Generalized spectral method for near-field optical microscopy

TL;DR

This paper develops a generalized spectral method to analyze electromagnetic interactions in near-field optical microscopy, revealing how probe shape and material properties influence resonance behavior and spectral features.

Contribution

It introduces an efficient numerical approach for calculating surface polariton resonances for various probe geometries, including large and strongly momentum-dependent cases.

Findings

Resonance parameters depend on probe shape and surface reflectivity.

Highly resonant materials exhibit multi-peak spectra and nonmonotonic distance dependence.

Spheroidal models are reliable for less resonant materials like silicon oxide.

Abstract

Electromagnetic interaction between a sub-wavelength particle (the `probe') and a material surface (the `sample') is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe, as well as the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials such as aluminum oxide (by itself or covered with graphene) reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with the radiative damping included perturbatively.