Modulation Instability Induced By Cross-Phase Modulation With Higher-Order Dispersions And Cubic-Quintic Nonlinearities In Metamaterials

Cross-phase modulation (XPM) instability is some modulation instability phenomenon due to the interaction of the nonlinear effect between beams which occurs when two or several light beams with different wavelengths transmission in the medium. Pulse compression, optical switch and the reciprocity effects caused by XPM have been used in optical communication devices. Metamaterials especially left-hand material (LHM) was first made out in2000, it attracted the attention of many scholars at home and abroad because its permittivity and permeability are both negative and its outstanding performance that ordinary materials do not have. The electromagnetic properties of metamaterials are dispersive, which make some of the theories applied in conventional media useless. Therefore, research of cross-phase modulation instability in metamaterials is very necessary.Modulation instability is mainly caused by dispersions and nonlinear effects, the research of conventional nonlinear materials has been perfect, but the research of the XPM when dual-beam transmission in metamaterials is still in low-level group velocity dispersion and low-level nonlinearity. There is little research in these aspects in metamaterials, therefore it is necessary to study the effects of higher-order dispersions and higher-order nonlinearities on cross-phase modulation instability in metamaterials.Starting from the expansion of coupled nonlinear Schrodinger equations, based on the lossless Drude dispersion model, through two beams of lights with same direction transmission in metamaterials considered higher-order dispersions and3rd-5th-order nonlinearities, this article deduced two gain equations of cross-phase modulation instability (XMI), one is in the case of group-velocity and third order dispersions are not equal and the other is both of them are equal. Through MATLAB simulation, we emphatically analyzed the effects of the higher-order dispersions to the production and gain spectrum of XMI.The innovation of this paper:(1). In research of cross-phase modulation in metamaterials, it’s the first time take higher-order dispersions and higher-order nonlinear effects into account at the same time;(2). Used method of variables separation to study the effect of the high-order dispersion coefficient individually in XMI in metamaterials.