Electromagnetic Scattering in Micro- and Nanostructured Materials

The research fields of optical microstructures and plasmonic nanostructures are particularly active these years, and interesting applications in, e.g., quantum information technology in the former and novel types of solar cells in the latter, drive the investigations. Central in both fields is the interaction of light with matter, in the forms of semiconductors and metals in the two cases, and fundamental understanding of the interactions is important to optimize technological designs.

To address this, we in the present thesis develop a formalism for determining the electric field in a homogeneous three dimensional space with spherical inhomogeneities embedded. The formalism accounts fully for the multiple reflections the field undergoes in such structures, and likewise the vectorial nature of the field is treated rigorously.

The formalism is based on the Lippmann-Schwinger equation and the electromagnetic Green’s tensor and uses an expansion of the field on spherical wavefunctions. Addition theorems for these are extensively used, and all parts of the formalism are expressed analytically. With the formalism, we show that the simpler approach of modeling the spherical scatterers as polarizable dipoles, which is often alluded to in the literature, breaks down in the limit of closely spaced scattering objects.

The study of metallic nanoparticles is particularly intriguing when these are in close proximity, due to the coupling of their near-fields, and the breakdown of the simpler approach reveals a need for the present formalism. Additionally, we study dimers and chains of metallic nanoparticles and analyze their spectra, when exposed to fields of different polarizations.

The spectral response is highly dependent on the polarization, and we demonstrate for the dimer, under polarization along the dimer axis, a d−1/2-dependence of the relative shift of the resonance wavelength, d being the distance between the particles. This dependence on d is softer than reported earlier, and thus constitutes the foundation for a more systematic study.

The correlation of distance and spectral properties may have applications within biosensing and -imaging on the nanoscale. For the chain, we demonstrate a next-nearest neighbor interaction between the nanoparticles through the study of its spectral properties. Finally, we present a calculation of the Green’s tensor for the dimer, illustrating that the formalism may likewise be used for modeling optical microstructures, e.g. three dimensional photonic crystals.