A Boundary Integral Equation Scheme for Simulating the Nonlocal Hydrodynamic Response of Metallic Antennas at Deep-Nanometer Scales

Abstract

Modeling the interaction between light and a plasmonic nanoantenna, whose critical dimension is of a few nanometers, is complex owing to the "hydrodynamic" motion of free electrons in a metal. Such a hydrodynamic effect inevitably leads to a nonlocal material response, which enables the propagation of longitudinal electromagnetic waves in the material. In this paper, within the framework of a boundary integral equation and a method of moments algorithm, a computational scheme is developed for predicting the interaction of light with 3-D nonlocal hydrodynamic metallic nanoparticles of arbitrary shape. The numerical implementation is first demonstrated for the test example of a canonical spherical structure. The calculated results are shown to be in the excellent agreement with the theoretical results obtained with the generalized Mie theory. In addition, the capability of treating 3-D structures of general shapes is demonstrated by ellipsoids and dimers.

Mesoscopic electrodynamics at metal surfaces

“…It almost goes without saying that the concept of surfaceresponse functions goes hand-in-hand with Green's function surface-integral methods [299], which have already been explored in the context of the hydrodynamic model [226,300,301]. Here, we aim for the leading-order quantum correction terms to the classical surface-integral eigenvalue equation for metallic domains in the quasi-static regime [302,303].…”

Second harmonic Rayleigh scattering optical activity of single Ag nanohelices in a liquid

“…6(b) are performed by using a potential-based boundary element method (PB-BEM). [52][53][54] The PB-BEM focuses on equivalent surface sources on the boundary of a nanoscatterer. By matching the potentials on both sides of the boundary, the method provides a set of integral equations, which further discretizes the boundary with triangular patches and converts the integral equations into matrix equations.…”

Parallel FDTD Modeling of Nonlocality in Plasmonics

“…In Ref. [23], a current density formulation is used. A benefit to using a polarization field formulation is that it gives ready access to the free electron density via Gauss's Law, as we demonstrate in Section V. In Ref.…”

“…Nonlocal hydrodynamic models have been implemented using several computational electromagnetic methods including the finite element method [21], the discontinuous Galerkin time domain method (DGTD) [22], and the boundary element method [23]. Due to their inhomogeneous mesh, finite element methods, including DGTD, offer computationally efficient calculations for systems containing sharp features, or a complex geometry especially when compared to finite difference methods.…”