Nonlocal formalism for nanoplasmonics: phenomenological and semi-classical considerations

TL;DR

This paper extends the local-response approximation in nanoplasmonics to include nonlocal effects, deriving a Laplacian correction that becomes significant at nanometer scales, especially around 1-10 nm.

Contribution

It introduces a phenomenological and semi-classical framework incorporating nonlocal electron gas response into plasmonic models, highlighting the importance of nonlocal effects at nanoscale dimensions.

Findings

Nonlocal effects become significant at 1-10 nm scales.

Laplacian correction term derived for electromagnetic wave equation.

Nonlocal response negligible at larger, macroscopic scales.

Abstract

The plasmon response of metallic nanostructures is anticipated to exhibit nonlocal dynamics of the electron gas when exploring the true nanoscale. We extend the local-response approximation (based on Ohm's law) to account for a general short-range nonlocal response of the homogeneous electron gas. Without specifying further details of the underlying physical mechanism we show how this leads to a Laplacian correction term in the electromagnetic wave equation. Within the hydrodynamic model we demonstrate this explicitly and we identify the characteristic nonlocal range to be vF/omega where vF is the Fermi velocity and omega is the optical angular frequency. For noble metals this gives significant corrections when characteristic device dimensions approach ~1-10 nm, whereas at more macroscopic length scales plasmonic phenomena are well accounted for by the local Drude response.