  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.
