Extremely tight focusing of light at the nanoapex of a metal microtip

We study the focusing of an optical electromagnetic wave into a nanoscale spatial region in the vicinity of the nanoapex of a metal microtip, arising due to a convergent surface plasmon wave. The metal boundary near the nanoapex is approximated by a paraboloid of revolution. It is proved that an increase in the metal absorption in approaching the nanoapex, associated with an increase in the frequency of collisions of electrons with the surface, is an essential but not limiting factor for this method of light nanofocusing. It is shown that the minimum possible size of the focusing region can be about of 1 nm.