Nanofocusing by sharp edges

We show that the near-field nanofocusing of the electromagnetic field is possible to implement not only by means of metallic but also dielectric structures with sharp edges. The effect of the extraordinary enhancement of the longitudinal electric field component near the sharp edges of an optical element microrelief is shown using vector Rayleigh-Sommerfeld integrals. A finite element method is used for modeling the diffraction of the electromagnetic radiation by the edges of high-refractive-index metal and dielectric structures. It is shown that the focal spot size (full width at half-maximum) depends on the radius of curvature of the sharp tip. An optical scheme for sharp focusing, which consists of a concentrator collecting and directing the radiation onto a nanofocuser, is offered. A refractive axicon is suggested as the concentrator that directs the radiation on its vertex where an aluminium or silicon nanosphere is located (a nanofocuser). Illumination of this focuser by an optical vortex beam provides the nanofocusing with high diffraction efficiency. It is necessary to illuminate an axicon by a vortex beam of the first order or by a radially polarized beam. The scheme proposed is able to confine the radiation within a light spot of size l/400 at the half maximum of the intensity.