# Strength of the electric field in apertureless near-field optical microscopy

## Abstract

Enhancement y of the electrical field at the end of a tip relative to the incident field in a focused radiation beam is calculated by the finite-element time-domain (FETD) method. First, the reliability of the FETD method is established by calculating the electric field on simple structures like thin cylinders, spheres, and ellipsoids, and comparing the results with analytical solutions. The calculations on these test structures also reveal that phase retardation effects substantially modify y when the size of the structure is larger than approximately λ/4, λ being the radiation wavelength. For plasmon resonance, in particular, phase retardation severely reduces the resonance and the expected field enhancement for a gold tip. The small value of λ= 4 calculated by FETD is about an order of magnitude smaller than the value found in recent published work. Resonance effects can be recovered for special tips, which have a discontinuity or a different material composition at the end of the tip. Some tuning of the discontinuity dimension is needed to maximize the resonance. Under optimal conditions for plasmon resonance, an enhancement in the electric field of about 50 is calculated at the end of a small gold protrusion mounted on a wider silicon or glass tip. © 2001 American Institute of Physics.