Scaling in light scattering by sharp conical metal tips.

Using the electrostatic approximation, we analyze electromagnetic fields scattered by sharp conical metal tips, which are illuminated with light polarized along the tip axis. We establish scaling relations for the scattered field amplitude and phase, and verify the validity with numerical simulations. Analytic expressions for the wavelength at which the scattered field near the tip changes its direction and for the field decay near the tip extremity are obtained, relating these characteristics to the cone angle and metal permittivity. The results obtained have important implications for various tip-enhanced phenomena, ranging from Raman and scattering near-field imaging to photoemission spectroscopy and nano-optical trapping.