Tunable surface waves supported by graphene-covered left-handed material structures

Abstract

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.