Computational Methods for Light Scattering by Metallic Nanoparticles

The unifying theme of this thesis is that of light scattering by particles, using computational approaches. This contributions here are separated into two main areas. The first consists of examining the behaviour of the extended boundary-condition method and T-matrix method, and providing a modified set of equations to use to calculate the relevant integrals. From this, some linear relations between integrals were found, which hint at the possibility of a more efficient means of performing these calculations. As well as this, the severe numerical problems associated with this method were investigated, and the primary source of these problems was identified in the case of two commonly-used shapes, spheroids and offset spheres. The cause of these numerical problems is that dominant, leading terms in the power series expansion of the integrands integrate identically to zero, but in practice, numerical calculations have insufficient precision to compute this exactly, and the overwhelming errors from this lead to drastically incorrect results. Following this identification, a new formulation of the integrals for spheroids is presented, which allows the much easier treatment of spheroids, approaching the level of ease of calculations for spheres in Mie theory. This formulation replaces some terms in the integrands with modified terms, that do not contain the parts of the power series that cause problems. As these should integrate to zero, we are able to remove them from the integrand without affecting the correct result. The second area of this thesis is concerned with calculations of the near-field for systems of interest in plasmonics, and specifically in surface-enhanced Raman spectroscopy. Here, the enhancement of the electric field in the vicinity of a metallic surface has a large effect on measured signals. The contribution of this thesis is to study the geometric parameters that influence the distribution of the field enhancement at the particle's resonance, specifically focusing on different effects caused by the overall shape of the particle, as opposed to those effects due to the local shape of the particle in regions of high enhancement. It is shown that the overall shape determines the location of the resonance, while the local shape determines how strongly the enhancement is localised. Understanding the factors that influence the enhancement localisation will help in guiding the design of suitable plasmonic substrates.