08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access Advanced numerical and semi-analytical scattering matrix calculations for modern nano-optics(2011) Weiss, Thomas; Giessen, Harald (Prof. Dr.)The optical properties of nanostructures such as photonic crystals and metamaterials have drawn a lot of attention in recent years. The numerical derivation of these properties, however, turned out to be quite complicated, especially in the case of metallo-dielectric structures with plasmonic resonances. Hence, advanced numerical methods as well as semi-analytical models are required. In this work, we will show that the scattering matrix formalism can provide both. The scattering matrix approach is a very general concept in physics. In the case of periodic grating structures, the scattering matrix can be derived by the Fourier modal method. For an accurate description of non-trivial planar geometries, we have extended the Fourier modal method by the concept of matched coordinates, in which we introduce a new coordinate system that contains the material interfaces as surfaces of constant coordinates. In combination with adaptive spatial resolution, we can achieve a tremendously improved convergence behavior which allows us to calculate complex metallic shapes efficiently. Using the scattering matrix, it is not only possible to obtain the optical properties for far field incidence, such as transmission, reflection, absorption, and near field distributions, but also to solve the emission from objects inside a structure and to calculate the optical resonances of a system. In this work, we provide an efficient method for the ab initio derivation of three-dimensional optical resonances from the scattering matrix. Knowing the resonances in a single system, it is in addition possible to obtain approximated resonance positions for stacked systems using our method of the resonant mode coupling. The method allows describing both near field and far field regime for stacked two-layer systems, including the strong coupling to Fabry-Perot resonances. Thus, we can study the mutual coupling in such systems efficiently. The work will provide the reader with a basic understanding of the scattering matrix formalism and the Fourier modal method. Furthermore, we will describe in detail our extensions to these methods and show their validity for several examples.