Anomalous Reflection Phase of Graphene Plasmons and its Influence on Resonators

TL;DR

This paper reveals that the reflection phase of high-momentum graphene plasmons at edges is approximately -3π/4, differing from the commonly assumed -π, affecting the design and understanding of plasmonic resonators.

Contribution

It demonstrates that the reflection phase for high-momentum graphene plasmons is approximately -3π/4, independent of various parameters, due to excitation of evanescent modes, which is a novel insight.

Findings

Reflection phase is approximately -3π/4 for high-momentum plasmons.

Reflection phase is independent of chemical potential, wavelength, and substrate.

Knowledge of the phase aids in estimating resonator properties.

Abstract

The phase picked up by a graphene plasmon upon scattering by an abrupt edge is commonly assumed to be $-\pi$. Here, it is demonstrated that for high plasmon momenta this reflection phase is $\approx -3\pi/4$, virtually independent on either chemical potential, wavelength or dielectric substrate. This non-trivial phase arises from a complex excitation of highly evanescent modes close to the edge, which are required to satisfy the continuity of electric and magnetic fields. A similar result for the reflection phase is expected for other two-dimensional systems supporting highly confined plasmons (very thin metal films, topological insulators, transition polaritonic layers, etc.). The knowledge of the reflection phase, combined with the phase picked up by the plasmon upon propagation, allows the estimation of resonator properties from the dispersion relation of plasmons in the infinite monolayer.