Extended frequency range of transverse-electric surface plasmon polaritons in graphene

TL;DR

This paper introduces a new method to analyze surface plasmon polaritons in graphene, extending the frequency range and revealing lossless propagation of transverse-electric modes at finite temperature.

Contribution

It proposes a novel approach calculating dispersion relations in complex frequency and real wave vector space, overcoming previous frequency limitations for TE modes in graphene.

Findings

Extended the frequency range of TE surface plasmon polaritons in graphene.

Demonstrated lossless TE mode propagation at finite temperature.

Provided an accurate analytic approximation for dispersion relations.

Abstract

The dispersion relation of surface plasmon polaritons in graphene that includes optical losses is often obtained for complex wave vectors while the frequencies are assumed to be real. This approach, however, is not suitable for describing the temporal dynamics of optical excitations and the spectral properties of graphene. Here, we propose an alternative approach that calculates the dispersion relation in the complex frequency and real wave vector space. This approach provides a clearer insight into the optical properties of a graphene layer and allows us to find the surface plasmon modes of a graphene sheet in the full frequency range, thus removing the earlier reported limitation (1.667 < $\hbar\omega/\mu$ < 2) for the transverse-electric mode. We further develop a simple analytic approximation which accurately describes the dispersion of the surface plasmon polariton modes in graphene. Using this approximation, we show that transverse-electric surface plasmon polaritons propagate along the graphene sheet without losses even at finite temperature.