Study On Modulation Instabilities Induced By The Cross-phase Modulation Effects In Metamaterials

Metamaterial (MM) is a new type of artificial electromagnetic material, and has electromagnetic properties that are not found in nature and can be artificially tuned at will. MMs can be used to control the propagation of electromagnetic waves resulting in novel electromagnetic phenomena. Thus, the study on the interaction between MM and electromagnetic wave not only has important scientific significance, but also has vital values of practical application for the design of communication systems. In this paper, the cross-phase modulation (XPM) induced modulation instabilities (MIs) of electromagnetic wave in MMs are investigated by combining the conventional nonlinear optical theory and the novel properties of MMs, the obtained results are listed below:First, nonlinear coupled equations describing the copropagation of two electromagnetic pulses of different central frequencies in MMs are derived, based on the Drude model, the characteristics of XPM induced MIs (XMIs) are analyzed when both pulses copropagate simultaneously in the positive-refractive region, negative-refractive region and two pulses copropagate in different refractive index regions of MMs. It is shown that, in the absence of group-velocity mismatch, the property of MI only depends on the sign of group-velocity dispersion the two pulses experience, irrespective of the sign of refractive index. The group-velocity mismatch plays an important role in the occurrence of MI, especially when the centre frequencies of the two pulses near the electric or magnetic plasma frequency of the MMs. The theoretical results are confirmed by numerical simulations.Second, we disclose the influence of the anomalous self-steeping (SS) on XMIs. The gain expression of XMI considering the SS effect is calculated by the standard linear-stability analysis, and the influence of the anomalous SS resulting from the dispersive and controllable magnetic permeability in MMs on XMIs is detailed analyzed, when both pulses copropagate simultaneously in the positive-refractive region, negative-refractive region and two pulses copropagate in different refractive index regions. It is shown that, the SS effect enhances and then decreases the gains when both pulses experience normal group-velocity dispersion of negative-refractive region, different from other cases the SS restrains the XMI when both pulses copropagate in the same refractive region; the most abnormal phenomena is that the critical frequency of XMI is not start at zero but shifts to the higher frequencies in the case that two pulses copropagate in different refractive region. Numerical simulations confirm the obtained theoretical results and show that negative self-steepening moves the center of the generated pulse toward the leading side, opposite to the case of ordinary positive self-steepening.Third, we investigate the XPM effect of electric field and magnetic field and find when the electromagnetic wave frequency far away the band edges XPM promotes the occurrence of spatial MI, when the electromagnetic wave frequency near the band edges, only nonlinear polarization or nonlinear magnetization solely affects the spatial MI, which is induced by self-phase modulation. Moreover, both linear loss and nonlinear loss decrease the peak gain and compress the spatial bandwidth of MI.