Methods for Describing the Electromagnetic Properties of Silver and Gold Nanoparticles

Abstract

This Account provides an overview of the methods that are currently being used to study the electromagnetics of silver and gold nanoparticles, with an emphasis on the determination of extinction and surface-enhanced Raman scattering (SERS) spectra. These methods have proven to be immensely useful in recent years for interpreting a wide range of nanoscience experiments and providing the capability to describe optical properties of particles up to several hundred nanometers in dimension, including arbitrary particle structures and complex dielectric environments (adsorbed layers of molecules, nearby metal films, and other particles). While some of the methods date back to Mie's celebrated work a century ago, others are still at the forefront of algorithm development in computational electromagnetics. This Account gives a qualitative description of the physical and mathematical basis behind the most commonly used methods, including both analytical and numerical methods, as well as representative results of applications that are relevant to current experiments. The analytical methods that we discuss are either derived from Mie theory for spheres or from the quasistatic (Gans) model as applied to spheres and spheroids. In this discussion, we describe the use of Mie theory to determine electromagnetic contributions to SERS enhancements that include for retarded dipole emission effects, and the use of the quasistatic approximation for spheroidal particles interacting with dye adsorbate layers. The numerical methods include the discrete dipole approximation (DDA), the finite difference time domain (FDTD) method, and the finite element method (FEM) based on Whitney forms. We discuss applications such as using DDA to describe the interaction of two gold disks to define electromagnetic hot spots, FDTD for light interacting with metal wires that go from particle-like plasmonic response to the film-like transmission as wire dimension is varied, and FEM studies of electromagnetic fields near cubic particles.

Nanoplasmonics: a frontier of photovoltaic solar cells

“…It is a timedomain technique, which allows solutions to be obtained for a wide range of frequencies in a single simulation. Since the FDTD method calculates the electric, E , and magnetic, H , fi elds everywhere in the computational domain as they evolve in time, it is straightforward to simulate the electromagnetic fi eld movement through the model [66] . There are many commercially available FDTD software vendors [67] , which are easy-to-use and can simulate 2D and 3D cases.…”

“…Although powerful, fi nite difference methods are limited in their modeling capability due to their grid-based nature. Geometries are approximated using a discrete grid, which must be suffi ciently sized to resolve both the smallest electromagnetic wavelength and the smallest geometrical feature in the model, which may result in computationally intense solutions [66] .…”

“…The FEM is suitable for modeling irregular geometries as well as large domains containing fi ne details and is accomplished by using small elements in regions where materials or fi elds are expected to change abruptly and simulating larger elements in the less important regions [66] . The COMSOL Multiphysics software [69] , which uses the FEM, was applied to design plasmonic nanostructures for maximum performance enhancement of various PV devices [15, 26, 62, 63, 70 -72] .…”

Generalized theoretical method for the interaction between arbitrary nonuniform electric field and molecular vibrations: Toward near-field infrared spectroscopy and microscopy

“…[34][35][36][37][38][39][40][41] On the other hand, multipole effects concerning the nonuniform light-matter interaction (i.e., beyond the dipole approximation) were discussed in nanoparticles 37,39 and molecular compounds. 36 Also recent studies clarifies the field gradient intrinsically causes the non-linear responses.…”

“…42 Concerning the vibrational spectroscopy, the mechanism of SERS has extensively been studied, in particular, in the field of molecular science with main focus on the mechanisms of surface enhancements. 35,43,44 However, corresponding theoretical studies for the infrared absorption have been scarce, in particular, studies focusing on the effects of spatial structures of near-fields, and theoretical tools still need to be developed. In this study, we propose a theoretical method for infrared absorption spectroscopy with near-field on the basis of the multipolar Hamiltonian.…”