Objects of maximum electromagnetic chirality

We introduce a definition of the electromagnetic chirality of an object and show that it has an upper bound. Reciprocal objects attain the upper bound if and only if they are transparent for all the fields of one polarization handedness (helicity). Additionally, electromagnetic duality symmetry, i.e., helicity preservation upon interaction, turns out to be a necessary condition for reciprocal objects to attain the upper bound. We use these results to provide requirements for the design of such extremal objects. The requirements can be formulated as constraints on the polarizability tensors for dipolar objects or on the material constitutive relations for continuous media. We also outline two applications for objects of maximum electromagnetic chirality: a twofold resonantly enhanced and background-free circular dichroism measurement setup, and angle-independent helicity filtering glasses. Finally, we use the theoretically obtained requirements to guide the design of a specific structure, which we then analyze numerically and discuss its performance with respect to maximal electromagnetic chirality.Comment: This version contains an example of how to use the theoretically derived constraints for designing realistic structures. It also contains a discussion related to the optical chirality densit

Dual and chiral objects for optical activity in general scattering directions

Optically active artificial structures have attracted tremendous research attention. Such structures must meet two requirements: Lack of spatial inversion symmetries and, a condition usually not explicitly considered, the structure shall preserve the helicity of light, which implies that there must be a vanishing coupling between the states of opposite polarization handedness among incident and scattered plane waves. Here, we put forward and demonstrate that a unit cell made from chiraly arranged electromagnetically dual scatterers serves exactly this purpose. We prove this by demonstrating optical activity of such unit cell in general scattering directions.Comment: This document is the unedited Authors version of a Submitted Work that was subsequently accepted for publication in ACS Photonics, copyright American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/articlesonrequest/AOR-3yvzAibCIU6wdTuzx9c

Optics in Self-Assembled Metamaterials

How does an object scatter or absorb electromagnetic radiation? A very elegant analytic solution can be found for a single sphere with the Mie coefficients. In this thesis, an approach is used that is very similar. The amplitudes of the incident and scattered fields are connected by the T-matrix. We present a method to obtain the T-matrix of arbitrary objects. Furthermore, an extension is shown, where the scattering from several of such objects forming a cluster can be calculated

Optical Force and Torque on Dipolar Dual Chiral Particles

On the one hand, electromagnetic dual particles preserve the helicity of light upon interaction. On the other hand, chiral particles respond differently to light of opposite helicity. These two properties on their own constitute a source of fascination. Their combined action, however, is less explored. Here, we study on analytical grounds the force and torque as well as the optical cross sections of dual chiral particles in the dipolar approximation exerted by a particular wave of well-defined helicity: A circularly polarized plane wave. We put emphasis on particles that possess a maximally electromagnetic chiral and hence dual response. Besides the analytical insights, we also investigate the exerted optical force and torque on a real particle at the example of a metallic helix that is designed to approach the maximal electromagnetic chirality condition. Various applications in the context of optical sorting but also nanorobotics can be foreseen considering the particles studied in this contribution.Comment: 7 pages, 5 figure

Computing the T-matrix of a scattering object with multiple plane wave illuminations

Given an arbitrarily complicated object, it is often difficult to say immediately how it interacts with a specific illumination. Optically small objects, e.g., spheres, can often be modeled as electric dipoles, but which multipole moments are excited for larger particles possessing a much more complicated shape? The T-matrix answers this question, as it contains the entire information about how an object interacts with any electromagnetic illumination. Moreover, a multitude of interesting properties can be derived from the T-matrix such as the scattering cross section for a specific illumination and information about symmetries of the object. Here, we present a method to calculate the T-matrix of an arbitrary object numerically, solely by illuminating it with multiple plane waves and analyzing the scattered fields. Calculating these fields is readily done by widely available tools. The finite element method is particularly advantageous, because it is fast and efficient. We demonstrate the T-matrix calculation at four examples of relevant optical nanostructures currently at the focus of research interest. We show the advantages of the method to obtain useful information, which is hard to access when relying solely on full wave solvers

Refraction limit of miniaturized optical systems: A ball-lens example

We study experimentally and theoretically the electromagnetic field in amplitude and phase behind ball-lenses across a wide range of diameters, ranging from a millimeter scale down to a micrometer. Based on the observation, we study the transition between the refraction and diffraction regime. The former regime is dominated by observables for which it is sufficient to use a ray-optical picture for an explanation, e.g., a cusp catastrophe and caustics. A wave-optical picture, i.e. Mie theory, is required to explain the features, e.g., photonic nanojets, in the latter regime. The vanishing of the cusp catastrophe and the emergence of the photonic nanojet is here understood as the refraction limit. Three different criteria are used to identify the limit: focal length, spot size, and amount of cross-polarization generated in the scattering process. We identify at a wavelength of 642 nm and while considering ordinary glass as the ball-lens material, a diameter of approximately 10 µm as the refraction limit. With our study, we shed new light on the means necessary to describe micro-optical system. This is useful when designing optical devices for imaging or illumination

Refraction limit of miniaturized optical systems: a ball-lens example

We study experimentally and theoretically the electromagnetic field in amplitude and phase behind ball-lenses across a wide range of diameters, ranging from a millimeter scale down to a micrometer. Based on the observation, we study the transition between the refraction and diffraction regime. The former regime is dominated by observables for which it is sufficient to use a ray-optical picture for an explanation, e.g., a cusp catastrophe and caustics. A wave-optical picture, i.e. Mie theory, is required to explain the features, e.g., photonic nanojets, in the latter regime. The vanishing of the cusp catastrophe and the emergence of the photonic nanojet is here understood as the refraction limit. Three different criteria are used to identify the limit: focal length, spot size, and amount of cross-polarization generated in the scattering process. We identify at a wavelength of 642 nm and while considering ordinary glass as the ball-lens material, a diameter of approximately 10 µm as the refraction limit. With our study, we shed new light on the means necessary to describe micro-optical system. This is useful when designing optical devices for imaging or illumination

Consensus Algorithms for Networks of Systems with Second- and Higher-Order Dynamics

This thesis considers homogeneous networks of linear systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilizable. We show that, in continuous-time, consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. For networks of continuous-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback. For networks of discrete-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Schur. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. We show that consensus can always be achieved for marginally stable systems and discretized systems. Simple conditions for consensus achieving controllers are obtained when the Laplacian eigenvalues are all real. For networks of continuous-time time-variant higher-order systems, we show that uniform consensus can always be achieved if systems are quadratically stabilizable. In this case, we provide a simple condition to obtain a linear feedback control. For networks of discrete-time higher-order systems, we show that constant gains can be chosen such that consensus is achieved for a variety of network topologies. First, we develop simple results for networks of time-invariant systems and networks of time-variant systems that are given in controllable canonical form. Second, we formulate the problem in terms of Linear Matrix Inequalities (LMIs). The condition found simplifies the design process and avoids the parallel solution of multiple LMIs. The result yields a modified Algebraic Riccati Equation (ARE) for which we present an equivalent LMI condition