Scaling in light scattering by sharp conical metal tips

TL;DR

This paper develops scaling relations for electromagnetic scattering by sharp conical metal tips, providing analytic expressions for field behavior and phase changes, with implications for nano-optical applications.

Contribution

It introduces new scaling laws and analytic formulas for light scattering by conical metal tips, validated through numerical simulations.

Findings

Scaling relations for scattered field amplitude and phase.

Analytic expression for wavelength where field direction reverses.

Field decay characteristics near the tip extremity.

Abstract

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.