超材料中精确的空间啁啾暗孤子解及其传输特性

Exact Solution of Spatial Chirped Dark Soliton in Metamaterials and Its Propagation Characteristics

采用Hirota方法研究了描述超材料中电磁波传输的非线性薛定谔方程,解析得到了线性增益和非线性吸收平衡下两个精确的空间啁啾暗孤子解:暗孤子I(DSI)和暗孤子II(DSII)。基于Drude模型,研究了DSI和DSII在不同电和/或磁极化非线性超材料中的形成条件、存在区域和传输特性,并进行了数值验证。研究发现:存在于负折射区的DSI,传输过程中速度逐渐增加,而存在于正折射区的DSII,传输过程中速度逐渐减慢;DSI具有正的啁啾,而DSII具有负啁啾;DSII的波束宽度远小于DSI的波束宽度;DSI和DSII的背景幅度和半峰全宽由其系统模型的参数决定,因此与入射波的频率直接相关,在每种非线性情况下DSI和DSII的传输特性都不同。这些研究结果表明,通过选择不同的非线性超材料和入射电磁波频率可以控制啁啾暗孤子的传输特性。

The nonlinear Schr?dinger equation, which describes the propagation of electromagnetic waves in metamaterials(MMs), are studied by the Hirota method, and two exact spatially-chirped dark solitons, called Dark Soliton I(DSI) and Dark Soliton II(DSII), are obtained under the balance of linear gain and nonlinear absorption. Based on the Drude model, the formation conditions, the existence regions and the transmission characteristics of DSI and DSII in the nonlinear MMs with different electric and/or magnetic polarizations are investigated, and the analytical results are numerically verified as well. It is found that the speed of DSI existing in the negative refraction region gradually increases while the speed of DSII existing in the positive refraction region gradually decreases during the transmission. DSI has a positive chirp, while DSII has a negative chirp. In addition, the beam width of DSII is much smaller than that of DSI. Their background amplitudes and full widths at half maximum are determined by the model parameters, related to the incident wave frequency. Moreover, the transmission characteristics of DSI and DSII are quite different when the MMs are with different nonlinear polarizations. The obtained results indicate that the transmission properties of the chirped dark solitons can be controlled by selecting different nonlinear MMs or different incident wave frequencies.