Study Of Modulation Instabilities In Metamaterials

The metamaterial is produced artificially which are characterized by the dispersive permittivity and the dispersive permeability simultaneously, and its peculiar electromagnetic properties which the absolute absence of naturally occurring materials have important influence on the fields of electromagnetics, material, optics and communication and widen the traditional fields greatly.In this paper, firstly, we introduced the basic definition, characrteristics and construction of metamaterial, and we summaized respectively the study of microwave and optical frequency metamaterial both at home and abroad. In this part, we also gave a brief account of the main applications of metamaterial.Secondly, we adopted split-step Fourier method in this paper in ordrer to develop the numerical procedures of non-linear Schr?dinger equation, which describes the ultrashort pulse transmission in metamaterial. It set the foundation to the study of ultrashort pulse transimission of metamaterial. The implementations of these procedures were divided into three parts: data initialization; linear treatment; nonlinear treatment. Compared to the other methods, Fourier method is simple and higher accuracy.Thirdly, we obtained spectrum modulation instability expression of single, double pulse by using standard linear-stability analysis, then we combined the spectrum modulation instability expression with Drude dispersive model to study the influence of modulation instability under the effect of group-velocity dispersion and self-steepening.Finally, using two different frequencies respectively and with a perturbation of continuous light and chatter in the hyperbolic secant pulse of the metamaterial ,we simulated the situation when they transmit, and we confirmed that the occurence of modulation instability by using numerical simulation. At the same time,we found that the negative self-steepening moves the center of modulated wave of generated pulse toward the leading side, opposite to the case of positive self-steepening in ordinary material.