Using effective medium theories to design tailored nanocomposite materials for optical systems

Modern optical systems are subject to very restrictive performance, size and cost requirements. Especially in portable systems size often is the most important factor, which necessitates elaborate designs to achieve the desired specifications. However, current designs already operate very close to the physical limits and further progress is difficult to achieve by changing only the complexity of the design. Another way of improving the performance is to tailor the optical properties of materials specifically to the application at hand. A class of novel, customizable materials that enables the tailoring of the optical properties, and promises to overcome many of the intrinsic disadvantages of polymers, are nanocomposites. However, despite considerable past research efforts, these types of materials are largely underutilized in optical systems. To shed light into this issue we, in this paper, discuss how nanocomposites can be modeled using effective medium theories. In the second part, we then investigate the fundamental requirements that have to be fulfilled to make nanocomposites suitable for optical applications, and show that it is indeed possible to fabricate such a material using existing methods. Furthermore, we show how nanocomposites can be used to tailor the refractive index and dispersion properties towards specific applications.Comment: This is a draft manuscript of a paper published in Proc. SPIE (Proceedings Volume 10745, Current Developments in Lens Design and Optical Engineering XIX, Event: SPIE Optical Engineering + Applications, 2018

The multipole description of complex plasmonic nanostructures

Zusammenfassend konnte gezeigt werden, dass mit der Multipolentwicklung bis zur zweiten Ordnung sowohl die mikroskopischen als auch die makroskopischen optischen Eigenschaften von Metamaterialien in konsistenter Form beschrieben werden können. Zu Grunde liegt der dabei eingesetzten und sehr allgemeinen Methode ein spezielles mikroskopisches Modell zur Beschreibung der Ladungsträgerdynamik in der Struktur. In dieser Arbeit wurde dafür ein System gekoppelter Oszillatoren eingesetzt, welches allerdings auch durch andere Modelle oder Methoden ersetzt werden kann. Diese einfachen Annahmen reichten jedoch aus, um eine qualitative und quantitative Beschreibung der komplizierten Licht-Materie Wechselwirkung in den untersuchten Metamaterialien zu erhalten. Diese Art der Modellierung bestehend aus mikroskopischer Ladungsträgerbeschreibung und anschließender Multipolentwicklung ist ein wesentliches Resultat dieser Arbeit. Für die Erforschung der Metamaterialien stellt diese Methode ein physikalisches, analytisches und methodisch intuitives Werkzeug dar, um auch komplexere Strukturen verstehen oder gezielt entwerfen zu können

Transparency in Formal Proof

The oft-emphasized virtue of formal proof is correctness; a machine-checked proof adds greatly to our confidence in a result. But the rigors of formalization give rise to another possible virtue, namely clarity. Given the state of the art, clarity and formality are at odds: complexity of formalization obscures the content of proof. To address this, we develop a notion of proof strategies which extend the well-known notion of proof tactics. Beginning with the foundations of logic, we describe the methods and structures necessary to implement proof strategies, concluding with a proof-of-concept implementation in CheQED, a web-based proof assistant

Decomposing the scattered field of two-dimensional metaatoms into multipole contributions

We introduce a technique to decompose the scattered near field of two-dimensional arbitrary metaatoms into its multipole contributions. To this end we expand the scattered field upon plane wave illumination into cylindrical harmonics as known from Mie theory. By relating these cylin- drical harmonics to the field radiated by Cartesian multipoles, the contribution of the lowest order electric and magnetic multipoles can be identified. Revealing these multipoles is essential for the design of metamaterials because they largely determine the character of light propagation. In par- ticular, having this information at hand it is straightforward to distinguish between effects that result either from the arrangement of the metaatoms or from their particular design

Verfassungsrechtliche Grundlagen der Raumplanung

Den verfassungsrechtlichen Hintergrund der Raumplanung bilden die Gesetzgebungs- und Planungskompetenzen, die kommunale Selbstverwaltungsgarantie, das Grundrecht auf Eigentum sowie weitere verfassungsrechtliche Prinzipien. Die Raumplanung beruht auf einer Vielzahl von Kompetenztiteln. Einfluss auf die Raumplanung und ihre Teilaspekte nehmen dabei Grundrechte, Staatszielbestimmungen und grundrechtsgleiche Rechte

Plasmonic rod dimers as elementary planar chiral meta-atoms

Electromagnetic response of metallic rod dimers is theoretically calculated for arbitrary planar arrangement of rods in the dimer. It is shown that dimers without an in-plane symmetry axis exhibit elliptical dichroism and act as "atoms" in planar chiral metamaterials. Due to a very simple geometry of the rod dimer, such planar metamaterials are much easier in fabrication than conventional split-ring or gammadion-type structures, and lend themselves to a simple analytical treatment based on coupled dipole model. Dependencies of metamaterial's directional asymmetry on the dimer's geometry are established analytically and confirmed in numerical simulations.Comment: 3 page

Electromagnetic multipole theory for optical nanomaterials

Optical properties of natural or designed materials are determined by the electromagnetic multipole moments that light can excite in the constituent particles. In this work we present an approach to calculate the multipole excitations in arbitrary arrays of nanoscatterers in a dielectric host medium. We introduce a simple and illustrative multipole decomposition of the electric currents excited in the scatterers and link this decomposition to the classical multipole expansion of the scattered field. In particular, we find that completely different multipoles can produce identical scattered fields. The presented multipole theory can be used as a basis for the design and characterization of optical nanomaterials