Analytical solution for the diffraction of an electromagnetic wave by a graphene grating

TL;DR

This paper presents an analytical approach to model the diffraction of electromagnetic waves by a periodically modulated graphene sheet, providing explicit formulas for optical coefficients and plasmon properties, validated by numerical simulations.

Contribution

It introduces a novel analytical method considering both interface corrugation and conductivity modulation for graphene diffraction analysis.

Findings

Explicit expressions for reflection, transmission, absorption, and transformation coefficients.

Derived dispersion relation and decay rates for graphene plasmons.

Identified optimal parameters for matching incident light with graphene plasmons.

Abstract

An analytical method for diffraction of a plane electromagnetic wave at periodically-modulated graphene sheet is presented. Both interface corrugation and periodical change in the optical conductivity are considered. Explicit expressions for reflection, transmission, absorption and transformation coefficients in arbitrary diffraction orders are presented. The dispersion relation and decay rates for graphene plasmons of the grating are found. Simple analytical expressions for the value of the band gap in the vicinity of the first Brillouin zone edge is derived. The optimal amplitude and wavelength, guaranteeing the best matching of the incident light with graphene plasmons are found for the conductivity grating. The analytical results are in a good agreement with first-principle numeric simulations.