Field singularities and super-localized plasmons at sharp metal corners and tips

Electromagnetic field behavior near ideally sharp and controllably smoothed metal corners and tips is explored theoretically. We reveal the critical regions of the relative metal permittivity and the apex angle, where, independently of the smoothing radius, the light energy is strongly localized near the apex and the optical phase varies rapidly. Close quantitative links are established between such field singularities and the super-localized plasmon resonances in nano-scale metal particles, wires and surface perturbations possessing sharp shape features.