The active tuning of surface waves supported by left-handed materials (LHMs) is a major challenge for their practical applications and usability, and graphene has been proposed as an agent for the active tuning of surface waves. In this study, tunable surface waves supported by graphene-layered LHM structures are investigated theoretically. The analytical and numerical results are computed for transverse electric (TE) and transverse magnetic (TM)-polarized surface waves. According to the spectral range, two configurations of LHMs (i.e., gigahertz (GHz)-LHM and terahertz (THz)-LHM) are discussed. The physical modeling of graphene is done using the conductivity model based on random phase approximation-based Kubo formalism. The split ring resonator (SRR) model and Kramers–Kronig relations-based causality principle are used for the physical realization of LHMs. To simulate the graphene-layered LHM interface, impedance boundary conditions (IBCs) are applied. Numerical results are computed for dispersion curves, effective wave numbers, and field profiles of surface waves supported by graphene-covered GHz-LHM and THz-LHM. The influence of graphene parameters on the resonance frequency, dispersion curves, and confinement characteristics of surface waves is analyzed for both configurations of LHMs. It is concluded that the graphene-covered GHz-LHM structure supports the tunable surface waves as surface plasmon polaritons (SPPs) support TM-polarized waves. However, with the TE-polarized surface wave, the structure supports the surface polaritons, which do not depend upon the graphene parameters. For the case of the graphene-covered THz-LHM structure, it is concluded that the structure supports the plasmon modes for both polarized waves and the resonance frequency ranges from THz to infrared (IR). The confinement of the TE-polarized surface waves on the graphene layer can be enhanced up to fourfold as compared to the suspended monolayer graphene by using a THz-LHM substrate. Further, the numerical results are found to be consistent with the literature under special conditions. The proposed graphene-layered LHM structure may have potential uses in the active tuning of surface waves, near-field communication and imaging devices, surface waveguide design, and LHM-based metasurfaces.

左手材料（LHM）支持的表面波的主动调谐是其实际应用和可用性的主要挑战，并且石墨烯已被提议作为表面波的主动调谐的代理。在这项研究中，理论上研究了石墨烯层状LHM结构所支撑的可调谐表面波。计算了横向电（TE）和横向磁（TM）极化的表面波的分析结果和数值结果。根据频谱范围，讨论了LHM的两种配置（即，千兆赫（GHz）-LHM和太赫兹（THz）-LHM）。石墨烯的物理建模是使用基于基于随机相位近似的Kubo形式主义的电导率模型完成的。裂环谐振器（SRR）模型和基于Kramers-Kronig关系的因果关系原理用于LHM的物理实现。为了模拟石墨烯层的LHM界面，应用了阻抗边界条件（IBC）。计算了色散曲线，有效波数和由石墨烯覆盖的GHz-LHM和THz-LHM支持的表面波的场轮廓的数值结果。分析了LHMs两种配置的石墨烯参数对共振频率，色散曲线和表面波限制特性的影响。结论是，石墨烯覆盖的GHz-LHM结构支持可调谐表面波，因为表面等离激元极化子（SPP）支持TM偏振波。但是，通过TE极化的表面波，该结构支持表面极化子，不依赖于石墨烯参数。对于石墨烯覆盖的THz-LHM结构，可以得出结论，该结构支持两种极化波的等离激元模式，共振频率范围从THz到红外（IR）。与使用THz-LHM衬底的悬浮单层石墨烯相比，石墨烯层上TE极化表面波的限制可以提高到四倍。此外，发现数值结果在特殊条件下与文献一致。所提出的石墨烯层状LHM结构在表面波的主动调谐，近场通信和成像设备，表面波导设计以及基于LHM的超颖表面中可能具有潜在用途。结论是该结构支持极化波的等离激元模式，共振频率范围从THz到红外（IR）。与使用THz-LHM衬底的悬浮单层石墨烯相比，石墨烯层上TE极化表面波的限制可以提高到四倍。此外，发现数值结果在特殊条件下与文献一致。所提出的石墨烯层状LHM结构在表面波的主动调谐，近场通信和成像设备，表面波导设计以及基于LHM的超颖表面中可能具有潜在用途。结论是该结构支持极化波的等离激元模式，共振频率范围从THz到红外（IR）。与使用THz-LHM衬底的悬浮单层石墨烯相比，石墨烯层上TE极化表面波的限制可以提高到四倍。此外，发现数值结果在特殊条件下与文献一致。所提出的石墨烯层状LHM结构在表面波的主动调谐，近场通信和成像设备，表面波导设计以及基于LHM的超颖表面中可能具有潜在用途。与使用THz-LHM衬底的悬浮单层石墨烯相比，石墨烯层上TE极化表面波的限制可以提高到四倍。此外，发现数值结果在特殊条件下与文献一致。所提出的石墨烯层状LHM结构在表面波的主动调谐，近场通信和成像设备，表面波导设计以及基于LHM的超颖表面中可能具有潜在用途。与使用THz-LHM衬底的悬浮单层石墨烯相比，石墨烯层上TE极化表面波的限制可以提高到四倍。此外，发现数值结果在特殊条件下与文献一致。所提出的石墨烯层状LHM结构在表面波的主动调谐，近场通信和成像设备，表面波导设计以及基于LHM的超颖表面中可能具有潜在用途。