Propagation length control of graphene surface plasmon polaritons using metamaterial substrate with near-zero refractive index

Abstract This study aims to investigate the conditions necessary to control, enhance, and modify the propagation length of graphene surface plasmon polaritons (SPPs) at room temperature, using an all-dielectric metamaterial substrate in comparison to suspended graphene. The analysis is conducted within a photonic crystal framework using COMSOL Multiphysics software to study the resonant modes of the all-dielectric metamaterial. Our results confirm the existence of a near-zero effective refractive index (NZERI) regime at the $\Gamma\text{-point }$ in the photonic crystal approach. In this NZERI regime, triply degenerate eigenmodes occurs in a certain frequency range when the effective refractive index of the metasurface approaches zero. Our central idea is that the NZERI regime in the all-dielectric metasurface of a graphene substrate can be used to control, enhance, and modify of SPPs the propagation . We applied several independent theoretical methods to obtain the effective refractive index of a metasurface in the NZERI frequency range for metasurface structures with a graphene layer. the simulation results demonstrate that the effective permittivity and permeability simultaneously attain near-zero values at closely spaced yet distinct frequencies, thereby establishing spectral regions with an effectively vanishing refractive index. 
Key contributions include the first demonstration of NZERI metasurfaces as graphene-supporting platforms for enhancing SPPs, a quantitative approach to balancing propagation distance and field confinement, and practical design guidelines that align with the current nanofabrication capabilities.
Our simulations further demonstrate that when graphene is placed on (or between two) all-dielectric metasurfaces operating in the NZERI regime, the SPP propagation length can be significantly increased.