# Generation of surface plasmon-polaritons by edge effects

## TL;DR

This paper investigates how edges of atomically thin metamaterial sheets generate surface plasmon-polaritons, using numerical and analytical methods to understand their behavior and influence in nanophotonics.

## Contribution

It introduces a combined numerical and analytical approach to model edge-induced SPPs on 2D metamaterial sheets, highlighting the impact of geometry and conductivity changes.

## Key findings

- Edges act as sources of dominant SPPs.
- Sharp geometries significantly affect plasmon behavior.
- Adaptive mesh refinement improves simulation accuracy.

## Abstract

By using numerical and analytical methods, we describe the generation of fine-scale lateral electromagnetic waves, called surface plasmon-polaritons (SPPs), on atomically thick, metamaterial conducting sheets in two spatial dimensions (2D). Our computations capture the two-scale character of the total field and reveal how each edge of the sheet acts as a source of an SPP that may dominate the diffracted field. We use the finite element method to numerically implement a variational formulation for a weak discontinuity of the tangential magnetic field across a hypersurface. An adaptive, local mesh refinement strategy based on a posteriori error estimators is applied to resolve the pronounced two-scale character of wave propagation and radiation over the metamaterial sheet. We demonstrate by numerical examples how a singular geometry, e.g., sheets with sharp edges, and sharp spatial changes in the associated surface conductivity may significantly influence surface plasmons in nanophotonics.