Hydrodynamic Model for Plasmonics: A Macroscopic Approach to a Microscopic Problem

Abstract

In this concept, we present the basic assumptions and techniques underlying the hydrodynamic model of electron response in metals and demonstrate that the model can be easily incorporated into computational models. We discuss the role of the additional boundary conditions that arise due to nonlocal terms in the modified equation of motion and the ultimate impact on nanoplasmonic systems. The hydrodynamic model captures much of the microscopic dynamics relating to the fundamental quantum mechanical nature of the electrons and reveals intrinsic limitations to the confinement and enhancement of light around nanoscale features. The presence of such limits is investigated numerically for different configurations of plasmonic nanostructures.

Third-harmonic generation in the presence of classical nonlocal effects in gap-plasmon nanostructures

“…The free-electron portion is treated using the hydrodynamic model, an extension of the Drude model that accounts for the effect of the electron pressure 35 . In particular, the free-electron pressure gives rise to the nonlocal portion of the polarization, and may be determined from the equation:…”

van der Waals interactions at the nanoscale: The effects of nonlocality

“…It is this saturation with which we are concerned in this paper and to treat it, we need to go beyond the conventional description of a solid by a permittivity, «ðωÞ, that depends only on the frequency, ω. Here we recognize that the response of a solid depends on the length scale of the fluctuations and introduce a formalism using a generalized nonlocal permittivity, «ðω; kÞ (5)(6)(7)(8)(9)(10)(11)(12)(13), that also depends on the wave vector, k, and hence takes into account the saturation. Neglect of nonlocality leads to an unphysical diverging van der Waals force at short distances.…”

Nonlocal effects occurred in the metallic nano chain driven by longitudinal or transverse modes

“…These differences are especially pronounced in each peak electric field located from 590 nm to 610 nm and then we have confirmed that the peak wavelengths in the hydrodynamic Drude model slightly shift toward the shorter wavelength compared with the conventional Drude one. Such shifting is one of typical tendencies in the nonlocal effects [9]. On the other hand the color distributions E DH and E obtained from the transverse mode are shown in Fig.…”

“…The hydrodynamic Drude model utilizes the following equation of motion for an electron inside the metallic object interacted with the electromagnetic fields [9]:…”

“…The key ingredient in the recipe for incorporating the nonlocal effects is to employ recently developed hydrodynamic Drude model which takes into consideration the spatial dispersibility of metallic objects [9] and is used by combining with FDTD (:Finite-Difference Time-Domain) algorithm, namely as an ADE (:Auxiliary Differential Equation)-FDTD scheme [10]. The resultant trends have clarified the relationships between the nonlocal effects and shape of the metallic nano chain characterized by the smallness and adjacency which deeply affect to also the longitudinal and transverse modes.…”