Surface Plasmon Scattering by Gold Nanoparticles and Two-Dimensional Agglomerates

There has long been an interest in nanosized metallic particles for numerous novel applications, from the productions of colored glass in medieval times to the molecular-level sensors of today. These particles are known to display considerably different, and size-dependent, optical properties than those of their bulk counterparts. Yet it is very difficult to determine the size and structure of these particles in situ, such as monitoring the actual self-assembly process, because of their small size. In this paper, we present a methodology to predict the patterns of nanosized particles and agglomerates subjected to surface plasmon waves. For this characterization, the scattering patterns of different types of particles and agglomerates on or near the surface are needed. A combination of the T-matrix method, image theory, and a double interaction model are considered. The incident and scattered fields are expanded by employing spherical harmonic functions. The surface effects are incorporated using the Fresnel equations, in the incident-field expansion coefficients, and by including particle-surface interaction fields. The premise of the method is that the T-matrix is independent of incident and scattered fields and hence can be used effectively for cases involving incident surface waves. By obtaining the T-matrix for clusters or agglomerates of metallic particles, the scattering matrix elements (⁠$M11$⁠, $M12$⁠, $M33$⁠, and $M34$⁠) of agglomerated structures on the surface are calculated using an additional T-matrix operation. The effect of size, shape, and orientation of gold nanosized particles on their scattering patterns are explored both in the visible spectrum and at resonance wavelengths. The results show that the normalized scattering matrix elements at certain observation angles and incident wavelengths provide significant information to monitor the structural change of gold nanosized particles on a gold substrate.