Accurate Computation of Electric Field Enhancement Factors for Metallic Nanoparticles Using the Discrete Dipole Approximation

A Eugene Deprince,Robert J Hinde

doi:10.1007/s11671-009-9511-7

Abstract

We model the response of nanoscale Ag prolate spheroids to an external uniform static electric field using simulations based on the discrete dipole approximation, in which the spheroid is represented as a collection of polarizable subunits. We compare the results of simulations that employ subunit polarizabilities derived from the Clausius–Mossotti relation with those of simulations that employ polarizabilities that include a local environmental correction for subunits near the spheroid’s surface [Rahmani et al. Opt Lett 27: 2118 (2002)]. The simulations that employ corrected polarizabilities give predictions in very good agreement with exact results obtained by solving Laplace’s equation. In contrast, simulations that employ uncorrected Clausius–Mossotti polarizabilities substantially underestimate the extent of the electric field “hot spot” near the spheroid’s sharp tip, and give predictions for the field enhancement factor near the tip that are 30 to 50% too small.

Highlights

We model the response of nanoscale Ag prolate spheroids to an external uniform static electric field using simulations based on the discrete dipole approximation, in which the spheroid is represented as a collection of polarizable subunits
The assumption that only dipolar interactions among subunits and between the subunits and the external field need be considered, an assumption that is implicit in discrete dipole approximation (DDA)-based simulations, is generally thought to be a reasonable one provided that the subunits are small enough so that the electric field is nearly constant across an individual subunit; this assumption is frequently tested by comparing the results obtained from simulations at two or more levels of discretization
Recent work [9, 10] suggests that the use of subunit polarizabilities that properly account for the anisotropic local environment of DDA subunits near surfaces can increase substantially the accuracy with which highly averaged far-field quantities, such as absorption and scattering cross-sections, can be computed using DDA-based methods. We employ these corrected polarizabilities in DDA-based simulations of nanoscale Ag prolate spheroids in homogeneous static electric fields; we find that the new polarizabilities, which include a local environmental correction (LEC) to the Clausius– Mossotti (CM) polarizabilities, substantially improve the description of spatially resolved near-field quantities, such as localized electric field enhancement factors, computed in these simulations

Summary

Introduction

Abstract We model the response of nanoscale Ag prolate spheroids to an external uniform static electric field using simulations based on the discrete dipole approximation, in which the spheroid is represented as a collection of polarizable subunits.

Results

Conclusion