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Engineered Materials and Metamaterials: Design and Fabrication
Author(s): Richard A. Dudley; Michael A. Fiddy
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Book Description

The field of metamaterials arose from a deepened understanding of how electromagnetic waves interact with materials and subwavelength-scale scattering structures. The exploitation of these more-complex material–wave interactions has generated much global research activity. We can, in principle, engineer materials to greatly extend the selection of those currently available.

This Tutorial Text presents the electromagnetic properties of both naturally occurring and manmade materials, focusing especially on structured or engineered metamaterials. After a review of Maxwell’s equations and material properties, the concepts of resonant meta-atoms and composite media are introduced. The fabrication of metamaterials and the properties of negative-index materials are explained. The difficulties associated with reducing the size of meta-atoms for use at optical frequencies are described, and the use of metamaterials for superresolution imaging is presented in some detail.

Book Details

Date Published: 28 March 2017
Pages: 220
ISBN: 9781510602151
Volume: TT106

Table of Contents
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Table of Contents


1 Introduction
1.1 Historical Perspective
1.2 Basic Electromagnetic Properties of Materials
1.3 Maxwell's Equations
1.4 Differential Form of Maxwell's Equations
      1.4.1 Polarization
      1.4.2 Conductivity
      1.4.3 Dispersion
      1.4.4 Permittivity
      1.4.5 Birefringence
      1.4.6 Permeability
      1.4.7 Index of refraction
      1.4.8 A phenomenological description of refractive index
1.5 The Six Velocities of Light
      1.5.1 Free-space velocities
      1.5.2 Waves in a medium
      1.5.3 Superluminal speeds

2 Material Properties
2.1 Material Classification
2.2 Metals
      2.2.1 Drude model
2.3 Dielectrics
      2.3.1 Lorentz oscillator model
      2.3.2 Kramers–Kronig relations
      2.3.3 Semiconductors
      2.3.4 Debye relaxation model
      2.3.5 Nonlinear dispersion
2.4 Equivalent Circuit Overview
      2.4.1 Impedance
      2.4.2 Capacitance
      2.4.3 Inductance
      2.4.4 RLC descriptions

3 Meta-atoms
3.1 Overview
3.2 Meta-atom Building Blocks
      3.2.1 Spherical particles: dipole response
      3.2.2 Spherical particles: resonant response
3.3 Metal Resonators
      3.3.1 The first metallic metamaterial
3.4 Split-Ring Resonators
      3.4.1 SRR equivalent circuit theory
      3.4.2 SRR size limitations
      3.4.3 SRR geometrical scaling
      3.4.4 SRR scaling considerations
3.5 Constitutive Parameter Estimation
3.6 Metasurfaces

4 Composite Media and Effective Medium Approximations
4.1 Composite Media
      4.1.1 Spherical particles
      4.1.2 Birefringent materials
      4.1.3 Homogenization
4.2 Form-Birefringent Metamaterials
      4.2.1 Other limitations of EMAs
      4.2.2 Bounds for effective permittivity
4.3 Summary

5 Anisotropic Microwave Metamaterials
5.1 Form-Birefringent Materials: A Case Study
      5.1.1 Gigantic anisotropies
      5.1.2 Inexpensive higher-index microwave metamaterials
      5.1.3 Tunable negative group delay
5.2 Example Microwave Material
      5.2.1 High-index materials: a case study
      5.2.2 Physical mechanisms

6 Negative Index
6.1 History of Negative Index
      6.1.1 Principle of least action
      6.1.2 Re-radiation from a negative-index material
      6.1.3 Double-negative material (DNM) possibilities
      6.1.4 The 'perfect' lens
      6.1.5 Evanescent amplification revisited
      6.1.6 Pendry's negative-index formalism
      6.1.7 A rigorous solution to the 'perfect' lens
6.2 Graphical Examples of Wave Propagation

7 Numerical Simulations
7.1 Frequency-Dependent Numerical Models
7.2 Negative-Index Properties and Computational Restrictions
      7.2.1 Practical discussion of 'exactly' n = –1
      7.2.2 Segmented metamaterials

8 Making Smaller Structures: Optical Metamaterials
8.1 Material Challenges
8.2 Plasma Waves and Plasmonics
      8.2.1 Bulk polaritons: the Drude model
      8.2.2 Surface plasmon-polaritons
8.3 Optical Metamaterials
8.4 Hyperbolic Metamaterials
      8.4.1 Photonic density of states

9 Optical Materials and Fabrication Challenges
9.1 Thin Films
9.2 Thin Dielectric Gaps between Metal Surfaces
9.3 Fabrication Methods and Challenges
      9.3.1 Electron beam lithography
      9.3.2 Dry etching
9.4 Process Impact of Reactive Ion Etching and E-Beam Lithography
      9.4.1 Metal deposition and lift-off process
      9.4.2 Focused-ion meam (FIB) milling
9.5 Focused Ion Beam Challenges
      9.5.1 Interference lithography
      9.5.2 Nanoimprint lithography (NIL)
      9.5.3 Fabrication of multilayer structures
      9.5.4 Two-photon photo-polymerization (TPP) technology

10 Superresolved Imaging
10.1 Superresolution Using Metamaterials: a Case Study
10.2 The Inverse-Scattering Problem
10.3 Degrees of Freedom
10.4 Numerical Examples
10.5 Perfect Imaging
10.6 Slab Imaging Example
10.7 Compressive Sampling



The intent of this tutorial text is to inform the reader of both the usual and unusual electromagnetic properties of materials, especially human-made or engineered "metamaterials." This term, which surfaced well after Victor Vesalago's paper on double-negative materials, stimulated a new understanding of the complexities of material interaction with electromagnetic waves. The history of light, and, more generally, electromagnetic radiation, dates back to the origin of the universe. Although the historical records only go so far back, even the very first of the known pre-Socratic philosophers, Hesiod, acknowledged the differences between darkness and light:

      "From Chaos there came into being Erebos (Darkness) and black night
      From Night, Aither (bright upper air) and Hemera (Day)
      which she conceived and bore after uniting in love with Erebos."1

For much of the history that followed, Western civilization's knowledge of electromagnetic radiation was grounded in the ideas presented by Hesiod. Studies of reflection or refraction of some kind followed with every major philosopher or scientist since Aristotle; however, there was a common premise that held back the theoretical understanding of light. The physical world was assumed to consist of all the same kinds of stuff, atoms, substance, or matter. This paradox frustrated scientists and philosophers for millennia, as debates about the origins of the universe collided with human experience. Even with this barrier, much knowledge about the nature of light has been discovered. Although possibly suggested first by Thales of Miletos, describing the attractive nature of amber rubbed with fur to that of a lodestone, it was not until over 2000 years later that the links between electricity and magnetism were formalized. Even then, the community still believed that light was submersed in an 'Aither.' At any moment, we should never be complacent about assumptions on which we build our understanding of the universe. There are sure to be many more surprises!

1R. D. McKirahan, Philosophy Before Socrates, Hackett Publishing Company Inc., 3rd Ed., 1994.

Richard A. Dudley
Michael A. Fiddy
March 2017

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