This paper presents a theoretical study on the propagation of electromagnetic surface waves supported by the metamaterial-filled bi-layered graphene structure. The effective surface conductivity approach based upon the Kubo’s formalism is used to model the atomically thick graphene layer, while the analytical modeling of the metamaterials used the framework of causality principle-based Kramers-Kroing relations. With respect to the index of refraction, the two configurations of metamaterials have been considered—i.e., double positive (DPS) and double negative (DNG). The impedance boundary conditions (IBCs) have been employed at the interface for the computation of characteristics equations of odd and even surface modes under DPS and DNG configurations. The numerical results regarding the dispersion relations, effective mode index, and phase speed for the odd and even modes of electromagnetic surface waves supported by each configuration of structure have been presented. Further, the influence of chemical potential and thickness of metamaterial filling in parallel graphene layers on the wave propagation characteristics has been analyzed. To check the accuracy of the numerical results, special conditions were employed, which converge to the published results. The proposed work may have potential applications in plasmonic based logic designs, renewable energy devices, THz surface wave guides, and near-field communication devices.

本文提出了由超材料填充的双层石墨烯结构支撑的电磁表面波传播的理论研究。使用基于Kubo形式主义的有效表面电导率方法对原子厚的石墨烯层进行建模，而对超材料的分析建模则使用基于因果原理的Kramers-Kroing关系框架。关于折射率，已经考虑了超材料的两种配置-即双正（DPS）和双负（DNG）。在DPS和DNG配置下，在界面上采用了阻抗边界条件（IBC）来计算奇数和偶数表面模式的特征方程。有关色散关系，有效模式指数的数值结果，提出了每种结构形式所支持的电磁表面波奇数和偶数模式的相速度。此外，已经分析了化学势和平行石墨烯层中填充的超材料的厚度对波传播特性的影响。为了检查数值结果的准确性，采用了特殊条件，这些条件收敛到已发布的结果。拟议的工作可能在基于等离激元的逻辑设计，可再生能源设备，太赫兹表面波导和近场通信设备中具有潜在的应用。分析了平行石墨烯层中化学势和超材料填充厚度对波传播特性的影响。为了检查数值结果的准确性，采用了特殊条件，这些条件收敛到已发布的结果。拟议的工作可能在基于等离激元的逻辑设计，可再生能源设备，太赫兹表面波导和近场通信设备中具有潜在的应用。分析了平行石墨烯层中化学势和超材料填充厚度对波传播特性的影响。为了检查数值结果的准确性，采用了特殊条件，这些条件收敛到已发布的结果。拟议的工作可能在基于等离激元的逻辑设计，可再生能源设备，太赫兹表面波导和近场通信设备中具有潜在的应用。