A general theoretical and experimental framework for nanoscale electromagnetism

Abstract

Local, bulk response functions, e.g. permittivity, and the macroscopic Maxwell equations completely specify the classical electromagnetic problem, which features only wavelength λ and geometric scales. The above neglect of intrinsic electronic length scales L 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 e and λ.

Beyond Ti3C2Tx: MXenes for Electromagnetic Interference Shielding

“…The advantage of the transfer matrix modeling for ultrathin shielding layers, compared to Simon's formula that neglects multiple reflection between the layers, is shown in Figure S1. In absence of a model capturing the physics behind interactions of atomically thin materials and EM waves 28 , this looks like the best option available today.…”

Far-field excitation of single graphene plasmon cavities with ultracompressed mode volumes

“…Although we can experimentally thin down the hBN spacer until the monolayer case (16), we note that below thicknesses of 1 to 2 nm, strong nonlocal effects in the graphene should be introduced (16,34), given that we estimated the relative correction due to nonlocal effects to be~23% in our experiment (21). In addition, we estimated the nonlocal response of the metal (17,35,36) and found it to be negligible above 1 nm (21). The inclusion of these requires a special treatment that cannot be introduced into our numerical simulations.…”

Nonlocality Induced Cherenkov Threshold

“…The nonlocal electron screening refers to spatial spreading of surface charge densities over boundaries of metals, originating from the quantum repulsion of electrons or the electron gas pressure. [39,44] The oscillation of free electron gas due to the pressure gives rise to a longitudinal response of metals. The corresponding longitudinal permittivity is wavevector…”

“…The nonlocal electron screening refers to spatial spreading of surface charge densities over boundaries of metals, originating from the quantum repulsion of electrons or the electron gas pressure. [ 39,44 ] The oscillation of free electron gas due to the pressure gives rise to a longitudinal response of metals. The corresponding longitudinal permittivity is wavevector‐dependent, that is, , [ 45 ] where ω p is the plasma frequency, γ is the damping rate, and k L is the wavevector of longitudinal electric fields.…”

“…[35] has remained difficult, probably because of the elusive role of nonlocality which is generally ignored in previous theoretical studies. Although nonlocality is known to modify dramatically the electromagnetic responses of metamaterials, [36][37][38][39][40][41][42] its influence on the threshold behaviors of Cherenkov radiation still remains unexplored.…”