Second-order calculation of the local density of states above a nanostructured surface

TL;DR

This paper develops a second-order perturbation method to calculate the local density of states above nanostructured surfaces, enabling better understanding of thermal near fields and the resolution limits of near-field thermal microscopy.

Contribution

It introduces a numerical implementation of a second-order perturbation series for electromagnetic fields above rough surfaces, extending previous first-order approaches.

Findings

Second-order contributions significantly affect the local density of states.

The method estimates the resolution limit of an idealized Near-Field Scanning Thermal Microscope.

Results show the importance of higher-order terms in thermal near-field calculations.

Abstract

We have numerically implemented a perturbation series for the scattered electromagnetic fields above rough surfaces, due to Greffet, allowing us to evaluate the local density of states to second order in the surface profile function. We present typical results for thermal near fields of surfaces with regular nanostructures, investigating the relative magnitude of the contributions appearing in successive orders. The method is then employed for estimating the resolution limit of an idealized Near-Field Scanning Thermal Microscope (NSThM).