  Surface plasmons dominate the optical response of metal surfaces, and their
nature is controlled by surface geometry. Here we study metasurfaces containing
singularities in the form of sharp edges and characterized by three quantum
numbers despite the two-dimensional nature of the surface. We explore the
nature of the plasmonic excitations, their ability to generate large
concentrations of optical energy, and the transition from the discrete
excitation spectrum of a non-singular surface to the continuous spectrum of a
singular metasurface.
