because when light interacted with the atoms of conventional materials,the interaction of atoms with the magnetic component of light is too weak,so we usually neglect it and just consider the contribution of the electric component.While metamaterials(MMs)broken the classical rule,MMs is artificial materials with rationally designed properties,can allow both field components of light to be coupled to meta-atoms,enabling entirely new optical properties and exciting applications with such "two-handed" light.MMs have many fantastic optical properties which is impossible in natural materials.In past ten years,MMs are widely researched for many interesting applications all over the world.It is expected to have an impact across the entire range of technologies where electromagnetic radiation is used,including wireless communication,optical communication,radar,super-resolution imaging,absorber and electromagnetic invisibility and so on.In recent years,nonlinear MMs have been realized and attracted much attention of researchers on the nonlinear propagation of electromagnetic wave.For the presence of dispersive permeability,MMs have rich nonlinear properties.Furthermore,the nonlinear coefficients of propagation equation in MMs can be tailored at will for our expected goals,combining the dependence of the permittivity and permeability on the intensity of the electromagnetic field,the transmission properties of electromagnetic wave in MMs can be controlled dynamically.Hence,under such important research background,combining the fascinating properties of MMs with the conventional nonlinear optical theory,we study the nonlinear propagation properties of electromagnetic wave including modulation instability and spatial XPM-paired solitons in MMs,to real the mechanism of the nonlinear response and some abnormal optical phenomenon,for the ultimate goal of new novel optoelectronic devices,the main innovative research results are listed below:Firstly,we investigate spatial XPM-paired solitons in nonlinear MMs based on the(1 +1)-dimensional coupled nonlinear Schrodinger equation(NLSE)describing the co-propagation of two optical beams of different frequencies in the MM with a Kerr-type nonlinear polarization.Three types of XPM-paired solitons including bright-bright,bright-dark and dark-dark solitons for different combination of the signs of refractive index experienced by the two beams,respectively,are obtained by using a generalized hyperbolic function method.We find that,(?)when both beams propagate in positive-index region,this case is as same as that in the conventional materials;(?)when both beams propagate in negative-index region,coupled bright-bright solitons can form for self-defocusing nonlinearity and coupled dark-dark solitons can form for self-focusing nonlinearity,which is contrary to that when both beams propagate in positive-index region;(?)More interestingly,when two beams propagate in different index regions,there exist particular bright-dark spatial soliton pairing,as is fully analogous to the temporal case when two pulses propagate in different dispersive regions.Furthermore,numerical simulations based on standard split-step Fourier method confirmed the theoretical results convictively.The results enrich the dynamic behaviors of electromagnetic wave propagation in MMs,and suggest new ways of generating optical solitons.Secondly,we investigate the time-domain modulation instability of ultra-short pulse in nonlinear metamaterials.The nonlinear propagation model of ultrashort pulses in metamaterials containing the Raman scattering effect is drived.Based on this model,the expression for the gain of modulation instability in metamaterials is obtained by a standard linear stability analysis,and then based on the instability gain spectrum of expression,by drawing the diagram of the gain,the impact of negative self-steep and second-order nonlinear dispersion effects combined Raman effect in metamaterials on the gain spectrum is qualitatively analyzed.The results show that,for self-focusing nonlinearity,Raman effect will make the pulses in both normal dispersion or anomalous dispersion region have gain with no cutoff frequency region,and with the enhancement of the Raman effect,the amplitude showing the gain increases monotonically with frequency will be larger;Furthermore,the second-order nonlinear dispersion effects always suppress the generation of modulation instability;finally,the role of the additional negative self-steepening has little effect on modulation instability in normal dispersion region,however,in the anomalous dispersion region,it will greatly suppress the occurrence of modulation instability.Modulation instability phenomena in metamaterials containing Raman effect in previous research work have not yet been reported.The findings have important guiding significance on many practical applications such as the generating of ultrashort light pulse train and the manipulation of solitons in future.