Focusing of light at the nanoapex of a metal microtip located above the plane of a dielectric or metal

We study the focusing of the optical electromagnetic radiation energy into a nanoscale spatial region in the vicinity of the nanoapex of a metal microtip located near a dielectric or metal plane. Focusing arises from a symmetric convergence of a surface plasmon TM wave at the nanoapex. The metal boundary near the nanoapex is approximated by a paraboloid of revolution. A numerical model, based on the method of moments, is developed to find the electric field near the tip apex. Calculation results show that, compared to a single tip, the presence of a plane leads to an additional concentration of the electric field near the nanoapex.