Enhanced discretization of surface integral equations for resonant scattering analysis of sharp-edged plasmonic nanoparticles

Abstract

The surface integral equation (SIE) method, discretized with the method of moments, is a well-established methodology for the scattering analysis of subwavelength plasmonic nanoparticles. SIEs are usually discretized with low-order basis functions that preserve the normal continuity of the surface currents across the edges arising in the meshed boundary, such as Rao-Wilton-Glisson (RWG) functions. However, the plasmonic enhancement modeling on sharp-edged particles is an extremely challenging task, especially due to the singular fields exerted at sharp corners, exposing a slow (or no) convergence in the computation of the scattering and absorption spectra. In this paper, we propose an alternative discretization strategy based on a discontinuous basis function set in conjunction with a volumetric-tetrahedral testing scheme. We demonstrate the potential of the proposed discretization scheme by studying scattering and absorption spectra of three canonical plasmonic polyhedra, i.e., a hexahedral, an octahedral, and a tetrahedral silver inclusion. The results expose an improved accuracy and faster convergence in both far-field and near-field regions when compared to the standard RWG implementation. The proposed discretization scheme can offer faster and more accurate routes towards the exploration and design of the plasmonic resonant spectrum of sharp-edged nanoparticles and nanoantennas.

Quantum Plasmonics in Nanorods: A Time-Dependent Orbital-Free Density Functional Theory Study with Thousands of Atoms

“…The Friedel oscillations inside the nanorod are the result of screened charge oscillations on the surface. The small charge density distribution at the corners of the nanorod ( l / d = 1.1) is induced by the sharp edges, similar to that in nanosquares. , Clearly, the longitudinal LSPRs of the nanorods exhibit the typical dipolar character, whereas the multipolar resonances at higher energies induced by the electron density spill-out effect are much weaker, quite different from Na spherical nanoparticles …”

“…The small charge density distribution at the corners of the nanorod (l/d = 1.1) is induced by the sharp edges, similar to that in nanosquares. 53,54 Clearly, the longitudinal LSPRs of the nanorods exhibit the typical dipolar character, whereas the multipolar resonances at higher energies induced by the electron density spill-out effect are much weaker, quite different from Na spherical nanoparticles. 47 The longitudinal LSPRs are found to be strongly correlated with the aspect ratio, and their energies have a red shift of 1.0 eV as l/d increases from 1.1 to 6.5.…”

$T$-matrix method for calculation of second-harmonic generation in clusters of spherical particles

“…In order to circumvent this pitfall, a TMM that exploits the discrete VSWFs has been introduced [50]. However, if one needs to determine very accurately the optical near-field in the vicinity of sharp tips, as required for example in sensing applications, MoM-SIE is the method of choice [52].…”

Subwavelength Hexahedral Plasmonic Scatterers: History, Symmetries, and Resonant Characteristics

“…First, even for finely constructed (grown) cubes, there is always a finite edge-vertex curvature due to molecular and atomic considerations. From a numerical point of view, an extremely sharp corner introduces certain modeling difficulties, and hence special remedies should be considered (see for example the discussions in [24,41] and the references therein).…”