Plasmon Resonances of Graphene-Dielectric-Metal Structures Calculated by the Method of Recurrence Relations

Gerardo Gonzalez De La Cruz,Maurice Oliva-Leyva

doi:10.1007/s11468-021-01466-x

Abstract

Graphene supports surface plasmons in the terahertz range, and compared with noble-metal plasmons, they show an extreme level of field confinement and relatively long propagation distances, with the advantage of being highly tunable via electrostatic field. Nevertheless, its interaction with light is normally rather weak. To obtain a more powerful capability of excite plasmons, a combination of graphene and artificial structures (metamaterials) present a powerful tunability for enhancing light-matter interaction. These features make graphene metamaterials a promising candidate for plasmonics and surface plasmon resonance for biological sensors. In this work, we study the plasmon spectra in a finite number of graphene layers on a metallic-dielectric substrate surrounded by materials with different dielectric constants. It is shown that using standard electromagnetic boundary conditions and solving the recurrence relation (a suitable alternative to transfer matrix method) for the coefficients of the electric potential between graphene layers, an explicit effective dielectric function of the metamaterial can be obtained giving the plasmon dispersion relations. It is found that the metal-dielectric-layered graphene structure supports both high-energy optical plasmon oscillations and out-of-phase low-energy acoustic charge density excitations. Experimentally, the Kretschmann configuration can be used to excite the surface plasmon resonances. It is based on the observation of a sharp minimum in the reflection coefficient versus angle (or wavelength) curve.

Highlights

Surface waves propagating along the boundary between a metal and dielectric medium are called surface plasmons
Long-range Coulomb interactions in the metamaterial lead new set spectra of surface plasmons, which depend on a certain characteristic parameters of each material in metal-dielectric-layered graphene structure
The acoustic plasmons emerge in this metamaterial structure characterized by a linear dependence on the momentum, which can be observed by electron energy los spectroscopy (EELS)

Summary

Introduction

Surface waves propagating along the boundary between a metal and dielectric medium are called surface plasmons. The field confinement of these reported metamaterials are relatively weak and exhibit high intrinsic dissipative losses with strong damping of surface plasmons and slow damage by chemical action [7]. To overcome these shortcomings, improvement research of new physical mechanisms and better electronic and optical properties has been achieve for new plasmonic materials, among them, graphene has emerged as an alternative, unique twodimensional material able to extend the field of plasmonics for terahertz to mid-infrared applications [8,9,10,11]. The recurrence method offers an alternative method to study plasmon modes in multilayer structures

Theoretical approach

Numerical results

Conclusions