Unusual resonances in nanoplasmonic structures due to nonlocal response

Abstract

We study the nonlocal response of a confined electron gas within the hydrodynamical Drude model. We address the question whether plasmonic nanostructures exhibit nonlocal resonances that have no counterpart in the local-response Drude model. Avoiding the usual quasi-static approximation, we find that such resonances do indeed occur, but only above the plasma frequency. Thus the recently found nonlocal resonances at optical frequencies for very small structures, obtained within quasi-static approximation, are unphysical. As a specific example we consider nanosized metallic cylinders, for which extinction cross sections and field distributions can be calculated analytically.

Performance of Nonlocal Optics When Applied to Plasmonic Nanostructures

“…Finally, since damping processes in this system are mainly due to the scattering of moving electrons by the barrier potential at the cylinder surface, γ must be of the order of hv F /R ∼ 0.3 eV. 36 The sets of differential equations for classical local and semi-classical non-local HDA optics are solved numerically using the finite element COMSOL package 37 following the prescription by Raza et al 25,38 and Hiremath et al 39 Unlike it was done in some previous applications of the HDA to nanowires, 22,23 such an implementation does not neglect the transverse component of the induced electric field. It is known that this simplification enforces the definition of additional but artificial boundary conditions to obtain a unique solution of the HDA problem, which results in the appearance of spurious resonances in the absorption spectrum.…”

“…It is known that this simplification enforces the definition of additional but artificial boundary conditions to obtain a unique solution of the HDA problem, which results in the appearance of spurious resonances in the absorption spectrum. 25 Regarding the quantum simulations, we use the Octopus package in which the TD-DFT equations are solved in real space and time domains. [40][41][42] We have implemented the translational symmetry of the nanowires in Octopus for both static (ground state) and time-dependent calculations by imposing periodic Born-von Kár-mán boundary conditions on the Z direction (no supercell is defined on the XY plane since Octopus is a real-space code).…”

“…The hydrodynamic equation (1) together with Maxwell's equations defines a self-consistent problem that can be solved analytically for selected geometries and numerically by using, for instance, finite-elements methods. 12,18,[21][22][23][24][25][26][27] The HDA dispersion relation for longitudinal bulk plasmons is ω 2 = ω 2 P + β 2 k 2 , where ω P = (4πe 2n /m e ) 1/2 is the bulk plasma frequency. 28 Therefore, the velocity β quantifies the dispersion in the EM response.…”

Visualizing hybridized quantum plasmons in coupled nanowires: From classical to tunneling regime

“…We note that some of these effects, in particular the non-local response and spillout, can be incorporated into semi-classical hydrodynamic models. 1,18,19 However, the validity and predictive power of such an approach in the true quantum regime is not fully clarified, and the standard hydrodynamic approximation, not including spill-out, has been found to fail for calculations on small nanometric gabs due to a insufficient description of induced charges in the interface. 20 One important hallmark of the quantum regime is electron tunneling, which occurs when two systems are brought into close proximity.…”

Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties

“…The phenomenology of nonlocal contributions of free electrons on the optical response of nanoscale plasmonic structures has been widely discussed in literature. [22][23][24][25][26][27][28] Typical manifestations of the nonlocal, free-electron gas pressure are blue shift and broadening of plasmonic resonances, anomalous absorption, 29 unusual resonances above the plasma frequency, 25 and limitation of field enhancements. 28 These effects are more pronounced when the electron wavelength (~1 nm) becomes comparable to the radius of curvature of metallic nanostructures or to the distance between the metal boundaries of larger structures.…”