Studies On Quasi-solitons And Dipole Solitary Wave In Metamaterials

Metamaterials(MMs)are a kind of artificial materials which can achieve special electromagnetic properties by adjusting the shapes and sizes of their structure units.MMs not only possess the dispersive permittivity and permeability,but have both negative permittivity and permeability simultaneously in certain ranges of frequencies,leading to negative refraction.In recent years,with the development of linear and nonlinear NIMs from microwave to optical frequencies,one dimension to multidimension,many experts and scholars focus on the investigation of ultrashort electromagnetic pulse propagation in MMs.In this paper,on the basis of the nonlinear Schrodinger equations(NLSEs)which describe the ultrashort pulse propagation in MMs,three exact new types of quasi-soliton solutions with the free parameters and one type of dipole solitary wave solution are presented by ansatz method.Using the Drude model,theoretically analyzed their formation conditions,existence regions and propagation properties.Finally,the stabilities of quasi-soliton and dipole solitary wave are discussed by numerical simulation.The research results of this paper provide a theoretical reference for exploring more types of solitary waves in MMs.The main contents of this paper are as below:(1)Briefly introduced the research backgrounds,current status and main applications of MMs,as well as the related researches of theories,experiments and soliton solutions for the ultrashort electromagnetic pulse propagation in MMs.(2)Three exact new types of quasi-soliton solutions are demonstrated by using ansatz method based on the generalized NLSE in MMs.Analytical studies show that by choosing the appropriate free parameter B,the bright,dark and bright-gray quasi-solitons may exist in the anomalous dispersion regimes of self-focusing positive index and self-defocusing negative index regions,and the bright and dark quasi-solitons may also respectively exis in the anomalous dispersion regimes of self-defocusing positive index,self-focusing negative index regions.Moreover,the bright-gray quasi-soliton can present the form of bright or gray soliton according to the value of B.Finally,as examples,the stabilities of the bright-gray quasi-soliton under the nonzero self-steepening parameters caused by frequency fluctuation and the finite pulse width perturbation are discussed.The results show that the stable propagation of bright-gray quasi-soliton can be achieved by adjusting the value of free parameter B.(3)An exact new type of combined solitary wave behaving dipole distribution is obtained by ansatz method in weakly nonlinear MMs with the third-order dispersion(TOD)and the fourth-order dispersion(FOD).Through the Drude model,the paper finds that the dipole solitary wave may exist in the normal dispersion regimes of self-focusing and self-defocusing negative index MMs,anomalous dispersion regimes of self-defocusing negative and positive index MMs.Moreover,Kerr nonlinearity only influences the existence regions of solitary wave,while the group-velocity dispersion,the TOD and the FOD play important roles in its existence regions and characteristics.It is also found that its propagation properties can be controlled by adjusting the frequency of incident waves.Finally,the stabilities of dipole solitary waves under the finite pulse width fluctuation and the white noise perturbation are numerically discussed.