# A General Theoretical and Experimental Framework for Nanoscale Electromagnetism

## TL;DR

This paper introduces a comprehensive theoretical and experimental approach to nanoscale electromagnetism that incorporates electronic length scales via surface-response functions, enabling accurate modeling and measurement of nonclassical effects in nanostructures.

## Contribution

It develops a general framework using Feibelman d-parameters to include electronic length scales and proposes an experimental method to measure these parameters in nanostructures.

## Key findings

- Spectral shifts exceeding 30% observed in experiments.
- Breakdown of classical broadening mechanisms like Kreibig.
- Validation of the framework through measurements on nanoresonators.

## Abstract

Local, bulk response functions, e.g permittivity, and the macroscopic Maxwell equations completely specify the classical electromagnetic problem, which features only wavelength $\lambda$ and geometric scales. The above neglect of intrinsic electronic length scales $L_{\text{e}}$ leads to an eventual breakdown in the nanoscopic limit. Here, we present a general theoretical and experimental framework for treating nanoscale electromagnetic phenomena. The framework features surface-response functions---known as the Feibelman $d$-parameters---which reintroduce the missing electronic length scales. As a part of our framework, we establish an experimental procedure to measure these complex, dispersive surface response functions, enabled by quasi-normal-mode perturbation theory and observations of pronounced nonclassical effects---spectral shifts in excess of 30% and the breakdown of Kreibig-like broadening---in a quintessential multiscale architecture: film-coupled nanoresonators, with feature-sizes comparable to both $L_{\text{e}}$ and $\lambda$.