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, whose validity is verified with numerical simulations. Analytic expressions for the wavelength, at which the scattered field near the tip changes its direction, and field decay near the tip extremity are obtained, relating these characteristics to the cone angle and metal permittivity. The results obtained have important implications to various tip-enhanced phenomena, ranging from Raman and scattering near-field imaging to photoemission spectroscopy and nano-optical trapping.