Surface plasmons and singularities.

We apply the conformal transformation technique to study systematically a variety of singular plasmonic structures, including two-dimensional sharp edges, rough surfaces, and nanocrescents. These structures are shown to exhibit two distinct features. First, different from a planar metallic surface, the surface plasmon excitations on the examined structures have a lower bound cutoff at a finite frequency; second, the electric field diverges below a critical frequency even when metallic losses are considered. For rough surfaces and open-crescent nanostructures, the influence of the structure shapes on the absorbance characteristics is also discussed. Our analysis gives a unique insight into the light capture process on singular structures and holds the promise of detection of single molecules and greatly enhanced nonlinear effects.