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 in uence surface plasmons in nanophotonics.
Bibliographical noteFunding Information:
in part by ARO MURI Award W911NF-14-1-0247. The second author research was supported in part by NSF DMS-1412769.
- Finite element method
- Singular geometry
- Surface plasmon-polariton
- Time-harmonic Maxwell's equations
- Weak discontinuity on hypersurface