NAVAIR Seminar
Metamaterials, Cloaking,
and Acoustics
Steven A. Cummer
Electrical and Computer Engineering Department
Duke University
Other Team Members:
Prof. David Smith (Duke)
Prof. Sir John Pendry (Imperial College London)
Prof. David Schurig (NC State)
Dr. Anthony Starr (SensorMetrix, Inc.)
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Presentation Overview
• Metamaterials and cloaking theory development are
independent but practical realization tightly connected.
• Acoustics ideas are entirely built on comparable ideas
from electromagnetics.
• Easiest to describe in essentially chronological order:
• Electromagnetic metamaterials
• Electromagnetic cloaking
• Acoustic cloaking and metamaterials
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
How to Control the Electromagnetic
Properties of a Material?
• Mechanical and other properties of materials
engineered all the time. Why not EM?
• Electromagnetic properties of natural materials are
fairly limited:
• Few magnetic materials
• Few strongly anisotropic materials
• Available dielectric constants not continuous
• How can you design and fabricate a “material” with
the properties you need?
• Two approaches.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
One Approach:
Photonic Bandgap Materials
• Idea dates to Yablonovitch
[PRL, 1987.]
• Resonant (Bragg) scattering
from defects or structure
spaced every half wavelength.
• Occurs in nature and now in
engineered devices such as
optical fiber.
• Properties: almost always
anisotropic, depends critically
on half-wavelength structure,
can’t be smaller.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Another Approach: Metamaterials
• Common definition: artificial
subwavelength structure that
generates net magnetic and/or
electric dipole moment in response
to applied fields.
• Mimics the physics of conventional
materials (Si shown here).
• Properties: isotropic or anisotropic,
in principle doesn’t have to be
periodic, structure must be
subwavelength (how small is an
interesting question).
Shelby et al., Science, 2001
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Metamaterials History
• Like many good ideas, history
goes back a long time.
• Brown [1953], Rotman [1961]:
array of wires aligned with
electric field create a large electric
susceptibility.
• Schelkunoff and Friis [1952]:
capacitively loaded loop creates a
resonant magnetic susceptibility.
• Last 7 years have seen lots of MM
building on the independent
rediscovery and extension of these
ideas by Pendry [1996, 1999].
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Magnetic Metamaterials
• Need a big electric or dipole
moment per volume to create
non-free space.
• Split ring resonator [Pendry et
al., 1999] resonantly amplifies
the induced voltage.
• Results in a large magnetic
susceptibility (+ or –) near
resonant frequency.
• Isotropy can be controlled.
• In theory arrangement
doesn’t have to be regular, but
in practice it is easier.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
Bext
x
MB
20 February
2008
NAVAIR Seminar
Electric Metamaterials
• For permittivity, wire array
produces cutoff (Drude)
response, but electrical
continuity is a challenge.
• Or can make self-resonant
elements that create an electric
dipole moment in response to
an applied electric field
[Schurig et al., APL, 2006].
• Again, isotropy can be
controlled, most positive and
negative values possible.
• But bandwidth limited.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
Eext ME
20 February
2008
NAVAIR Seminar
Metamaterial Resurgence: Negative
Refractive Index
• Much of metamaterial research in past 10 years
originally motivated by one idea.
• By combining resonant electric and magnetic elements,
could make a material with negative  and  at the
same frequency, i.e. a negative refractive index?
• Idea explored theoretically by Veselago [1968], who
derived many unusual reversals (Doppler, etc.) in
negative index material (NIM).
• But idea didn’t go anywhere because no one knew how
to make such a material.
• But in 1999 all the pieces were in place to actually do it.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Negative Refraction
• Negative
refraction first
experimentally
demonstrated
by Shelby et al.
[Science, 2001].
• Some
controversy
erupted over
some theoretical
issues, but these
were quickly
resolved.
QuickTime™ and a
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are needed to see this picture.
Shelby et al., Science, 2001
Cummer, APL, 2003
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Electromagnetic Metamaterials
Summary
• Electromagnetic properties can be engineered with precise
control using metamaterial ideas: negative, large positive,
smoothly inhomogeneous, anisotropic, etc.
• Some limitations related to bandwidth and losses.
• Many possible applications: antennas, lenses, surfaces,
radomes, etc.
• Electromagnetic material design space dramatically
broadened, but not always easy to make an already
optimized device work better with metamaterials.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Cloaking and Transformation Optics
• Is it possible to smoothly bend light around an
object?
• No backscatter, no shadow = effectively invisible.
• Can there really be such an interesting solution still
lurking in classical electromagnetics? Pendry et al.
[Science, 2006] showed how it can be done.
• Key realization: coordinate transformations on
electromagnetic fields are completely equivalent to
a nonuniform permittivity and permeability.
• Curve space by opening a hole (mapping 0 to R2 to
R1 to R2): everything, including electromagnetic
fields, are curved around the hole.
• Or, surround the “hole” with a shell from R1 to R2
containing very specific permittivity and
permeability: electromagnetic fields are curved
around the hole (but nothing else).
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Cloaking Theory Example
• Example: cloaking a 2D
cylinder.
• Required  and
specified by theory.
• Strongly anisotropic,
values from 0 to very
large (not negative).
• 10 years ago this would
have been completely
unrealizable, especially
anisotropy.
• With metamaterials,
however, there is hope of
actually creating such a
material.

r  R1     r
 r  r 


r  R1
r
2
 R2  r  R1
 z   z  

R2  R1  r

Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Cloaking Theory Simulations
• Theory undoubtedly wonderful, but it gives no clues as to how
sensitive the solution is to small parameter perturbations.
• Is it like perfect focusing in that it completely falls apart if the
material parameters aren’t realized with unachievable precision?
• Numerical simulations are a very
good tool for answering this
question.
• COMSOL Multiphysics enables
full tensor description of  and ,
even off-diagonal components
(needed for cartesian coords).
• Plane wave or Gaussian beam
incident on cloaked PEC scatter.
• BCs either absorbing or
equivalent to periodic.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Baseline Simulations:
No Scatterer and No Cloak
QuickTime™ and a
decompressor
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QuickTime™ and a
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• No scatterer: plane wave is undisturbed.
• No cloak: strong scattering especially in forward (shadow)
direction.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Ideal Cloak Simulations
• Ideal cloak smoothly
bends electromagnetic
power around scattering
object.
• Validates original
prediction in noapproximations form.
• Scattering is small, even
in forward direction (but
not zero).
• Simulating cloaking
physics not especially
challenging, bodes well
for experiment.
• Parameter sensitivity not
extreme.
QuickTime™ and a
decompressor
are needed to see this picture.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Non-Ideal Cloak Simulations
• Concept is
robust.
• Loss: absorbs
but does not
scatter.
• Staircase
approximation
not too bad.
• Reduced
parameter set:
worse but
basic ray and
phase front
bending still
visible.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Cloak Design (1)
• Goal to demonstrate basic physics of field bending.
• 2D TE polarization (Ez, Hr, H), reduced parameter set gives easiest path
to realization. Only radially varying radial component of permeability.
• Approximate continuous
permeability variation with 10
discrete layers.
• Step 1: Design 10 different
magnetic resonators to give 10
different values (from 0 to
about 1) for radial
permeability at a single
frequency.
• This is done with simulations of
single metamaterial particles.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Cloak Design (2)
• Step 2: Pattern each of
10 cells onto sheets of
flexible printed circuit
board material.
• Step 3: Bend into
circles per original
design.
• Result: A good
approximation of a
material with a
continuously variable
radial permeability.
• Cheap to fab, design
requires only modest
simulations.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Cloaking Experiment
• Fields measured in field mapping chamber [Justice et al.,
Opt. Exp., 2006].
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Cloaking Measurements
QuickTime™ and a
MPEG-4 Video decompressor
are needed to see this picture.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
What Next for Electromagnetic
Cloaking?
•
•
•
•
Make a better one: challenging for metamaterial design.
Other wave systems?
Other applications of “transformation optics”?
Invisibility at visible wavelengths? Losses are much too big at this point to be
useful.
• Transformation optics offers a new way of manipulating electromagnetic fields
with engineered materials.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Acoustic Cloaking
• Natural to wonder whether the
ideas behind transformation
optics [Pendry et al., Science,
2006] can be applied to other
kinds of waves.
• Coordinate transformation
invariance linked to relativity,
maybe does not work for non
EM waves?
• Milton et al. [New J. Phys., 2006] applied coordinate transform approach
to general elastodynamics with a specific assumption about how vectors
have to transform.
• Found that equation form is not preserved, even for acoustics.
• Concluded that ideal elastic or acoustic cloaking was not theoretically
possible.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
2D Acoustic Cloaking
• Some aspects of wave behavior are very general.
• Maybe non-ideal but still useful acoustic cloaking possible?
• We showed that 2D acoustics and 2D electromagnetics have exactly the same equation form
[Cummer and Schurig, New J. Phys., 2007].
• Thus 2D acoustic cloaking (i.e., a cylinder), and general sound field manipulation in 2D, is
feasible.
• Requires a fluid with inhomogeneous bulk modulus and anisotropic effective mass density.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
3D Acoustic Cloaking
R2  R1 slightly smaller
than background
R2
2


R R
r
near background
r  2 1 
 to very large
R2 r  R1 
   


R2  R1 3 r 2
background
  
 
 near
 R2  r  R1  to very large
• No clear EM/acoustic analogy holds for three dimensions (i.e., a sphere).
• But scattering theory can be used to derive the acoustic parameters of a
theoretically perfect 3D spherical cloaking shell [Cummer et al., PRL, 2008].

• Requires similar fluid properties,
details slightly different than 2D.
• Almost certain it can be shown that arbitrary sound field manipulation can be
done with specific material properties, analogous to electromagnetics.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Effective Mass Anisotropy
• Both 2D and 3D acoustic
cloaking require anisotropic
effective mass density.
• Strange sounding idea, but not
difficult to imagine how to
realize.
• Milton et al. [NJP, 2006]
describe a conceptual model of
a composite with anisotropic
effective mass density.
• Springs mean that when force
is applied, the magnitude of the
net motion in different
directions is not the same.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
A Simpler Method for Realizing
Anisotropic Effective Mass
• Simple rigid scatterers are
also resonant.
• Torrent and Sanchez-Dehesa
[NJP, 2008]: array of rigid
scatterers in a fluid controls
the anisotropy of the effective
mass density of the array.
• Nonspherical scatterers
almost certainly give greater
control over that key
parameter.
• Design approach same as EM: simulate single material cells,
assemble into a functional material.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
General Cloaking Limitations
• Electromagnetic metamaterial losses
are difficult to control and are large
enough that it would be difficult to
build an X band cloaking shell larger
than ~10–20 wavelengths.
• Losses are low in many rigid
materials and so a higher quality,
lower loss acoustic metamaterial is a
realistic possibility.
QuickTime™ and a
decompressor
are needed to see this picture.
• Electromagnetic cloaking is inherently bandlimited because of speed of
light issues.
• No fundamental speed limit on acoustic waves, hence broadband acoustic
cloak is in principle possible.
• Thinner cloaking shells are more challenging to realize.
• Cloaking theory + metamaterials give a completely new way to manipulate
and reduce scattering of large objects, even forward scattering.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Conclusions
• Metamaterial ideas are proven in their ability to yield engineered
electromagnetic materials with desired effective, bulk properties such as
strong anisotropy.
• There is every reason to expect that these same properties can be
engineered into acoustic metamaterials.
• These engineered properties are exactly what is required to realize the
newly discovered electromagnetic and acoustic cloaking shells.
• There are undoubtedly practical limitations to how well these shells can
perform in practice, i.e. thickness, scatter reduction, losses.
• But the field has made a LOT of progress very quickly, and I would not
be surprised to see things move equally quickly in acoustics and further
in electromagnetics.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Perfect Focusing with NIMs
• Pendry [PRL, 2000]
showed that the
amplitude of evanescent
waves is restored by a
negative index slab in the
same way as phase
restored for propagating
waves.
• Causal simulations [Cummer, APL, 2003] showed that
occurs exactly as predicted by Pendry [PRL, 2000].
• Substantial limitations include exponential material
sensitivity, rendering it a largely near field effect.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Active Metamaterials
• Metamaterials approach lends itself to
embedding active devices into structure to
expand capabilities at both RF and optical.
• Lots of work presently on switching and
tunable elements to switch between two
states or continuously tune material
properties.
• Plenty to be done here: challenges are low
loss elements and similarity from element to
element.
• But what about powered active devices,
such as amplifiers?
• In principle, active devices can eliminate
losses and control dispersion.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Gain Metamaterials
• Resonant particles can do a wonderful job, but properties like loss and
dispersion are difficult to control.
• Resonant particles work by resonant gain:
Vind  VC  VL

Iind
Vind
VL


1
j[L  (C) ] jL
VL
jL

Vind j[L  (C) 1 ]

• What if we let an amplifier do
the work in generating gain?
• Certainly more complicated,
are advantages. For
but there
example, gain is not nearly as
frequency dependent.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Non-Reciprocal Metamaterials
• Have done a bunch of initial experiments, but I will jump to some very
exciting (to me) results for a full metamaterial.
• How to make a one-way material at RF?
 D  E  H
B  H
• Non-reciprocal 1D dispersion relation:
k 2   2   k

• Non-reciprocal magnetoelectric coupling
breaks symmetry and results
in a single polarization non-reciprocal
metamaterial.


Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Non-Reciprocal Metamaterial
Measurements
• Built a 5 cell-wide slab of this “material”.
• Measured 2-way TEM wave transmission through the material:
Highly non-reciprocal, just as we’d hoped.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008
NAVAIR Seminar
Cloak Scattering
• Interesting sidebar: How
does the near-ideal cloak
scatter?
• It scatters like a 1D line
at the center of the
cloaked region.
• Pretty unusual: not many
electrically large objects
that scatter isotropically.
• Especially surprising
because these
computations are done on
a unstructured grid.
Prof. Steve Cummer
http://www.ee.duke.edu/~cummer
20 February
2008