Conference Session #A6
Paper #2253
ACHIEVING INVISIBILITY VIA METAMATERIAL CLOAKING
Morgan Skapik (mas426@pitt.edu), Donald Voland (dkv3@pitt.edu)
Abstract- Through the fabrication of new materials,
engineers have gained the ability to put theory to the test,
allowing for the creation of several new and exotic
technologies. This paper will describe recently developed
metamaterials designed for the purpose of concealing
objects from a range of wavelengths of light. The theory and
development of these metamaterials will be discussed as well
as their applications concerning military aircraft and spinoff technologies.
The device discussed belongs to a unique category of
material called metamaterial. Due to their structure and
design, these materials possess unnatural qualities that
allow them to behave in ways contrary to traditional matter.
An explanation for these properties will be given as well as
theory involving the controlled manipulation of these
parameters for practical application. Like any new
technology, a cost/benefit analysis must be made in regards
to the manufacturing process and usefulness of the devices.
The final consideration of metamaterial cloaking will be its
ethical and social implications and whether or not
technology such as this could be used without privacy
standards.
Key Words- Cloaking, Electric Permittivity, Electromagnetic
Wave, Left-handed Material, Magnetic Permeability,
Optical Transformation, Refraction Index, Right Hand Rule
of metamaterials are many individual units, or cells, that
combine to form the template of the material and give it the
unnatural ability to control the flow of light itself. With this
ability, one of the most mythical pieces of technology, the
invisibility cloak, is finally within reach.
THE THEORY BEHIND METAMATERIALS
In comparison to normal materials, metamaterials exhibit a
somewhat opposite behavior in respect to their
electromagnetic properties such as negative refraction,
backward-wave propagation, reversed Doppler shift, and
backward Cerenkov radiation [1]. The unnatural values of
electric permittivity, ε, and magnetic permeability, μ, are the
determining factors in much of these qualities. To create
devices capable of being effective cloaking mechanisms,
scientists and engineers must create new materials with
specific values of ε and μ. Once these parameters are
appropriate, the material will be able to perform optical
transformations and thereby control the propagation of light
waves around it. With the device designed in such a way that
it can bend incoming light waves from any direction, a
working cloak has been established. However, this does not
guarantee that it is highly effective. Until recently, most
cloaks have been designed with the capacity to affect only a
small portion of light on the electromagnetic spectrum.
Subsequently, the range of wavelengths that the device can
control has been relatively small. In order to widen the scope
of this technology, new and innovative theory has been put
to the test. Only by conducting thorough research in the
following subsections can we gain the knowledge of how to
create highly efficient and applicable cloaks.
REALIZING THE DREAM OF INVISIBILITY
It has long been the fantasy of human beings to become
invisible. From ancient epics to modern day tales such as
H.G. Well’s The Invisible Man, Harry Potter, and Wonder
Woman, there exist countless examples of references
towards invisibility. In The Invisible Man, the main
character himself becomes invisible. Likewise, in Harry
Potter, Harry is able to shield himself from sight through the
use of an invisibility cloak. Finally, Wonder Woman owns
an invisible jet. Although this is science fiction, recent
research has shown that feats such as these may be closer to
reality than ever before. Through the use of modern day
technology involving metamaterials, these dreams may soon
be realized.
Metamaterial vs. Left-handed Material
As stated above, all normal materials have an explicit
electric permittivity, ε, and a magnetic permeability, μ.
Electric permittivity is defined as “the ability of a material to
resist the formation of an electric field strength generated by
an electric charge in the material” [2]. Likewise, magnetic
permeability is defined as “the ability of a substance to
sustain a magnetic field, equal to the ratio between magnetic
flux density and magnetic field strength” [3]. In nature, the
thinnest material is air, which has a permittivity of ε o and a
permeability of μo [1]. These values stand as the basis for the
relative permittivity and permeability of any other material,
as depicted in (1) and (2).
WHAT ARE METAMATERIALS?
Although a great deal of research has been done concerning
metamaterials over the last decade, the scientific community
has yet been able to universally define the term. According
to Dr. David Smith, a leading researcher in the field at Duke
University, the true definition of a metamaterial is a
“macroscopic composite of periodic or non-periodic
structure, whose function is due to both the cellular
architecture and the chemical composition” [1]. At the heart
[1]
University of Pittsburgh
Swanson School of Engineering
ε𝑟 = ε⁄ε𝑜
(1)
μ
μ𝑟 = ⁄μ𝑜
(2) [1]
March 1, 2012
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Morgan Skapik
Donald Voland
In most cases, a natural material will have a permeability
of μo and a permittivity greater than εo [1]. This is depicted
in Figure 1 by a horizontal line in the first quadrant. It is also
worth noting that, by taking the root of the product of the
values found above, another important material property
may be derived, the refractive index.
n = √ε𝑟 μ𝑟
incoming light waves around it without any scatter or
shadows.
Optical Transformations
In order to create a working invisibility cloak, the
metamaterial must be capable of bending light waves from
behind it completely around itself without disturbing their
overall flow pattern. To do this, the engineer of the cloak
must make use optical transformations to control the
propagation of light waves. Much like how gravity is
distorted by different masses, materials with unique
electromagnetic properties, such as the ones described in the
preceding section, are able to effectively bend light waves.
This is the concept behind an optical transformation
To understand an optical transformation at work, imagine
a two dimensional grid such as the one shown in figure (2)
with the grid lines intersecting at right angles. In this system,
light waves travel along these grid lines. In figure (2a),
surface S1 represents the surface of a material which does
not employ an optical transformation. However, in figure
(2b), an optical transformation has occurred and the lines
become curved. Even though these lines are curved, the right
angles between the light waves are conversed [6]. With the
right angles are unchanged, the properties of the light waves
are not distorted, creating no scattering or shadows, thus
making the transformation unnoticeable. Since the light
waves are bent around it, an observer would not be able to
see the object with surface S2.
(3) [1]
Above, (3) is the mathematical formula for calculating
the refractive index. This value, n, refers to “the ratio of the
velocity of light in a vacuum to that in a medium” [4].
Recent research has shown that if both the electric
permittivity and magnetic permeability are negative for a
material, then the resulting refractive index may in fact be
negative, offering a reversal of natural electromagnetic
properties [5]. As seen below in Figure 1, when both values
are negative, the material may be regarded as ‘Left-Handed’.
FIGURE 1
RESULTING MATERIAL PROPERTIES WITH RESPECT TO ELECTRIC
PERMITTIVITY AND MAGNETIC PERMEABILITY [1]
FIGURE 2
Being a left-handed material, LHM, simply means that
wave propagation is reversed in the system with respect to
the Right Hand Rule. Occurring spontaneously from the
Maxwell curl equations, the Right Hand Rule states that the
propagation vector k is given by the cross product of the
electric field E and the magnetic induction B, E × H [5]. In
LHM, the rule is reversed and the energy flow propagates in
the opposite direction.
Once a material has been created with such unnatural
electric permittivity and magnetic permeability values as
described above, a negative refraction index may be
obtained, allowing scientists and engineers the opportunity
to design highly exotic technology. However, creating a
material with these properties alone will not result in a cloak
of invisibility. Next, the device must be able to bend
IN FIGURE 2A, A COORDINATE GRID WITH AN ARBITRARY SURFACE. IN
FIGURE 2B, A COORDINATE GRID WITH AN OPTICAL TRANSFORMATION.
[7]
Although this figure only represents a two dimensional
object, an actual invisibility cloak must operate on a threedimensional level. As the objects and the system become
more complex, the mathematics behind the transformation
becomes increasingly complicated as well. Even though the
science behind it is intricate, application of this technology
on a small scale has proven the theory presented above
correct. However, current metamaterial design has yet to
catch up to theory fully and modern cloaks only work on a
narrow bandwidth. For this reason, a large portion of
research has been dedicated to creating metamaterials with a
more extensive range of effectiveness.
Without the
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Donald Voland
capability to shield an object from a large spectrum of
wavelengths, the device would ultimately fail to cloak the
target from view.
THE FABRICATION OF METAMATERIAL CLOAKS
How metamaterials are made is an essential piece of turning
theory into practice. To create a working metamaterial cloak,
engineers must design it in such a way that it will perform
the desired optical transformations. When making
metamaterials, engineers have traditionally used large
complicated series of magnetic resonators that are not very
efficient and likewise are take a long time to produce [1].
However, more recently, engineers have developed new
methods of creating metamaterials by using layers of
dielectric materials that reach the size requirements
necessary for visible light cloaking [1]. In order to create a
working metamaterial cloak, engineers must thoroughly
research and experiment with not only the individual
components of the cloak, but the overall design as well.
Range of Effectiveness
Over the past six years, metamaterial cloaks have evolved
tremendously. One year after the theory was proposed,
researchers at Duke University successfully shielded an
object from microwaves for the first time [8]. Since then,
efforts have been focused at cloaking targets from view of
waves of shorter wavelength, namely infrared and visible
light waves. Although it may not sound like a terrific task, it
has taken a great amount of research and testing to bring this
technology into the visible realm. So far, however, even the
best cloaking devices are unable to divert light from the
entire visible spectrum. This has been the main hurtle for
metamaterial researchers over the last decade.
The reason as to why the metamaterial works on such a
small bandwidth is that the optical transformations which
take place in the metamaterials only operate on certain
frequencies of light [9]. Furthermore, a cloak will only
shield an object from view if its constitute parts are smaller
than the wavelength of the incoming light waves. Since
visible light waves are on the scale of nanometers instead of
meters and centimeters like radio- and microwaves, true
invisibility cloaks will need to be designed at the Nano scale
[10]. This concept will be discussed in further detail in the
next section.
Take, for example, a new kind of cloaking device that is
proven to shield an object from wavelengths of light of 650580 nanometers. This covers that range of light that is
observed as the color orange [11]. Therefore, any part of the
object that is orange would be hidden from view. However,
since the cloak will only work on discrete frequencies of
light, the red parts of the object will not be hidden, but in
fact distorted [9]. If the cloak were more effective, the red
parts would also be hidden from view since red light has a
higher wavelength than orange light, making the waves
affected by the optical transformation as well. Finally, the
colors with a smaller wavelength, yellow, green, etc., would
not be shielded at all, as the frequency is too high for the
optical transformation to affect.
So far, so-called ‘carpet cloaks’ have been shown to
cloak objects the size of a red blood cell from human sight
[12]. Although cloaking at this scale is almost nothing next
to the overall goal of this technology, this accomplishment is
a large milestone in the quest to create a working, full
spectrum invisibility cloak.
With the theory behind metamaterial cloaking strongly
supported by successful experimentation, the only thing that
bars engineers from realizing a perfected invisibility cloak is
the fabrication of the cloak itself.
Cellular Design
The first step to creating a metamaterial cloak has been to
manufacture individual components, or cells, that together
have the desired negative electric permittivity, magnetic
permeability, and refractive index described above.
FIGURE 3
DEPICTION OF A SPLIT RING RESONATOR AND SURROUNDING
ELECTROMAGNETIC FLUX [1]
The resonant metamaterials are constructed out of a series
of split ring resonators, SSRs, as seen in Figure (3). These
may be made out of a non-magnetic conductor such as
copper. As magnetic flux from incoming electromagnetic
fields flows towards the metal ring, it interacts with the
rotating currents within the rings, and is unable to move past
it depicted by the moving arrows in Figure (3) [1]. Due to
the splits in the rings, the SRR can handle incoming resonant
wavelengths larger than the diameter of the rings.
[http://www.sciencemag.org/content/314/5801/977.full]. The
dimensions of the ring have to be smaller than the resonant
wavelengths of the incoming wave. This allows the
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metamaterial to prevent the microwave from passing through
the structure. This negative permeability and permittivity
status can be used in conjunction with the negative dielectric
constant that another SRR produces to create a negative
refractive index within the material [1]. There are several
types of SRRs that all preform largely the same service,
including I shapes T shapes and figure 8’s.
Figure (5) depicts a ground plane cloak. The way a
ground plane cloaks works is that as electromagnetic waves
attempt to pass through the metamaterial from the top, they
are forced to change their propagation in such a way that
anything placed under it will be rendered invisible from
detection by microwaves [1]. This design is the basis for
much of the rest of the work on metamaterials.
These types of metamaterials are effective for diverting
microwaves because of the relatively large size of the waves.
However, problems arise when trying to divert waves with
much smaller wavelengths. In order to create metamaterials
small enough to block visible light waves, new
manufacturing techniques had to be developed.
Cloak Design
A single SRR by itself will not completely block incoming
electromagnetic waves just like a single link of chainmail
will not stop an incoming arrow. The SSRs, similar to the
chain links, must be combined together in order to maximize
the effect. There exists several different ways that engineers
go about combining the SRRs in patterns conducive to
forming the desired negative refractive index.
In order to take advantage of the opposing dielectric
constants created by the SRRs, the individual pieces must be
arranged 180 degrees opposite each other and are often
printed on fiberglass circuit board. The SRR’s are then
arranged very close together to maximize the effect they will
have on an incoming wave. Due to this high proximity, the
incoming wave is physically incapable of passing through it
directly [13]
FIGURE 5
SRRS ARRANGED IN A GROUND PLANE CLOAK [14]
Manufacturing
As the frequency of the electromagnetic waves
increases, the resonant wavelength gets increasingly smaller.
This creates an issue when trying to design effective
metamaterial cloaks. The microwaves that have been
previously diverted in the lab setting have hade wavelengths
of .01 meters, or about the width of your finger. The
wavelengths of visible light are much smaller, ranging from
390 to 750 nanometers, almost ten million times shorter.
Metamaterials work by not allowing electromagnetic waves
to pass though the material that are larger than the space in
the material, so this creates an extreme demand for
components of the metamaterials to be as small as possible.
Out of this need for very small components, engineers
have been looking for new ways to create metamaterials
smaller than the 390nm wavelength required to shield an
object from visible light. John Rogers and his team at the
University of Illinois have created a method for producing
metamaterials at the Nano scale with stamp based printing
that were able to cloak infrared waves from detecting an
object [15]. To fabricate their cloaks, his team first makes a
hard plastic stamp that is then coated with alternating layers
of metamaterial substances including silver and magnesium
fluoride. The stamp is next placed on a sheet of plastic and
FIGURE 4
SRRS ARRANGED IN CONCENTRIC CIRCLES IN ORDER TO FORM A CLOAK AT
THE ORIGIN [13]
The concentric circular cloak pictured in Figure (4) works
by forcing microwaves to go around it instead of passing
through like they usually would. This is similar to putting a
rock in a stream - the water is forced to move around the
stone because it cannot go through it. Any objects placed in
the center of the rings in Figure (4) would be shielded from
microwave detection coming in from any side of the circle
as long as the microwaves were pointed laterally, that is, in
two dimensions. This is the setup first used by David Smith
in his initial metamaterial testing in 2006 [1].
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Morgan Skapik
Donald Voland
adhered. This technique allows for the creation of
metamaterials sheets a few inches wide while still
maintaining the optical properties of the metamaterials.
These new types of metamaterials do not rely on a series of
single SRRs but rather a mesh of metals that are patterned on
the Nano scale to have the same effect as the SRRs do but on
a much smaller scale. This technique has been reproduced
and modified to work with visible light which allows for the
creation of metamaterials that are capable of blocking visible
light.
Now, engineers are working on making the metamaterials
larger and more quickly than ever before. Improving the
manufacturing techniques is the only way to make the
metamaterials effective in large-scale use and application in
the world outside the lab.
size constraint barrier previously not overcome before. This
is the type of metamaterials, when scaled up to
accommodate larger objects, which may one day be used to
create a full-body invisibility cloak.
A Covert Military
The military has always been trying to attain the greatest
level of stealth referred to as low observable technology to
make their vehicles less visible to radar, sonar and infrared
detection methods. Over the last sixty years, aircraft have
been the primary focus of this stealth technology. Beginning
with the U-2 bomber in the 1950s, the Air Force has been
continuously working on trying to create aircraft less
vulnerable to radar and other detection methods [17].
The most obvious use for metamaterials cloaking of the
light spectrum will be for military applications involving
stealth warfare. A material capable for cloaking a piece of
military hardware from the visible light spectrum would
ideally also work with micro- and infrared waves because
those electromagnetic frequencies have longer wavelengths
than those of visible light. What this means is that any
vehicle equipped with a cloaking mechanism would not only
be undetectable to the naked eye but to radar, sonar, and
infrared detectors as well.
If this technology were to be coupled with an aircraft, it
would become completely untraceable by conventional
means. With this advantage, the Air Force would be able to
gather significantly better reconnaissance information which
would keep our fighting forces better informed about what
the opposition is doing. This information will ultimately help
keep our soldiers out of the line of fire. The Air Force
would also be able to perform covert strikes against potential
threats under a veil of complete invisibility. This would
allow for more precision and less civilian casualties during
an airstrike because there would be no threat of enemies
destroying your aircraft while you are carrying out your
mission. This ultimately lowers the cost of war because
fewer munitions would be wasted and the only buildings
destroyed are the intended targets of air force strikes, which
also eliminates the money needed to rebuild an area after it
was bombed.
THE APPLICATION OF METAMATERIAL CLOAKS
Currently, the applications for metamaterials are limited to
the lab setting, but as the technology involved in the
manufacturing process continues to improve it is only a
matter of time before metamaterials are able to be used in
real life applications. Research is underway, moving what
can be done in the lab to practical applications as well as
creating more effective metamaterials that will ultimately
cloak objects form the visible light spectrum. Much
advancement in the field of metamaterial research has come
about in the last few years. Within six years, engineers have
gone from being able to only divert microwaves to now
being able to cloak objects from visible light as well.
The Current State of Cloaking
For the first time ever, in 2006, engineers at Duke University
were able to successfully cloak an area of space from
detection of a beam of microwave radiation with the series
of electromagnetic resonators described earlier [13].
However, this cloak was limited to working only in two
dimensions. Obviously, this would not be useful for real
world application, but it serves as a useful learning tool for
scientists to base new projects off of.
Then, in 2008, Xiang Zhang and his team of researchers
at UC Berkley were able to conceal an object from
microwaves using a dielectric carpet cloak made out of
nanostructured silicon with the technique of stamping
similar to the one John Rodgers used to make his
metamaterials. This cloak is capable of shielding in all three
dimensions. Though the carpet itself remains visible while
looking at it, the object it conceals disappears from view
[16].
Recently, in 2011, the same team of researchers at
Berkley used a more advanced carpet cloak consisting of
layers of silicon oxide and silicon nitride etched in an
intricate pattern to conceal an object five micrometers in
diameter from a beam of visible light. This was the first time
that a team was able to cloak an object from visible light.
Although the object they cloaked was small, they broke the
Other Uses for Metamaterial Cloaks
Though the primary purpose of these optical metamaterials
will likely be for military concerns, there are several other
uses for this technology that would involve the broader
public. One of the largest problems in the laboratory setting
is the need for standardization. One possible application for
this technology would be for the prevention of interference
in the research and development of new technologies where
electromagnetic radiation may cause inaccurate results. If a
shield of metamaterial cloak were to be placed over a lab,
the researchers would not need to worry about the potential
disruptive effects of ambient electromagnetic radiation.
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Donald Voland
David Smith of Duke University said that metamaterials
optical devices could be used to concentrate light energy
instead of turning it away. This could improve solar cells by
making structures that increase the field strength of the light
[8]. The metamaterials would essentially magnify the light
that is already coming from the sun by funneling it into a
certain point as opposed to spreading it away. This would
ultimately bring about the effect of more sunlight in a given
time, allowing for more efficient solar panels.
Nicholas Fang, a professor of mechanical science and
engineering at the University of Illinois, has been working
on using transformative optics to create “hyper lenses”
capable to gathering up light that is misses by normal lenses,
this could provide better telescopes and camera equipment.
He and his team have already developed narrow band hyper
lenses which make the molecular workings of a cell visible.
[8]. High powered lenses would also be useful in the fields
of photography and astronomy where the ability to gather
large amounts of light is crucial for accurate pictures of the
world around us.
Whether or not stealth technology is available in the next
decade, metamaterials will likely still be used for these
everyday applications with great success.
THE INVISIBLE REVOLUTION
Since the theory regarding metamaterial cloaking was
first established in 2005, over a thousand professional papers
have been published on the theory, design, and development
of optical transformations via metamaterials [19]. With this
massive volume of publications, it is obvious that the field is
expanding rapidly.
Within the first year of research, engineers and scientists
were not only able to develop new theory in the young field
of optical transformation, but also to put this theory into use
through the creation of Dr. David Smith’s split ring
resonators. Only a couple years later, with the theory wellestablished and the technology refined, infrared waves came
under the control of metamaterial cloaking. Now, engineers
are pushing against the size constraints, aiming to not only
cloak objects from certain wavelengths, but from the entire
visible light spectrum.
While researchers fine-tune the theory behind the process,
engineers have been continuously finding more effective and
efficient ways of creating metamaterial devices. Design has
progressed exponentially over the last seven years.
Beginning with large, blocky SSR units, engineers have
created much more sophisticated structures that rely on
nano-processed materials rather than previous geometrical
arrays of metallic cells. Along with advancement in the
design of the cloaks, manufacturers have found ways such as
John Roger’s stamping method. These new methods
eliminate a large about time and effort, allowing for more
experimentation and implementation. Also, with this
process, researchers are able to produce larger quantities of
metamaterials, which further aids in the testing process.
Clearly, there exists a great potential in the application of
metamaterial cloaks. Currently, the main application goal of
this technology is directed towards use in the military,
particularly onboard aircraft. By coating aircraft with a layer
of metamaterial cloaks, a single pilot’s efficiency may
increase tenfold, as there would be no need for massive air
strikes and carpet bombing. Furthermore, substantial
amounts of money and lives would be saved by the
implementation of this technology. It is for this reason that
the military has begun to invest large amounts of money into
projects involving metamaterials.
Besides military use, the field of transformation optics
via metamaterials is likely to expand exponentially within
the next few years due to the amount of research being put
forth. These applications include hyper lenses, improved
solar cells, wave-shape transformers, and light bending
devices [1]. Clearly, the uses behind this technology are
endless.
Although there may be potentially harmful consequences
that come with this technology, the benefits far outweigh the
risk. Like any other technology, there will sure to be
counter-technologies that will be used to both protect society
and ensure the continuation of the metamaterials’ use.
ETHICAL CONSIDERATIONS
With any new powerful technology comes the potential
for misuse and visible light cloaking is no exception. Patrick
Lin, the research director of the US-based Nanoethics Group
stated that metamaterial advancements “such as these would
be disruptive to society today” and that “the ability to
become invisible will have profound implications for
privacy as well as national security” [18]. It would seem
obvious that visible light cloaking is not a technology the
general public could handle using responsibly, that is to say,
without incidences of invisible people committing
undetectable crimes. But the bigger question is how
governments will be trusted to not spy on their citizens or
otherwise invading their private lives if they cannot be
detected in any way. Should laws be set in place to protect
US citizens from being spied on? Would those same laws
apply to citizens of other countries? And if so, when does it
become okay to break these laws? Policy makers as well as
the general public will need to address these implications
before any possible privacy violations or security breaches
happen [18].
Another possible route in solving these problems is antistealth technology. Metamaterials that can redirect visible
light would still be visible to a camera that took x-ray
photographs. Since x-rays are at a higher frequency and
shorter wavelength than visible light they are able to detect
objects that are being concealed by the invisibility cloaks
discussed in this paper. This is one possible solution to
counteract the technology, but the original questions posed
above must still be answered before this technology is put
into widespread use.
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Through the technology presented in this paper,
metamaterial invisibility cloaks may soon become a reality,
not only bring to the forefront a world-changing device, but
ushering in a revolution in electromagnetic technology as
well.
ADDITIONAL RESOURCES
Cai, U. Chettiar, A. Kildishev, and V. Shalaev. (2007, April 2). "Optical
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T. Cui, D. Smith, and R. Liu. (2009). Metamaterials: Theory, Design, and
Applications. New York, New York: Springer.
Halliday, Resnick, J. Walker. (2011). Fundamentals of Physics. United
States: John Wiley & Sons.
U. Leonhardt. (2007) "Optical metamaterials: Invisibility cup." Nature
Photonics.
[Online].
Available:
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(2011, January 25). “New Materials may bring Advanced Optical
Technologies,
Cloaking.”
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ACKNOWLEDGMENTS
We would like to thank Ryan Soncini, our Co-Chair, and our
Chairs, Matt Castiglia and Franklin Preuss, for giving us
valuable advice and ideas throughout the writing process.
Also, we thank our friends from floor three at Forbes Hall.
Furthermore, we would like to thank the Writing Center
Instructors for their guidance throughout this semester.
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