An advanced Jones calculus for the classification of periodic metamaterials

By relying on an advanced Jones calculus we analyze the polarization properties of light upon propagation through metamaterial slabs in a comprehensive manner. Based on symmetry considerations, we show that all periodic metamaterials may be divided into five different classes only. It is shown that each class differently affects the polarization of the transmitted light and sustains different eigenmodes. We show how to deduce these five classes from symmetry considerations and provide a simple algorithm that can be applied to decide by measuring transmitted intensities to which class a given metamaterial is belonging to only

Characterisation of optical metamaterials: effective parameters and beyond

Die vorliegende Arbeit beschäftigt sich mit der Charakterisierung von Metamaterialien. Für eine umfassendere Einführung in die Thematik sei auf Kapitel 1 verwiesen. Als künstliche Medien mit Perioden kleiner als die relevante Wellenlänge werden diese zumeist als effektiv homogene Materialien beschrieben. Diese Art der Beschreibung und deren kritische Untersuchung und Bewertung stehen im Mittelpunkt der Kapitel 2-4. Im Kapitel 2 werden die Grundlagen für die Beschreibung künstlicher Strukturen mittels homogener Maxwell Gleichungen und insbesondere der entsprechenden Materialgleichungen gelegt. In diesem Kapitel wird vor allem die Beschreibung künstlich magnetischer Materialien auf der Basis einer komplexen, räumlichen dispersiven Materialantwort abgeleitet. Die erzielten Materialgleichungen für Medien mit schwacher räumlicher Dispersion werden dann in Kapitel 3 zur Bestimmung der effektiven Eigenschaften zugrunde gelegt. Die Bestimmung erfolgt durch den sogenannten S-parameter retrieval, d.h. der Inversion der Fresnelgleichung für Reflexion und Transmission an einer optischen Schicht. Diese Methode wird ausführlich auch vom Standpunkt allgemein periodischer Medien her betrachtet, wodurch sich grundsätzliche Zusammenhänge und insbesondere Limitierungen ableiten lassen. In Kapitel 4 werden die zuvor bereitgestellten Methoden der Charakterisierung auf Metamaterialien mit zunehmender Symmetrie angewandt. Es wird gezeigt, dass eine Reduktion der optischen Antwort auf einzelne effektive Materialparameter selten möglich ist. In Konsequenz der vorherigen Resultate und mit Hinblick auf ein Design optischer Funktionalität anstatt des Designs etwaiger Materialien wird in Kapitel 5 eine Beschreibung der optischen Antwort auf Basis von Jones-Matrizen vorgeschlagen. Es wird ein Zusammenhang zwischen Symmetrie und allgemeiner Form der Jones-Matrix hergeleitet. Dieser Ansatz erlaubt sowohl die Beschreibung als auch das Design der polarisationsabhängigen Response von Metamaterialien

Homogenization of resonant chiral metamaterials

Homogenization of metamaterials is a crucial issue as it allows to describe their optical response in terms of effective wave parameters as e.g. propagation constants. In this paper we consider the possible homogenization of chiral metamaterials. We show that for meta-atoms of a certain size a critical density exists above which increasing coupling between neighboring meta-atoms prevails a reasonable homogenization. On the contrary, a dilution in excess will induce features reminiscent to photonic crystals likewise prevailing a homogenization. Based on Bloch mode dispersion we introduce an analytical criterion for performing the homogenization and a tool to predict the homogenization limit. We show that strong coupling between meta-atoms of chiral metamaterials may prevent their homogenization at all.Comment: 8 pages, 7 figure

Electrical and mechanical behaviour of metal thin films with deformation-induced cracks predicted by computational homogenisation

Motivated by advances in flexible electronic technologies and by the endeavour to develop non-destructive testing methods, this article analyses the capability of computational multiscale formulations to predict the influence of microscale cracks on effective macroscopic electrical and mechanical material properties. To this end, thin metal films under mechanical load are experimentally analysed by using in-situ confocal laser scanning microscopy (CLSM) and in-situ four point probe resistance measurements. Image processing techniques are then used to generate representative volume elements from the laser intensity images. These discrete representations of the crack pattern at the microscale serve as the basis for the calculation of effective macroscopic electrical conductivity and mechanical stiffness tensors by means of computational homogenisation approaches. A comparison of simulation results with experimental electrical resistance measurements and a detailed study of fundamental numerical properties demonstrates the applicability of the proposed approach. In particular, the (numerical) errors that are induced by the representative volume element size and by the finite element discretisation are studied, and the influence of the filter that is used in the generation process of the representative volume element is analysed

Validity of effective material parameters for optical fishnet metamaterials

Although optical metamaterials that show artificial magnetism are mesoscopic systems, they are frequently described in terms of effective material parameters. But due to intrinsic nonlocal (or spatially dispersive) effects it may be anticipated that this approach is usually only a crude approximation and is physically meaningless. In order to study the limitations regarding the assignment of effective material parameters, we present a technique to retrieve the frequency-dependent elements of the effective permittivity and permeability tensors for arbitrary angles of incidence and apply the method exemplarily to the fishnet metamaterial. It turns out that for the fishnet metamaterial, genuine effective material parameters can only be introduced if quite stringent constraints are imposed on the wavelength/unit cell size ratio. Unfortunately they are only met far away from the resonances that induce a magnetic response required for many envisioned applications of such a fishnet metamaterial. Our work clearly indicates that the mesoscopic nature and the related spatial dispersion of contemporary optical metamaterials that show artificial magnetism prohibits the meaningful introduction of conventional effective material parameters

Probing porosity in metals by electrical conductivity: Nanoscale experiments and multiscale simulations

Motivated by the significant influence of the underlying microstructure on the effective electrical properties of a material system and the desire to monitor defect evolution through non-destructive electrical characterisation, this contribution is concerned with a detailed study of conductivity changes caused by the presence of sub-microscale pores. Reducing the complexity of the material system, geometrically well-defined pore arrays are created by focused ion beam (FIB) milling in Cu thin films and characterised by 4-point probe electrical measurements. The experiment is designed such that it reduces to a (quasi-)one-dimensional electrical problem which is amenable to analytical techniques when invoking a computational homogenisation scheme to approximate the effective electrical properties of a given microstructure. The applicability of the proposed approach is shown in a first step by comparing simulation results for different pore volume fractions and pore shapes against their experimental counterparts. In a second step, a sensitivity analysis of the experimental data is carried out and the usefulness of the proposed modelling approach in interpreting the experimental data is demonstrated. In particular, the findings suggest that the proposed experimental method allows (at best) the determination of pore volume fractions with an accuracy of ±0.5%