Green function surface-integral method for nonlocal response of plasmonic nanowires in arbitrary dielectric environments

TL;DR

This paper introduces a computationally efficient Green-function surface-integral method to accurately model the nonlocal electromagnetic response of plasmonic nanowires in various dielectric environments, expanding the applicability of existing local-response techniques.

Contribution

It develops a nonlocal-response generalization of the GSIM/BEM, enabling accurate simulations of arbitrarily shaped nanowires in complex dielectric backgrounds with improved regularization techniques.

Findings

Nonlocal frequency blueshift increases with smaller nanowire radius and wavenumber.

Significant differences in extinction cross sections between local and nonlocal responses.

Regularization method effectively handles singularities when nanoparticles contact substrates.

Abstract

We develop a nonlocal-response generalization to the Green-function surface-integral method (GSIM), also known as the boundary-element method (BEM). This numerically light method can accurately describe the linear hydrodynamic nonlocal response of arbitrarily shaped plasmonic nanowires in arbitrary dielectric backgrounds. All previous general-purpose methods for nonlocal response are bulk methods. We also expand the possible geometries to which the usual local-response GSIM can be applied, by showing how to regularize singularities that occur in the surface integrals when the nanoparticles touch a dielectric substrate. The same regularization works for nonlocal response. Furthermore, an effective theory is developed to explain the numerically observed nonlocal effects. The nonlocal frequency blueshift of a cylindrical nanowire in an inhomogeneous background generally increases as the nanowire radius and the longitudinal wavenumber become smaller, or when the effective background permittivity or the mode inhomogeneity increase. The inhomogeneity can be expressed in terms of an effective angular momentum of the surface-plasmon mode. We compare local and nonlocal response of free-standing nanowires, and of nanowires close to and on top of planar dielectric substrates. Especially for the latter geometry, considerable differences in extinction cross sections are found for local as compared to nonlocal response, similar to what is found for plasmonic dimer structures.