Transformation Design and Metamaterials

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Transformation Designand Metamaterials

• David Schurig
• Duke University

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The Transformation Design Group

• John Pendry
• Imperial College
• David Smith
• Steve Cummer
• Jack Mock
• Bryan Justice
• Tony Starr
• SensorMetrix

Duke University
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Overview

• Metamaterials
• What are they?
• What can you do with them?
• Transformation design
• 2D Microwave cloak

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What are Metamaterials?

• Materials
• Intrinsic properties
• Described by a few parameters
• a0 ltlt a ltlt l
• Material scale order determines the properties

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Why bother?

• Custom meta-atoms
• Complete control of meta-atomic order
• Not constrained to thermodynamic assembly
• Unique material properties not previously
  observed
• Negative index
• Large controlled gradients
• Controlled Anisotropy

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Electromagnetic Parameter Space
m
1
e
1
0
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Resonance Mechanical Analog
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Ring and Cut Wire Resonators
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SRR Resonance
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Microscale Simulations
Commercial and custom codes can be used to find
the local fields for any unit cell.
A new approach to numerical effective medium
retrieval arises. Two examples are field
averaging and S-parameters retrieval.
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Microwave Metamaterial Samples
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Transformation Design
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Transformation Design

• Why a new design paradigm?
• Metamaterials provide unprecedented control over
  electromagnetic properties.
• Not obvious how to take advantage of this
  flexibility.

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Controlling Electromagnetic Fields
Traditional
Transformation Optics

• Index and shape
• Simple materials

• Coordinate transform
• Complex materials
• Simultaneous geometric and wave design
• Relfectionless design

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Transformation Design

• Imagine an interesting space
• Describe it with a coordinate transformation
• Calculate the material specification

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Space I

• Flat space
• 3D Cartesian
• Objects
• electromagnetic fields
• sources
• medium
• Physical Laws
• Maxwells Equations
• Constitutive Equations

James Maxwell
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Space II

• Flat space
• Minkowski space
• Objects
• electromagnetic fields
• sources
• medium
• Physical Laws
• Maxwells Equations
• Constitutive Equations

Hermann Minkowski
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Coordinate Transformations
Passive
Active
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Coordinate TransformationsCloak of Invisibility
Passive
Active
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Coordinate TransformationsCloak of Invisibility
Passive
Active
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Space II

• Flat space
• Minkowski space
• Objects
• electromagnetic fields
• sources
• medium
• Physical Laws
• Maxwells Equations
• Constitutive Equations

Hermann Minkowski
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Form Invariance
Transformation Properties
Hermann Weyl
Electromagnetic Equations
holonomic
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Resources
Maxwells Equations
Clifford
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Spatial Transformations
Time invariance
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Radial Transforms
spherical
cylindrical
Unity (free space)
Cloak
Concentrator
Non one-to-one (negative index)
Discontinuous (reflective)
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Radial Transforms Cloak
r
r
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Radial Transforms Concentrator
r
r
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Cloaking on a Ground Plane
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Concentrator
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Cloaking Arbitrary Shapes
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2D Microwave Cloak
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Metamaterial Implementation

• Design the unit cell
• Design the unit cell layout
• Fabrication patterning, cutting, assembly
• Measurement

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Cloak Design Theory
Transform Media
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Cloak Design Layout

• Space Filling
• but not crystalline
• Multiple environments
• Six fold symmetry

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Cloak Design Unit Cells

• Simulate rectangular unit cells
• Copper on FR4 or Duroid
• Magnetic and electric response from SRR
• Tune e with r and m with s

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Simulated Material Properties
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Tuning the Magnetic Resonance
Rem
w
0
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Tuning the Electric Resonance
Ree
w
0
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Cloak Design Measurement

• Scan range 20cm x 20cm
• Frequency range X-band
• 8.5 GHz (l/unit cell gt 10)

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Cloak Simulations
Ideal Cloak
Reduced parameter set
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Cloak Measurements
Bare scatterer measurement
Cloaked scatterer measurement
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Simulation Measurement Comparison
Simulation
Measurement
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Cloak Applications

• Concealing structures, vehicles, personnel
• Removing obstructions
• Shielding
• Nefarious

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The Future

• Better cloaks
• Other transformation designed devices
• Other wave phenomena
• Higher frequency

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Thank You