Communications in Mathematical Sciences

Volume 16 (2018)

Number 1

Generation of surface plasmon-polaritons by edge effects

Pages: 77 – 95



Matthias Maier (School of Mathematics, University of Minnesota Twin-Cities, Minneapolis, Mn., U.S.A.)

Dionisios Margetis (Department of Mathematics, Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, Md., U.S.A.)

Mitchell Luskin (School of Mathematics, University of Minnesota Twin-Cities, Minneapolis, Mn., U.S.A.)


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.


time-harmonic Maxwell’s equations, finite element method, surface plasmon-polariton, singular geometry, weak discontinuity on hypersurface

2010 Mathematics Subject Classification

65N30, 78A45, 78M10, 78M30

The first and third authors (MM and ML) were supported in part by ARO MURI Award W911NF-14-1-0247. The second author research was supported in part by NSF DMS-1412769.

Received 3 February 2017

Accepted 21 September 2017

Published 29 March 2018