Diffraction by a small aperture in conical geometry: Application to metal coated tips used in near-field scanning optical microscopy

TL;DR

This paper presents an analytical model for light diffraction through a small aperture in a conical metallic structure, explaining the diffraction behavior of near-field optical tips used in microscopy.

Contribution

It develops a multipole expansion method to solve Maxwell's equations for conical geometries with real metal conductivity, extending understanding of diffraction in near-field microscopy.

Findings

Model accurately predicts diffraction patterns of conical tips.

Reveals that tips behave like combined electric and magnetic dipoles.

Explains the large backward emission observed in experiments.

Abstract

Light diffraction through a subwavelength aperture located at the apex of a metallic screen with conical geometry is investigated theoretically. A method based on a multipole field expansion is developed to solve Maxwell's equations analytically using boundary conditions adapted both for the conical geometry and for the finite conductivity of a real metal. The topological properties of the diffracted field are discussed in detail and compared to those of the field diffracted through a small aperture in a flat screen, i. e. the Bethe problem. The model is applied to coated, conically tapered optical fiber tips that are used in Near-Field Scanning Optical Microscopy. It is demonstrated that such tips behave over a large portion of space like a simple combination of two effective dipoles located in the apex plane (an electric dipole and a magnetic dipole parallel to the incident fields at the apex) whose exact expressions are determined. However, the large "backward" emission in the P plane - a salient experimental fact that remained unexplained so far - is recovered in our analysis which goes beyond the two-dipole approximation.