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Duke University
Gaining Superpowers Through Metamaterials
Justin Garfinkle
Math 89s: Math of the Universe
Professor Bray
3/28/16
The role of metamaterials is making the seemingly impossible possible. Metamaterials
are artificially created materials that have properties often absent from materials occurring in
nature. The stuff of science fiction turned to scientific reality, the first version of a legendary
invisibility cloak was created right here at Duke University by engineering a metamaterial that is
able to cloak an object so that both the metamaterial cloak and the object inside it are invisible to
microwaves. There is a common game where people select which super power they wish to
have. Invisibility is not the only super power being made possible with metamaterials. Is the
goal x-ray vision? Metamaterials have been used to improve the resolution of MRI scans and to
create a high-resolution terahertz lens that could be used in place of X-rays so that the patient is
not exposed to potentially harmful radiation. If super-speed is the goal, metamaterials have the
potential to revolutionize information technology through increased speed and energy efficiency
of computers. Currently scientists are exploring the use of metamaterials to do everything from
protecting buildings against earthquakes to creating houses that could be folded to fit into a
backpack. In fact, the scientific community has only begun to explore all the “super powers”
that could be made possible through the development of various metamaterials.
The prefix “meta” is from the Greek word meaning “beyond” because metamaterials
typically have properties that go beyond what is found in natural materials (Cai 13). Although
not all sources agree on the origin of the term “metamaterial”, it was likely first used in 1999 by
Professor Rodger Walser from the University of Texas, Austin. In an invitation to a seminar
sponsored by the Defense Advanced Research Projects Agency (DARPA), Professor Walser
stated that DARPA was “gathering information concerning the area of artificially constructed
materials, or Meta-materials, which possess qualitatively new responses that do not occur in
nature” (Ziolkowski 1). The US Department of Defense continues to be a major funding source
for metamaterial research (Wagstaff).
There is currently no consensus definition of the term “metamaterial”, but many experts
continue to incorporate the concept of creating a material that has properties not found in nature.
Professors Wenshan Cai and Vladimir Shalaev point out, however, that people should be “truly
humble in the face of Mother Nature” (Cai 13). For example, a central focus of metamaterial
research is to create materials with a negative refraction index (discussed below), but this has
actually been observed in the compound eyes of some lobsters (Cai 13). More broadly, a
metamaterial is an artificially created material that attains its properties from the unit structure
itself and not any chemical reaction within the compound (Bargeron 7).
In nature, materials are comprised of atoms and molecules. In a metamaterial, very tiny
particles are used to create artificial “meta-atoms” and “meta-molecules” that are arranged in a
particular geometric pattern within the host material to create an entirely new material with a
unique set of properties (Cai 22). The tiny particles comprising the meta-atoms and metamolecules could be created using any metal, silicon or other natural material, depending upon the
properties being sought in the resulting metamaterial. The meta-atoms and meta-molecules do
not necessarily have to be the size of actual atoms and molecules, however. Since metamaterials
are developed to have particular properties when interfacing with light, sound, or some other
force, the meta-atoms and meta-molecules must simply be orders of magnitude smaller than the
applicable wave or force. For example, optical metamaterials that are designed to respond in a
particular manner to visible light could be constructed using meta-molecules that are bigger than
actual molecules but smaller than visible light waves. Whereas molecules are less than a
nanometer in size, the meta-molecules could be a few tens of nanometers and will still behave as
molecules relative to the visible light waves (Pendry). Any natural material, such as glass, water,
or iron, will respond to light based upon the average response of many billions of atoms within
the material that interact with the light wave. This averaging process will go on at the metamolecular level in a metamaterial as long as the meta-molecules are very small relative to the
applicable wavelength (Pendry). The subwavelength scale of the materials used to create the
meta-molecules results in an overall metamaterial that is uniform relative to the incoming wave,
which is why the metamaterial is considered a “material” rather than a “device” (Cai 13).
A metamaterial designed to work with radio waves, such as those used in satellites or
MRI scanners, could be comprised of meta-molecules that are much larger than the ones
designed for visible light since the size of the meta-molecule only has to be small relative to the
applicable wave. Whereas visible light waves are typically between 380 nanometers and 700
nanometers, radio waves have the longest wavelengths in the electromagnetic spectrum that
range between 1 millimeter and 100 kilometers. There are many applications for creating
metamaterials that interact with radio waves, microwaves or infrared waves that are easier to
create than applications for visible light because the meta-molecules created in the lab can be
much larger and therefore much easier to work with and build (Smith). Since visible light and
other forms of light like microwaves and radio waves are all electromagnetic radiation, they
share many similar features with the exception of their wavelengths and related frequencies.
Accordingly, these larger waves also can be used to test a metamaterial design that is then
adapted for visible light waves if that is the goal. This is why the Duke invisibility cloak was
created to cloak against microwaves rather than visible light waves in the initial demonstration
that invisibility is possible (Smith). For acoustical metamaterials, the size of the meta-molecules
would be determined relative to sound waves. In the field of mechanical metamaterials, the
constituent elements are scaled relative to the links that hold the materials together. (Brown,
quoting Professor Julia Greer).
The size of the meta-atoms and meta-molecules is not the only feature that is important
in creating a metamaterial that achieves a desired functionality. The nature and size of the metaatoms and meta-molecules, their respective shapes, their placement relative to each other, the
composition of the host material, the geometric pattern of the constituent parts, and the overall
structure of the compound are all important in the design of the metamaterial (Liu
57). Metamaterials are unique because, although they are artificially created, “they interact with
forces at the nanoscale in ways that we can only explain by using quantum mechanics” (Brown,
quoting Professor Julia Greer).
In 1827, Scottish botanist Robert Brown observed the zig zag motion of a grain of pollen
suspended in water. As discussed in my prior paper on Brownian motion, at the beginning of the
twentieth century, German theoretical physicist Albert Einstein and French experimental
physicist Jean-Baptiste Perrin were able to establish that the motion observed by Brown was the
result of the grain of pollen interacting with the water molecules (Nott 43). To me, this research
is the precursor to the modern efforts to use a nanoparticle as a synthetic molecule within the
host substance in order to develop a useful metamaterial. Interestingly, in a recent patent
application for a particular type of metamaterial, the inventors explained that “nanoparticles are
subject to Brownian motion… [and this] structural force on nanoparticles driving them into the
region of reduced order is used to produce metamaterials based on liquid crystal colloidal
dispersions with prescribed shape of building blocks” (Musevic).
Metamaterials were actually created thousands of years before the science behind their
creation was likely understood (Alu). In 300 A.D., an ancient Roman artist created the Lycurgus
Cup that is now on display at the British Museum in London. The Lycurgus Cup appears to be
jade green if illuminated from the front and translucent red if illuminated from the back. This
optical effect must have seemed magical at the time, but the effect was actually created by
melting tiny amounts of precious silver and gold alloys, ten thousand times smaller than a grain
of sand, into the glass. The color change occurs due to the interaction of light with these metallic
nanoparticles. The precise size and characteristics of the nanoparticles used in the Lycurgus Cup
and the precise spacing with which the nanoparticles were disbursed throughout the glass were
all necessary to create the optical effect of this ancient metamaterial (Alu).
The modern challenge for optical metamaterials is to control light in even more
fundamental ways than simply changing the perceived color of the observed material. Sir John
Pendry, a theoretical physicist at Imperial College London, describes light as a “dance” between
electricity and magnetism, since light is an oscillating magnetic field with an oscillating electric
field perpendicular to it (Pendry). Many metamaterials are created using a “delicate” balance of
metal and dielectric components in materials to interact in particular ways with electric and
magnetic fields (Cia 36). For example, round split-ring copper wires have been used as metamolecules to create a circuit when it comes in contact with a magnetic field, causing the resulting
metamaterial to have magnetic properties even though there is no iron, nickel or other
intrinsically magnetic component in it (Pendry). “Plasmonic” metamaterials enable optical
signals to be “squeezed into deep subwavelength scale, which helps to bridge length scale
mismatch between typical optical systems and on-chip electronics” (Cia 36). Potential
applications of plasmonics includes biochemical sensing and optical signal processing (Cia 36).
The electromagnetic properties of any material will depend upon its permittivity and its
permeability. When an electric field travels through matter, the resistance is known as its
permittivity. On an atomic scale, each atom has electrons with a net negative charge circling the
nucleus with a net positive charge. In a simple one-atom molecule of a material such as helium
gas, the electrons will feel a force toward the positive charge electric field. The reaction to an
electric field will depend upon the number of atoms in the molecules, the symmetry of the atoms
and their relative position. When a magnetic field travels through matter, the magnetic flux is
known as its magnetic permeability. Most materials are blind to the magnetic field of light at
visible and infrared wavelengths (Pendry). Conventional materials known to be transparent have
positive permittivity and positive permeability. Materials that have either a negative permittivity
or a negative permeability are opaque. Noble metals at optical frequencies have negative
permittivity but positive permeability, for example. In 1861, physicist and mathematician James
Clerk Maxwell published equations that, together with the Lorentz force law, have formed the
foundation of classic electrodynamics (Cia 19). Although not forbidden by Maxwell’s equations
or Lorentz force law, there are certain combinations and levels of permittivity and permeability
not found in nature (Cia 19). For example, there are no known natural non-magnetic materials
with permeability greater than 1. In addition, there are virtually no known natural materials that
have both negative permittivity and negative permeability. A “major focus” of metamaterial
research is “to create artificial materials that enter regions of parameter space that are not
forbidden by Maxwell’s equations but are not observed in conventional media, and to take
advantage of this expanded parameter space for better control of electromagnetic waves” (Cia
19).
The discovery in the year 2000 of a material with both negative permittivity and negative
permeability was actually the catalyst for the modern explosion in metamaterial development. In
1968, a Russian physicist named Victor Veselago had written a paper titled “The
electrodynamics of substances with simultaneously negative E [permittivity] & mu
[permeability]” (Smith). In the intervening years between 1968 and 2000, Veselago’s paper
received almost no attention because scientists thought it was impossible for there to be a
material that had both negative permittivity and permeability (Smith). Among the radical
predictions in Veselago’s paper was that a material with negative permittivity and negative
permeability would be transparent and would have a negative refractive index (Smith). A
negative refractive index would create very dramatic optical effects.
Refraction is the amount that the light will bend at the interface between the two
materials (Pendry). When light hits water, for example, the density of the water molecules
causes a change in the velocity and/or trajectory of the light beam. Light travelling through a
vacuum is assigned a refractive index of 1. This is the approximate refractive index for air. The
refractive index for any other material is based on how much resistance light has to travelling
through the medium relative to travelling through a vacuum. The refractive index of water is
1.333 because light travels about 1.333 times faster in air than it does in water
(Pendry). Virtually all known natural materials have a positive refractive index (Pendry). When
light moves from air to a denser material, if the ray approaches the material at an angle, it will
bend toward the boundary. This results can be demonstrated by viewing a straw placed in a glass
of water. The straw will appear to be bent due to the refraction of the light when it moves from
air to water. When light moves from a denser medium to a less dense medium, it will cause an
even more unusual optical illusion, such as a person seeing a mirage in the desert. Since cold air
is denser than hot air, as the sunlight passes down from cool air in the desert sky to hot air near
the desert ground, it gets bent upward so that the observer will perceive the refracted image of
the sky on the ground. The image of the sky on the ground will appear to be a pool of water to
the desert traveler. The optical illusion is even starker if there is a negative refractive index. A
material with a negative refractive index would bend light away from the boundary when it
meets the interface between air and the negative index material. If fish were swimming in a pool
of some type of liquid with a negative refractive index, the fish would appear to an external
observer be flying above the pool (Pendry). Creating a metamaterial with a negative refractive
index therefore opens dramatic opportunities in optics. For example, a typical microscope is not
able to have resolution beyond a half wavelength. If the lens were made of a metamaterial with a
negative refractive index, it could convey a perfect image at the molecular level to the observer
in the same way that the fish appears to be swimming above the “negative index” pool
(Pendry). Therefore, discovery of a negative index metamaterial opens up the possibility to
create a “perfect lens” (Pendry).
According to recent market research, the current metamaterials industry went from
relative obscurity in the year 2000 to an industry that is projected to reach $643 million within
the next several years (Markets). Many people credit David R. Smith of Duke University for
bringing “major attention” to the metamaterials field (Markets). Professor Smith was part of the
team that created the first invisibility cloak, which worked at microwave frequencies in 2006 and
then “perfected” this cloaking device in 2012 by controlling for absorption and other interference
(Knapp). Perhaps more significant, however, Professor Smith was part of the team that
discovered the first negative refraction metamaterial in 2000. The metamaterial had negative
refraction because it was created to have negative permittivity and negative permeability. This
double negative metamaterial was able to bend light in a way that was previously not thought
possible. Professor Smith, Professor Pendry, and several other European scientists won the 2005
Decartes Research Prize for the discovery of what is sometimes called a “left-handed
metamaterial” because the way in which the light bends backwards (Duke News Release).
Ironically, Professor Smith’s discovery of a metamaterial that responds to light in a
revolutionary way happened when he was trying to verify a finding in a different area
(Smith). In fact, he did not initially even comprehend the importance of what he had discovered
or its vast practical applications (Smith). Professor Smith was originally only trying to prove
that he had created artificial magnetism with negative permeability at microwave frequencies, as
had been previously postulated by Professor Pendry (Smith). Since two negatives make a
positive, Professor Smith incorporated a material with negative permittivity to see if the
compound would be transparent, as with double positive, rather than opaque as with one positive
and one negative with respect to permittivity and permeability. This process worked to prove
that Professor Smith had created a material with negative permeability, but as part of his test he
had actually created a material with both negative permeability and permittivity and therefore a
negative refraction index (Smith). As discussed above, this was believed impossible by the
scientific community. Professor Smith then re-discovered Veselogo’s paper discussed above on
the theoretical possibility of a double negative substance and all of its potential uses
(Smith). This marked the true beginning of the current effort to control waves in very special
and unique ways.
Professor Smith developed the invisibility cloak with the new techniques he had
discovered for controlling light. The theory behind the invisibility cloak is that it creates an
optical illusion that literally enables an observer to see behind an object without even seeing the
shadow of the object (Pendry). The way a person observes an object is that light interacts with
an object and is either reflected, refracted or absorbed. If the light, instead, moves around an
object and returns to its original path, the observer will receive the same image as if the object
were never there (Pendry). Professor Pendry suggests this is just like a river rushing around a
rock but then returning to its original path, wherein a downstream observer would not know that
the water had ever encountered the rock (Pendry). Professor Smith was able to bend microwaves
around a metamaterial cloak that surrounded a concealed object and refract the microwaves
around the cloaked object to return the trajectory of the waves to their original path
(Pendry). Other teams working on invisibility have used different techniques. For example, one
team of scientists was able to create a metamaterial invisibility cloak by sending waves from the
cloaking device that are exactly opposite to the incoming waves and thus countering their
effect. The problem with this technique is that it only works for the specific object being cloaked
(Pendry). One of Professor Pendry’s most interesting observations is that the only way to truly
make something invisible is through Einstein’s theory of general relativity and not through
metamaterials. If a cloak were massive enough to bend space-time, light coming toward the
cloaked object would travel around the object and then return to its original trajectory. Since this
is not possible as a practical matter, Professor Smith’s invisibility cloak attempts to simulate this
effect by bending light around the object through carefully structuring the refractive indices of
the metamaterial cloaking device (Pendry). Researchers are now working on creating
metamaterials that would cloak buildings against seismic waves to protect them from
earthquakes (Wogan). As techniques for creating metamaterials are expanded and perfected, the
possibilities for using metamaterials for different useful purposes could truly change the world
around us.
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