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Nanostructured Metamaterials EUROPEAN European Industrial COMMISSION Research Area research Nanostructured Metamaterials Exchange between experts in electromagnetics and material science STUDIES AND REPORTS Interested in European research? Research*eu is our monthly magazine keeping you in touch with main developments (results, programmes, events, etc.). It is available in English, French, German and Spanish. A free sample copy or free subscription can be obtained from: European Commission Directorate-General for Research Communication Unit B-1049 Brussels Fax (32-2) 29-58220 E-mail: [email protected] Internet: http://ec.europa.eu/research/research-eu EUROPEAN COMMISSION Directorate-General for Research Directorate G — Industrial Technologies Unit G.3 — Value-added materials Contact: Anne F. de Baas European Commission Office CDMA 4/066 B-1050 Brussels Tel. (32-2) 29-63586 Fax (32-2) 29-60550 E-mail: [email protected] EUROPEAN COMMISSION Nanostructured Metamaterials Exchange between experts in electromagnetics and material science Editor in Chief Anne F. de Baas Editors Sergei Tretyakov, Philippe Barois, Toralf Scharf, Volodymyr Kruglyak and Iris Bergmair Directorate-General for Research 2010 Unit G3 – Value-added Materials EUR 24409 EN EUROPE DIRECT is a service to help you fi nd answers to your questions about the European Union Freephone number (*): 00 800 6 7 8 9 10 11 (*) Certain mobile telephone operators do not allow access to 00 800 numbers or these calls may be billed LEGAL NOTICE Neither the European Commission nor any person acting on behalf of the Commission is responsible for the use which might be made of the following information. The views expressed in this publication are the sole responsibility of the author and do not necessarily reflect the views of the European Commission. More information on the European Union is available on the Internet (http://europa.eu). Cataloguing data can be found at the end of this publication. Luxembourg: Publications Office of the European Union, 2010 ISBN 978-92-79-07563-6 doi 10.2777/54953 Pictures: © Shutterstock images © European Union, 2010 Reproduction is authorised provided the source is acknowledged. Printed in Belgium PRINTED ON WHITE CHLORINE-FREE PAPER ❱ 3 Foreword It is my pleasure to present the publication Nanostructured Metamaterials – Exchange between experts in electromagnetics and material science. Metamaterials are one of the new discoveries of the last decade. They present exceptional properties, dominated by their geometrical structure and this publication will allow the reader to learn more about these ‘artificial’ materials and about their interesting (and yet unexploited) potential applications. The design and manufacturing of such materials has been made possible thanks to progress made in both materials science and electrical engineering. With the help of bottom-up manufacturing techniques, a large number of micrometer scale designs can now being scaled down to nanometer scale and therefore completely new solutions can be investigated. The tools needed to create metamaterials include modelling, geometry and property design, bottom-up manufacturing and structural and electron microscopy characterization at the atomic- and nano-scale. By controlling the reactivity of atoms and molecules to create inclusions and by controlling the positioning of these nano-inclusions, nanostructured metamaterials can been realised with interesting fields of applications where waves are involved, such as ICT applications and noise reduction. The 7th Framework Programme for Research (FP7), the European instrument for funding scientific research and technological development up to 2013, is targeting synergy between traditional scientific disciplines and this resulted in fostering four bottom-up manufacturing projects and a coordinated action on characterisation of metamaterials. Their total budget is EUR 20M with a FP7 contribution of EUR 15M. A workshop has been dedicated to metamaterials in December 2009 and its main outcome is presented in this publication. So often materials are the bottleneck or, positively, the enabler for technological progress resulting in novel and sustainable products made available to all citizens. Within the larger family of industrial technologies, material science and engineering show paramount potential to allow such progress with benefits for industry and the society as a whole. Metamaterials had a current market size of EUR 133 million in 2007 and are expected to grow to EUR 2.1 billion in 2013 (1), a compound annual growth rate (CAGR) of 26.5 %. I hope that the interdisciplinary and creative collaboration between material scientists and engineers together with ICT researchers will support this growth by allowing secure understanding and rapid progress in the innovative field of metamaterials, as this would allow exploiting their industrial (and later on, commercial) potential to the benefit of European industrial growth and the creation of jobs. Renzo Tomellini European Commission Head of Unit ‘Value-added Materials’ (1) Source and publisher: BCC Research, 35 Walnut Street, Suite 100, Wellesley, MA 02481. Email: [email protected] Report # AVM067A. ❱ 4 Nanostructured Metamaterials Contents Introduction 7 Chapter 1: Basic theory of nanostructured metamaterials 12 Introduction 12 1.1 Governing equations describing electromagnetic behaviour of materials 12 Maxwell’s equations in the time domain 12 Maxwell’s equations in the frequency domain 13 Temporal dispersion 14 Constitutive relations 15 Description of the behaviour of the metamaterial 16 1.2 Spin wave theory underpinning magnonic metamaterials 16 1.3 Bandgap and effectively continuous metamaterials 17 Bandgap materials 17 Effectively continuous media 18 1.4 Effectively continuous materials 18 1.4.1 Classes of effectively continuous materials 18 Isotropic media 18 Materials described only by permittivity 19 > Dielectrics 19 > Conductors 20 > Piezoelectric materials 21 Magnetic materials 21 Magneto-dielectric materials 21 > Magneto-dielectric materials with negative permittivity and permeability 21 Anisotropic and bi-anisotropic materials 22 Spin-wave/Magnonic metamaterials 23 1.4.2 Important Concepts 23 Backward-wave materials 23 Reciprocal materials 24 Spatially inhomogeneous materials and materials with spatial dispersion 25 > First-order spatial dispersion and chirality 27 > Second order dispersion and artificial magnetism 28 > Order of magnitude of effects 29 Nonreciprocal magneto-electric coupling 30 Wave phenomena in the quasi-static limit 30 Materials meeting the locality requirement 30 The relation between locality, spatial dispersion and optical density 30 1.5 Mathematical and numerical modelling 31 Mixing rules 31 > Maxwell Garnett formula 31 > Bruggeman mixing rule 32 Spin-wave metamaterials modeling 33 Circuit theory as a model for metamaterials 34 Numerical electromagnetic modelling and post-processing 36 Decomposition of fields into Bloch waves 38 Effective parameters and homogenisation 38 1.6 Resonances in permittivity and permeability 39 Lorentz model for dielectrics 39 Drude model for metals 40 Debye model for dielectric fluids with permanent electric dipole moments 40 Resonance of magnetic material 41 Mie scattering and resonant modes 41 Contents ❱ 5 1.7 Examples of metamaterial geometries 42 Artificial dielectrics and relevant inclusion geometries 42 Wire media 43 Artificial bi-anisotropic media and related inclusion geometries 44 > Reciprocal metamaterials 44 > Nonreciprocal bi-anisotropic metamaterials 44 Artificial magnetics and relevant inclusion geometries 45 1.8 References 47 1.9 Annex to Theory Chapter 50 1.9.1 Important concepts used to describe the behaviour of metamaterials 50 1.9.2 Phase velocity, group velocity, energy velocity 57 Chapter 2: Design of metamaterials in the projects 62 Magnonic meta-material designs 62 Design of nanostructured metamaterials in METACHEM 64 -1- Nanoclusters: 64 -2- Metal-dielectric composites: 64 -3- Super-lattices: 65 NANOGOLD meta-material designs 67 NIM_NIL meta-material designs 69 Chapter 3: Manufacturing Technologies of the projects 74 MAGNONICS Protein-guided assembly of (magnetic) nanostructures 74 METACHEM Nano-chemistry and self-assembly of nanoobjects 76 -1- Introduction: 76 -2- Nanochemistry of nanoobjects: 77 -3- Self assembly methods: 78 NANOGOLD Manufacturing of metamaterials with self organization and phase separation techniques based on liquid crystal and related technology 81 -1- Chemical synthesis of composite materials containing resonant entities: Fabrication of liquid crystal gold nanoparticles 81 -2- Nano-chemistry of composite metallic nanoentities based on chemical synthesis and physical chemistry 83 -3- Technology of composite nanomaterials based on phase separation and induced spatial ordering 86 NIM_NIL Fabrication of graphene inclusions 88 Fabrication of graphene layers 88 Fabrication of graphene metamaterials inclusions 88 Transfer printing method and exfoliation 89 Prepatterning of SiC and its transformation to graphene 89 Structuring graphene layers 90 Safety issues – Risks and hazards associated with the use and disseminations of nanoparticles 91 Chapter 4: Characterisation Theory and Measurements 96 Introduction 96 4.1 EM characterisation Theory 96 4.1.1 Classification of electromagnetic nanostructured materials 96 ❱ 6 Nanostructured Metamaterials 4.1.2 Classical characterisation techniques: Limitations on retrieved effective parameters 101 > State-of-the-art of retrieval techniques 101 > Dependence
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