What is the Smallest Volume Into Which Light Can Be Focused, Efficiently?

Electromagnetic waves, running in close proximity to a metal surface, can have surprisingly short wavelengths, as short as lambda=1 nm, at optical frequencies. Thus the phrase Optical frequencies but with X-ray wavelengths, is appropriate. In effect these plasmon waves can experience a high effective refractive index, nGt100, dependent on the exact guiding structure. We find moreover, that at these short wavelengths, the skin depth or exponential decay depth, inside the metal can be <1 nm, much shorter than the conventional collisionless skin depth, c/omega <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rho</sub> ~ 25 nm in Silver. We propose an innovative dimple geometry as a focusing structure that makes it possible to focus visible frequencies down to ~5 nm dimensions, with an efficiency of ~50%. This focusing structure is much more efficient, and leads to a much smaller spot size, than can be achieved with conventional pinhole structures. We introduce a new figure-of-merit for focusing that properly accounts for plasmonic energy dissipation. We find that the limit of focusing is reached when the electromagnetic plasmonic group velocity v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> becomes as slow as the electron Fermi velocity, v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</sub> .