Abstract
Nonlocal optical response is one of the emerging effects on the nanoscale for particles made of metals or doped semiconductors. Here we classify and compare both scalar and tensorial nonlocal response models. In the latter case the nonlocality can stem from either the longitudinal response, the transverse response, or both. In phenomenological scalar models the nonlocal response is described as a smearing out of the commonly assumed infinitely localized response, as characterized by a distribution with a finite width. Here we calculate explicitly whether and how tensorial models, such as the hydrodynamic Drude model and generalized nonlocal optical response theory, follow this phenomenological description. We find considerable differences, for example that nonlocal response functions, in contrast to simple distributions, assume negative and complex values. Moreover, nonlocal response regularizes some but not all diverging optical near fields. We identify the scalar model that comes closest to the hydrodynamic model. Interestingly, for the hydrodynamic Drude model we find that actually only one third (1/3) of the free-electron response is smeared out nonlocally. In that sense, nonlocal response is stronger for transverse and scalar nonlocal response models, where the smeared-out fractions are 2/3 and 3/3, respectively. The latter two models seem to predict novel plasmonic resonances also below the plasma frequency, in contrast to the hydrodynamic model that predicts standing pressure waves only above the plasma frequency.
Highlights
In plasmonics research, conducting materials are described on many levels, from classically all the way to atomistically [1, 2]
We focus on effects of nonlocal response that for metals emerge on the few-nanometer scale, which is the intermediate regime where deviations from classical electrodynamics occur while atomistic descriptions are not needed yet
Εcore(ω)δ (r) ωp2 β2 eiqr 4π r where q = ω(ω + iγD)/β as before. This scalar model does not have the same strongly divergent terms scaling as r−3 for small r as we found for the hydrodynamic Drude model (HDM), but a 1/r divergence still remains, and on top of that ε(r, ω) is again complex-valued
Summary
In plasmonics research, conducting materials are described on many levels, from classically all the way to atomistically [1, 2]. An intermediate nonlocal regime of gap sizes was anticipated to be well described by semiclassical models, with gaps too small for classical electrodynamics to be accurate, yet too large to allow short-circuiting due to electronic spill-out at both interfaces [16] [25] where it is shown that besides damping due to electron-hole pair creation in forward-scattering processes across the gap (i.e. tunneling) backward scattering processes at metal-air interfaces are important, the latter processes both for monomers and dimers Another very recent generalization of the standard hydrodynamic Drude model is the selfconsistent hydrodynamic model (with electron gas dynamics beyond the Thomas-Fermi approximation) that can describe electronic spill-out semiclassically [26]. Aim is to obtain a sharper intuition about the models considered and the phenomena that they describe, especially the analogies and differences between scalar and dyadic models
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