Comment on "Imaging the Local Density of States of Optical Corrals"

TL;DR

This paper critically examines the interpretation of electromagnetic local density of states (LDOS) in optical corral imaging, arguing that the commonly used quantity ${f G}_{f u}$ is not the correct measure for SNOM images and proposing a more accurate alternative.

Contribution

The paper provides a rigorous Green-tensor analysis showing that ${f G}_{f u}$ is not the appropriate quantity for interpreting SNOM images, challenging previous assumptions.

Findings

${f G}_{f u}$ is not the correct key quantity for SNOM image interpretation.

Measurements should be compared with a different Green-tensor related quantity.

Using ${f G}_{f u}$ can lead to unphysical results.

Abstract

In a recent letter Chicanne {\em et al.} [1] reported the experimental observation of the electromagnetic local density of states LDOS established by gold nanostructures. The obtained images have been compared with combinations of partial LDOSs defined in terms of the imaginary part of the Green-tensor ${\bf G}^I = [{\bf G}-{\bf G}^\dag]/(2i)$ calculated at the tip position. Moreover just this comparison was the criterion for the choice of the optimum tip design. These results support the point of view that ${\cal G}_{\bf u} =-({2 \omega}/{\pi c^2}) {\bf u} \cdot {\bf G}^I({\bf r}, {\bf r}, \omega) \cdot {\bf u}$ (${\bf u}$ is the unit vector used to define the effective dipole associated to the illuminating tip) is the key quantity to interpret SNOM images in analogy with the electronic LDOS measured by the scanning tunneling microscope (STM). Rigorous Green-tensor analysis shows that ${\cal G}_{\bf u}$ (that is also the key quantity determining spontaneous decay rates of molecular transitions) is not the correct key quantity, and that measurements in Ref. [1] should have been compared with a different quantity. Moreover the identification of ${\cal G}_{\bf u}$ with the detected SNOM signal can lead to unphysical results.