T-matrix method for the analysis of electromagnetic scattering

How to analyze optical scattering properties of an object or an ensemble of objects? It is often a nontrivial task to answer this question. There exists analytical formulas to calculate the scattering response of a simple object for a given illumination, and several numerical methods for more complicated structure can be used for the same purpose. However, probing the response of an object for one particular illumination scenario does not give the full picture as, in principle, there can be an infinite number of possible illumination scenarios. It is therefore a tedious task to consider all possible illumination scenarios to analyze the scattering properties of an object. To complicate the problem further, for an ensemble of randomly located and randomly oriented particles, it is almost impossible to predict exactly the response of the entire ensemble, and statistical means to extract observables quantities are needed.

To solve these problems, we rely in this thesis on a modal analysis of the T-matrix of the scatterer to analyze the optical scattering properties of a single object independent from a specific llumination. We also develop means to predict experimentally observables quantities of an ensemble of randomly oriented particles and analyze them in the context of modes sustained by its constituent scatterer. ... mehrFurthermore, an analysis in the context of an effective medium theory will be used to analyze the sensitivity of a hybrid optical sensor made from a dielectric disk covered with nanoparticles.

The entire work relies on a framework for the modal analysis to analyze scattering properties of an object. To extract the modes from the T-matrix of the considered object, wo spectral decompositions of a matrix will be presented. The first spectral decomposition, eigenvalue decomposition, is used to analyze the scattering properties of several objects. Using local and global coordinates formalisms, we show that complementary information can be obtained. To be able to discuss both approaches on the same level, a single, unified theory, to put both formalisms on the same ground will also be presented. This is done by a transformation formalism that converts eigenmodes in local coordinates into eigenmodes in global coordinates and vice versa. The second spectral decomposition, singularvalue decomposition, offers orthogonal modes, which in general cannot be provided by the modes obtained from eigenvalue decomposition. The orthogonality is beneficial to design an appropriate incident field for a desired optical response of a scatterer.

After we are done with the scattering analysis of a single particles, we proceed to analyze the optical response of an ensemble of randomly located and randomly oriented scatterers. To simplify the problem, we assume a very diluted solution in our analysis. We show that the experimentally observables quantities can be derived directly from the scattering properties of the constituent scatterer. Starting from this insights, we show that Fano properties, which arise from the coupling between nonorthogonal modes, can be identified in a strightforward manner from the experimentally observable quantities of the ensemble.

In the last part of this thesis, an analysis of an ensemble of nanoparticles around a microdisk is presented. Here, we focus our discussion on the sensitivity of such system, which shows a better performance compared to the traditional full coating approach, making it a promising structure to be used in optical sensing device.

In summary, we presented a theoretical framework to analyze the optical response of an objector ensemble of objects and its possible applications.