Rch On Modulatlon Instablliles And Slltons Propagation In Metamaterlals

The metamaterial (MM) is a kind of artificial synthetic material, which displays properties beyond those available in naturally occurring materials. As metamaterial in the near IR and optical range has been experimentally demonstrated, it has important influence on the field of electromagnetics, optics, material and communication, which will expand these fields greatly. In this paper, the nonlinear propagation properties for electromagnetic wave in nonlinear MMs are investigated by combining the basic theory of conventional nonlinear fiber optics and the novel properties of metamaterials. We obtained the formation condition and the propagation properties of bright and dark soliton in MMs, and then we study the coupling propagation of two beams in the MMs. The main research results are listed below:Firstly, by combining the generalized nonlinear Schr?dinger equation derivation methods and the properties of metamaterials, a theoretical model for electromagnetic wave copropagation in metamaterials is built. It is disclosed that there will occur new nonlinear terms including the additional self-steepening and second-order nonlinear dispersion effect, which will have effects on the propagation of electromagnetic wave.Secondly, based on the theoretical model, the expression for the gain of modulation instability in metamaterials is obtained by a standard linear stability analysis. As an example, it is applied to the Drude model to study the modulation instability features of the central frequency are in the positive-index region and negative-index region of MMs respectively, and the role of the additional self-steepening effect, second-order nonlinear dispersion effect, and pseudo five order nonlinear effect on the modulation instability are particularly analysed. The results show that that modulation instability (MI) may occur even in the normal group-velocity dispersion (GVD) regime and at the zero GVD point of the metamaterials (MMs). The physical origin of the MI is the additional second-order nonlinear dispersion term induced by the dispersive magnetic permeability, so the occuring of MI in zero GVD point broken this define, which provides a method for generating a train of ultrashort pulse in normal GVD regime, and there is significant value in the practical application. Thirdly, the exact solitary solutions of propagation equation of electromagneticwave are derived in metamaticals (MMs). Based on the solitary solutions, the influence of the additional self-steepening effect, second-order nonlinear dispersion effect, and pseudo five order nonlinear effect on the formation and propagation of the bright and dark electromagnetic solitons in the MMs is discussed. It is found that the bright and dark solitons can be formed in the case of anomalous linear group-velocity dispersion or normal linear group-velocity dispersion, even the dark solitons can be formed in the zero GVD point, which is gives new visual angle to soliton theory.Finally, a theoretical model for two beams copropagation in metamaterials is built. Based on a standard linear stability analysis, a detailed discussion on the role of the cross-phase modulation induced coupling between the beams in the transverse modulation instability (MI) in metamaterial (MM) is presented. Applied the model to Drude model, the MI when beams copropagate in the positive- and the negative-index region of the MMs respectively is studied. It is found that in the case of focusing nonlinearity, when the two beams both propagate in the positive- (negative-) index region, the transverse MI is equivalent with the temporal MI in optical fibers in the anomalous (normal) dispersion region; and when one beam propagates in the positive-index region and the other in the negative-index region, the transverse MI is equivalent with the temporal MI in the case of two pulse propagates in optical fibers in the anomalous and normal dispersion regions respectively. In the defocusing nonlinearity regime, the transverse MI can also find its temporal counterpart in optical fibers, which mean bright and dark electromagnetic spatial solitons may even generate simultaneously when beams copropagate in MM, which is a new way to generate spatial soliton pair for there is only leading to the generation of bright or dark spatial solitons in conventional material when two beams copropagate. And a numerical simulation is performed to the theoretical predictions.