Metamaterial Cloaking
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Metamaterial cloaking is the usage of
metamaterials A metamaterial (from the Ancient Greek, Greek word Meta, μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally ...
in an invisibility cloak. This is accomplished by manipulating the paths traversed by light through a novel optical material. Metamaterials direct and control the
propagation Propagation can refer to: *Chain propagation in a chemical reaction mechanism *Crack propagation, the growth of a crack during the fracture of materials *Propaganda, non-objective information used to further an agenda *Reproduction, and other forms ...
and transmission of specified parts of the
light spectrum The electromagnetic spectrum is the range of frequency, frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energy, photon energies. The electromagnetic spectrum covers electromagnetic waves with f ...
and demonstrate the potential to render an object seemingly
invisible Invisibility is the state of an object that cannot be seen. An object in this state is said to be ''invisible'' (literally, "not visible"). The phenomenon is studied by physics and perceptual psychology. Since objects can be seen by light in ...
. Metamaterial cloaking, based on
transformation optics Transformation optics is a branch of optics which applies metamaterials to produce spatial variations, derived from coordinate transformations, which can direct chosen bandwidths of electromagnetic radiation. This can allow for the construction ...
, describes the process of shielding something from view by controlling
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself.


Electromagnetic metamaterials

''Electromagnetic metamaterials'' respond to chosen parts of radiated light, also known as the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...
, in a manner that is difficult or impossible to achieve with
natural material A natural material is any product or physical matter stop changing it. Minerals and the metals that can be extracted from them (without further modification) are also considered to belong into this category. Natural materials are used as building ma ...
s. In other words, these
metamaterials A metamaterial (from the Ancient Greek, Greek word Meta, μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally ...
can be further defined as artificially structured
composite material A composite material (also called a composition material or shortened to composite, which is the common name) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or ...
s, which exhibit interaction with light usually not available in nature (
electromagnetic interaction In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
s). At the same time, metamaterials have the potential to be engineered and constructed with desirable properties that fit a specific need. That need will be determined by the particular application. The artificial structure for cloaking applications is a
lattice Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an ornam ...
design – a sequentially repeating network – of identical elements. Additionally, for
microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
frequencies, these materials are analogous to
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
s for
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
. Also, a metamaterial is composed of a sequence of elements and spacings, which are much smaller than the selected
wavelength of light In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adjac ...
. The selected wavelength could be
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upp ...
, microwave, or other radiations, now just beginning to reach into the
visible frequencies The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...
.
Macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena an ...
properties can be directly controlled by adjusting characteristics of the rudimentary elements, and their arrangement on, or throughout the material. Moreover, these metamaterials are a basis for building very small cloaking devices in anticipation of larger devices, adaptable to a broad spectrum of radiated light. Hence, although light consists of an
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
and a
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
, ordinary optical materials, such as
optical microscope The optical microscope, also referred to as a light microscope, is a type of microscope that commonly uses visible light and a system of lenses to generate magnified images of small objects. Optical microscopes are the oldest design of microsco ...
lenses, have a strong reaction only to the electric field. The corresponding magnetic interaction is essentially nil. This results in only the most common
optical effects Compositing is the process or technique of combining visual elements from separate sources into single images, often to create the illusion that all those elements are parts of the same scene. Live-action shooting for compositing is variously ca ...
, such as ordinary
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
with common diffraction limitations in lenses and
imaging Imaging is the representation or reproduction of an object's form; especially a visual representation (i.e., the formation of an image). Imaging technology is the application of materials and methods to create, preserve, or duplicate images. ...
. Since the beginning of optical sciences, centuries ago, the ability to control the
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
with materials has been limited to these common optical effects. Metamaterials, on the other hand, are capable of a very strong interaction, or coupling, with the magnetic component of light. Therefore, the range of response to radiated light is expanded beyond the ordinary optical limitations that are described by the sciences of
physical optics In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effec ...
and
optical physics Atomic, molecular, and optical physics (AMO) is the study of matter-matter and light-matter interactions; at the scale of one or a few atoms and energy scales around several electron volts. The three areas are closely interrelated. AMO theory in ...
. In addition, as artificially constructed materials, both the magnetic and electric components of the radiated light can be controlled at will, in any desired fashion as it travels, or more accurately propagates, through the material. This is because a metamaterial's behavior is typically formed from individual components, and each component responds independently to a radiated spectrum of light. At this time, however, metamaterials are limited. Cloaking across a broad spectrum of frequencies has not been achieved, including the
visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...
.
Dissipation In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy (internal, bulk flow kinetic, or system potential) transforms from an initial form to a ...
,
absorption Absorption may refer to: Chemistry and biology * Absorption (biology), digestion **Absorption (small intestine) *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which ...
, and
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
are also current drawbacks, but this field is still in its optimistic infancy.


Metamaterials and transformation optics

The field of
transformation optics Transformation optics is a branch of optics which applies metamaterials to produce spatial variations, derived from coordinate transformations, which can direct chosen bandwidths of electromagnetic radiation. This can allow for the construction ...
is founded on the effects produced by metamaterials. Transformation optics has its beginnings in the conclusions of two research endeavors. They were published on May 25, 2006, in the same issue of ''
Science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...
'', a peer reviewed journal. The two papers are tenable theories on bending or distorting
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
to electromagnetically conceal an object. Both papers notably map the initial configuration of the
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ...
s on to a
Cartesian Cartesian means of or relating to the French philosopher René Descartes—from his Latinized name ''Cartesius''. It may refer to: Mathematics *Cartesian closed category, a closed category in category theory *Cartesian coordinate system, modern ...
mesh. Twisting the Cartesian mesh, in essence, transforms the coordinates of the electromagnetic fields, which in turn conceal a given object. Hence, with these two papers, transformation optics is born. Transformation optics subscribes to the capability of bending
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
, or
electromagnetic waves In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) lig ...
and
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
, in any preferred or desired fashion, for a desired application.
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
do not vary even though
coordinates In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
transform. Instead it is the values of the chosen parameters of the materials which "transform", or alter, during a certain time period. So, transformation optics developed from the capability to choose the parameters for a given material. Hence, since Maxwell's equations retain the same form, it is the successive values of the parameters,
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
and permeability, which change over time. Furthermore, permittivity and permeability are in a sense responses to the
electric Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...
and
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
s of a radiated light source respectively, among other descriptions. The precise degree of electric and magnetic response can be controlled in a metamaterial, point by point. Since so much control can be maintained over the responses of the material, this leads to an enhanced and highly flexible gradient-index material. Conventionally predetermined
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
of ordinary materials instead become independent spatial gradients in a metamaterial, which can be controlled at will. Therefore, transformation optics is a new method for creating novel and unique
optical device Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
s.


Science of cloaking devices

The purpose of a ''cloaking'' device is to ''hide'' something, so that a defined region of space is invisibly isolated from passing electromagnetic fields (or
sound waves In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
), as with Metamaterial cloaking. Cloaking objects, or making them appear invisible with
metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...
s, is roughly analogous to a magician's sleight of hand, or his tricks with mirrors. The object or subject doesn't really disappear; the vanishing is an illusion. With the same goal,
researcher Research is " creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness ...
s employ metamaterials to create directed blind spots by deflecting certain parts of the
light spectrum The electromagnetic spectrum is the range of frequency, frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energy, photon energies. The electromagnetic spectrum covers electromagnetic waves with f ...
(electromagnetic spectrum). It is the light spectrum, as the
transmission medium A transmission medium is a system or substance that can mediate the propagation of signals for the purposes of telecommunication. Signals are typically imposed on a wave of some kind suitable for the chosen medium. For example, data can modulate ...
, that determines what the human eye can see. In other words, light is
refract In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
ed or reflected determining the view, color, or illusion that is seen. The visible extent of light is seen in a chromatic spectrum such as the
rainbow A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows c ...
. However, visible light is only part of a broad spectrum, which extends beyond the sense of sight. For example, there are other parts of the light spectrum which are in common use today. The microwave spectrum is employed by
radar Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
,
cell phone A mobile phone, cellular phone, cell phone, cellphone, handphone, hand phone or pocket phone, sometimes shortened to simply mobile, cell, or just phone, is a portable telephone that can make and receive calls over a radio frequency link whil ...
s, and
wireless Internet Wireless communication (or just wireless, when the context allows) is the transfer of information between two or more points without the use of an electrical conductor, optical fiber or other continuous guided medium for the transfer. The most ...
. The
infrared spectrum Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
is used for
thermal imaging Infrared thermography (IRT), thermal video and/or thermal imaging, is a process where a thermal camera captures and creates an image of an object by using infrared radiation emitted from the object in a process, which are examples of infrared i ...
technologies, which can detect a warm body amidst a cooler night time environment, and infrared illumination is combined with specialized
digital cameras A digital camera is a camera that captures photographs in digital memory. Most cameras produced today are digital, largely replacing those that capture images on photographic film. Digital cameras are now widely incorporated into mobile device ...
for
night vision Night vision is the ability to see in low-light conditions, either naturally with scotopic vision or through a night-vision device. Night vision requires both sufficient spectral range and sufficient intensity range. Humans have poor night vi ...
. Astronomers employ the
terahertz band Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the ITU-designated band of frequ ...
for submillimeter observations to answer deep
cosmological Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
questions. Furthermore, electromagnetic energy is light energy, but only a small part of it is
visible light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...
. This energy travels in waves. Shorter wavelengths, such as visible light and
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
, carry more energy per
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
than longer waves, such as
microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
s and
radio waves Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (short ...
. For the
science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...
s, the light spectrum is known as the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...
.


The properties of optics and light

Prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...
s,
mirror A mirror or looking glass is an object that Reflection (physics), reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the ...
s, and
lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
es have a long history of altering the diffracted visible light that surrounds all. However, the control exhibited by these ordinary materials is limited. Moreover, the one material which is common among these three types of directors of light is conventional
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
. Hence, these familiar
technologies Technology is the application of knowledge to reach practical goals in a specifiable and reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in medicine, science, ...
are constrained by the fundamental, physical laws of optics. With metamaterials in general, and the cloaking technology in particular, it appears these barriers disintegrate with advancements in materials and technologies never before realized in the natural physical sciences. These unique materials became notable because electromagnetic radiation can be bent, reflected, or skewed in new ways. The radiated light could even be slowed or captured before transmission. In other words, new ways to focus and project light and other radiation are being developed. Furthermore, the expanded optical powers presented in the science of cloaking objects appear to be technologically beneficial across a wide spectrum of devices already in use. This means that every device with basic functions that rely on interaction with the radiated
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...
could technologically advance. With these beginning steps a whole new class of optics has been established.


Interest in the properties of optics and light

Interest in the properties of optics, and light, date back to almost 2000 years to
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
(AD 85 – 165). In his work entitled ''Optics'', he writes about the properties of
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
, including
reflection Reflection or reflexion may refer to: Science and technology * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal reflection, in ...
,
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
, and
color Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are associ ...
. He developed a simplified equation for refraction without
trigonometric functions In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all ...
. About 800 years later, in AD 984, Ibn Sahl discovered a law of refraction mathematically equivalent to
Snell's law Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
. He was followed by the most notable Islamic scientist,
Ibn Al-Haytham Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the prin ...
(c.965–1039), who is considered to be "one of the few most outstanding figures in optics in all times." He made significant advances in the science of
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
in general, and
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
in particular. He anticipated the universal laws of light articulated by seventeenth century scientists by hundreds of years. In the seventeenth century both
Willebrord Snellius Willebrord Snellius (born Willebrord Snel van Royen) (13 June 158030 October 1626) was a Dutch astronomer and mathematician, Snell. His name is usually associated with the law of refraction of light known as Snell's law. The lunar crater Sn ...
and Descartes were credited with discovering the law of refraction. It was Snellius who noted that Ptolemy's equation for refraction was inexact. Consequently, these laws have been passed along, unchanged for about 400 years, like the laws of gravity.
Willebrord Snell
in ''Archimedes to Hawking: Laws of Science and the Great Minds Behind Them'' (Clifford A. Pickover, 2008).


Perfect cloak and theory

Electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
and matter have a symbiotic relationship. Radiation does not simply act on a material, nor is it simply acted upon by a given material. Radiation interacts with
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
. Cloaking applications which employ
metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...
s alter how objects interact with the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...
. The guiding vision for the metamaterial cloak is a device that directs the flow of light smoothly around an object, like water flowing past a rock in a stream, without
reflection Reflection or reflexion may refer to: Science and technology * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal reflection, in ...
, rendering the object invisible. In reality, the simple cloaking devices of the present are imperfect, and have limitations. One challenge up to the present date has been the inability of metamaterials, and cloaking devices, to interact at
frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
, or
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
s, within the visible light spectrum.


Challenges presented by the first cloaking device

The principle of cloaking, with a cloaking device, was first proved (demonstrated) at frequencies in the microwave radiation band on October 19, 2006. This demonstration used a small cloaking device. Its height was less than one half inch (< 13 mm) and its diameter five inches (125 mm), and it successfully diverted microwaves around itself. The object to be hidden from view, a small cylinder, was placed in the center of the device. The invisibility cloak deflected microwave beams so they flowed around the cylinder inside with only minor distortion, making it appear ''almost'' as if nothing were there at all. Such a device typically involves surrounding the object to be cloaked with a shell which affects the passage of
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
near it. There was reduced reflection of electromagnetic waves (microwaves), from the object. Unlike a homogeneous natural material with its material properties the same everywhere, the cloak's material properties vary from point to point, with each point designed for specific electromagnetic interactions (inhomogeneity), and are different in different directions (anisotropy). This accomplishes a
gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradi ...
in the material properties. The associated report was published in the journal ''
Science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...
''. Although a successful demonstration, three notable limitations can be shown. First, since its effectiveness was only in the microwave spectrum the small object is somewhat invisible only at microwave frequencies. This means invisibility had not been achieved for the
human eye The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. ...
, which sees only within the
visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...
. This is because the
wavelengths In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of the visible spectrum are tangibly shorter than microwaves. However, this was considered the first step toward a cloaking device for visible light, although more advanced nanotechnology-related techniques would be needed due to light's short wavelengths. Second, only small objects can be made to appear as the surrounding air. In the case of the 2006 proof of cloaking demonstration, the hidden from view object, a
copper Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...
cylinder, would have to be less than five inches in diameter, and less than one half inch tall. Third, cloaking can only occur over a narrow frequency band, for any given demonstration. This means that a broad band cloak, which works across the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...
, from
radio frequencies Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upper ...
to microwave to the
visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...
, and to
x-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10  nanometers, corresponding to frequencies in the range 30&nb ...
, is not available at this time. This is due to the dispersive nature of present-day metamaterials. The coordinate transformation (
transformation optics Transformation optics is a branch of optics which applies metamaterials to produce spatial variations, derived from coordinate transformations, which can direct chosen bandwidths of electromagnetic radiation. This can allow for the construction ...
) requires extraordinary material parameters that are only approachable through the use of
resonant Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
elements, which are inherently narrow band, and dispersive at resonance.


Usage of metamaterials

At the very beginning of the new millennium, metamaterials were established as an extraordinary new medium, which expanded control capabilities over
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
. Hence, metamaterials are applied to cloaking applications for a few reasons. First, the parameter known as material response has broader range. Second, the material response can be controlled at will. Third, optical components, such as lenses, respond within a certain defined range to
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
. As stated earlier – the range of response has been known, and studied, going back to
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
– eighteen hundred years ago. The range of response could not be effectively exceeded, because natural materials proved incapable of doing so. In scientific studies and research, one way to communicate the range of response is the
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
of a given optical material. Every
natural material A natural material is any product or physical matter stop changing it. Minerals and the metals that can be extracted from them (without further modification) are also considered to belong into this category. Natural materials are used as building ma ...
so far only allows for a positive refractive index. Metamaterials, on the other hand, are an innovation that are able to achieve negative refractive index, zero refractive index, and fractional values in between zero and one. Hence, metamaterials extend the material response, among other capabilities. However, negative refraction is not the effect that creates invisibility-cloaking. It is more accurate to say that gradations of refractive index, when combined, create invisibility-cloaking. Fourth, and finally, metamaterials demonstrate the capability to deliver chosen responses at will.


Device

Before actually building the device, theoretical studies were conducted. The following is one of two studies accepted simultaneously by a scientific journal, as well being distinguished as one of the first published theoretical works for an invisibility cloak.


Controlling electromagnetic fields

The exploitation of "light", the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...
, is accomplished with common objects and materials which control and direct the
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ...
s. For example, a glass
lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
in a camera is used to produce an image, a metal cage may be used to screen sensitive equipment, and
radio antenna In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies an ...
s are designed to transmit and receive daily FM broadcasts.
Homogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
materials, which manipulate or modulate
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
, such as glass lenses, are limited in the upper limit of refinements to correct for aberrations. Combinations of
inhomogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
lens materials are able to employ gradient
refractive indices In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
, but the ranges tend to be limited.
Metamaterials A metamaterial (from the Ancient Greek, Greek word Meta, μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally ...
were introduced about a decade ago, and these expand control of parts of the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...
; from
microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
, to terahertz, to
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
. Theoretically, metamaterials, as a
transmission medium A transmission medium is a system or substance that can mediate the propagation of signals for the purposes of telecommunication. Signals are typically imposed on a wave of some kind suitable for the chosen medium. For example, data can modulate ...
, will eventually expand control and direction of electromagnetic fields into the
visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye wil ...
. Hence, a design strategy was introduced in 2006, to show that a metamaterial can be engineered with arbitrarily assigned positive or negative values of
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
and permeability, which can also be independently varied at will. Then direct control of electromagnetic fields becomes possible, which is relevant to novel and unusual lens design, as well as a component of the
scientific theory A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluatio ...
for cloaking of objects from electromagnetic detection. Each component responds independently to a radiated
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
as it travels through the material, resulting in electromagnetic inhomogeneity for each component. Each component has its own response to the external electric and magnetic fields of the radiated source. Since these components are smaller than the radiated
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
it is understood that a
macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena an ...
view includes an effective value for both permittivity and permeability. These materials obey the
laws of physics Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) a ...
, but behave differently from normal materials. Metamaterials are artificial materials engineered to provide properties which "may not be readily available in nature". These materials usually gain their properties from structure rather than composition, using the inclusion of small inhomogeneities to enact effective macroscopic behavior. The structural units of metamaterials can be tailored in shape and size. Their composition, and their form or structure, can be finely adjusted. Inclusions can be designed, and then placed at desired locations in order to vary the function of a given material. As the lattice is constant, the cells are smaller than the radiated light. The design strategy has at its core
inhomogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
composite
metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...
s which direct, at will,
conserved quantities In mathematics, a conserved quantity of a dynamical system is a function of the dependent variables, the value of which remains constant (mathematics), constant along each trajectory of the system. Not all systems have conserved quantities, and c ...
of
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
. These quantities are specifically, the
electric displacement field In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...
D, the
magnetic field intensity A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
B, and the
Poynting vector In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area per unit time) or '' power flow'' of an electromagnetic field. The SI unit of the Poynting vector is the watt ...
S. Theoretically, when regarding the conserved quantities, or fields, the metamaterial exhibits a twofold capability. First, the fields can be concentrated in a given direction. Second, they can be made to avoid or surround objects, returning without
perturbation Perturbation or perturb may refer to: * Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly * Perturbation (geology), changes in the nature of alluvial deposits over time * Perturbatio ...
to their original path. These results are consistent with
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
and are more than only ray approximation found in
geometrical optics Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of ''rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstan ...
. Accordingly, in principle, these effects can encompass all forms of electromagnetic radiation phenomena on all length scales. The hypothesized design strategy begins with intentionally choosing a configuration of an arbitrary number of embedded sources. These sources become localized responses of
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
, ε, and
magnetic permeability In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by William ...
, μ. The sources are embedded in an
arbitrarily Arbitrariness is the quality of being "determined by chance, whim, or impulse, and not by necessity, reason, or principle". It is also used to refer to a choice made without any specific criterion or restraint. Arbitrary decisions are not necess ...
selected
transmission medium A transmission medium is a system or substance that can mediate the propagation of signals for the purposes of telecommunication. Signals are typically imposed on a wave of some kind suitable for the chosen medium. For example, data can modulate ...
with
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
and
magnetic Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particle ...
characteristics. As an electromagnetic system the medium can then be schematically represented as a grid. The first requirement might be to move a uniform
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
through space, but in a definite direction, which avoids an object or obstacle. Next remove and embed the system in an elastic medium that can be warped, twisted, pulled or stretched as desired. The initial condition of the fields is recorded on a Cartesian mesh. As the elastic medium is distorted in one, or combination, of the described possibilities, the same pulling and stretching process is recorded by the Cartesian mesh. The same set of contortions can now be recorded, occurring as
coordinate transformation In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
: :::::''a'' (x,y,z), ''b'' (x,y,z), ''c'' (x,y,z), ''d'' (x,y,z) .... Hence, the permittivity, ε, and permeability, µ, is proportionally calibrated by a common factor. This implies that less precisely, the same occurs with the refractive index. Renormalized values of permittivity and permeability are applied in the ''new'' coordinate system. For the renormalization equations see ref. #.


Application to cloaking devices

Given the above parameters of operation, the system, a metamaterial, can now be shown to be able to conceal an object of arbitrary size. Its function is to manipulate incoming rays, which are about to strike the object. These incoming rays are instead electromagnetically steered around the object by the metamaterial, which then returns them to their original trajectory. As part of the design it can be assumed that no radiation leaves the concealed volume of space, and no radiation can enter the space. As illustrated by the function of the metamaterial, any radiation attempting to penetrate is steered around the space or the object within the space, returning to the initial direction. It appears to any observer that the concealed volume of space is empty, even with an object present there. An arbitrary object may be hidden because it remains untouched by external radiation. A sphere with radius R1 is chosen as the object to be hidden. The cloaking region is to be contained within the annulus R1 < r < R2. A simple transformation that achieves the desired result can be found by taking all fields in the region r < R2 and compressing them into the region R1 < r < R2. The coordinate transformations do not alter Maxwell's equations. Only the values of ε′ and µ′ change over time.


Cloaking hurdles

There are issues to be dealt with to achieve invisibility cloaking. One issue, related to ray tracing, is the
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
effects of the material on the electromagnetic rays entering the "system". Parallel bundles of rays, (''see above image''), headed directly for the center are abruptly curved and, along with neighboring rays, are forced into tighter and tighter
arc ARC may refer to: Business * Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s * Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services * ...
s. This is due to rapid changes in the now shifting and transforming
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
ε′ and permeability µ′. The second issue is that, while it has been discovered that the selected metamaterials are capable of working within the parameters of the anisotropic effects and the continual shifting of ε′ and µ′, the values for ε′ and µ′ cannot be very large or very small. The third issue is that the selected metamaterials are currently unable to achieve broad,
frequency spectrum The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...
capabilities. This is because the rays must curve around the "concealed"
sphere A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
, and therefore have longer trajectories than traversing
free space A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
, or air. However, the rays must arrive around the other side of the sphere in
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
with the beginning radiated
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
. If this is happening then the
phase velocity The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...
exceeds the
velocity of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
in a
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
, which is the speed limit of the universe. (Note, this does not violate the laws of physics). And, with a required absence of frequency dispersion, the
group velocity The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope'' of the wave—propagates through space. For example, if a stone is thrown into the middl ...
will be identical with
phase velocity The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...
. In the context of this experiment, group velocity can never exceed the velocity of light, hence the analytical parameters are effective for only one
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
.


Optical conformal mapping and ray tracing in transformation media

The goal then is to create no discernible difference between a concealed volume of space and the propagation of electromagnetic waves through empty space. It would appear that achieving a perfectly concealed (100%) hole, where an object could be placed and hidden from view, is not probable. The problem is the following: in order to carry images, light propagates in a continuous range of directions. The
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
data of electromagnetic waves, after bouncing off an object or hole, is unique compared to light propagating through empty space, and is therefore easily perceived. Light propagating through empty space is consistent only with empty space. This includes microwave frequencies. Although mathematical reasoning shows that perfect concealment is not probable because of the wave nature of light, this problem does not apply to electromagnetic rays, i.e., the domain of
geometrical optics Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of ''rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstan ...
. Imperfections can be made arbitrarily, and
exponentially Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above * Exponential decay, decrease at a rate proportional to value *Exp ...
small for objects that are much larger than the wavelength of light. Mathematically, this implies ''n'' < 1, because the rays follow the shortest path and hence in theory create a perfect concealment. In practice, a certain amount of acceptable visibility occurs, as noted above. The range of the refractive index of the dielectric (optical material) needs to be across a wide
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
to achieve concealment, with the illusion created by wave propagation across empty space. These places where ''n'' < 1 would be the shortest path for the ray around the object without phase distortion. Artificial propagation of empty space could be reached in the microwave-to- terahertz range. In
stealth technology Stealth technology, also termed low observable technology (LO technology), is a sub-discipline of military tactics and passive and active electronic countermeasures, which covers a range of methods used to make personnel, aircraft, ships, subm ...
, impedance matching could result in absorption of beamed electromagnetic waves rather than reflection, hence, evasion of detection by
radar Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
. These general principles can also be applied to
sound waves In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
, where the index ''n'' describes the ratio of the local phase velocity of the wave to the bulk value. Hence, it would be useful to protect a space from any sound sourced detection. This also implies protection from sonar. Furthermore, these general principles are applicable in diverse fields such as
electrostatics Electrostatics is a branch of physics that studies electric charges at rest (static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber ...
,
fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...
,
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
, and
quantum chaos Quantum chaos is a branch of physics which studies how chaos theory, chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship betwee ...
. Mathematically, it can be shown that the
wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
propagation is indistinguishable from empty space where
light rays In optics a ray is an idealized geometrical model of light, obtained by choosing a curve that is perpendicular to the ''wavefronts'' of the actual light, and that points in the direction of energy transfer, energy flow. Rays are used to model t ...
propagate along straight lines. The medium performs an optical conformal mapping to empty space.


Microwave frequencies

The next step, then, is to actually conceal an object by controlling electromagnetic fields. Now, the demonstrated and theoretical ability for controlled electromagnetic fields has opened a new field, ''transformation optics''. This nomenclature is derived from coordinate transformations used to create variable pathways for the propagation of light through a material. This demonstration is based on previous theoretical prescriptions, along with the accomplishment of the prism experiment. One possible application of transformation optics and materials is electromagnetic cloaking for the purpose of rendering a volume or object undetectable to incident radiation, including radiated probing. This demonstration, for the first time, of actually concealing an object with electromagnetic fields, uses the method of purposely designed spatial variation. This is an effect of embedding purposely designed electromagnetic sources in the metamaterial. As discussed earlier, the fields produced by the metamaterial are compressed into a shell (coordinate transformations) surrounding the now concealed volume. Earlier this was supported theory; this experiment demonstrated the effect actually occurs. Maxwell's equations are scalar when applying transformational coordinates, only the permittivity tensor and permeability tensor are affected, which then become spatially variant, and directionally dependent along different axes. The researchers state: Before the actual demonstration, the experimental limits of the transformational fields were computationally determined, in addition to simulations, as both were used to determine the effectiveness of the cloak. A month prior to this demonstration, the results of an experiment to spatially map the internal and external electromagnetic fields of negative refractive metamaterial was published in September 2006. This was innovative because prior to this the microwave fields were measured only externally. In this September experiment the permittivity and permeability of the microstructures (instead of external macrostructure) of the metamaterial samples were measured, as well as the scattering by the two-dimensional negative index metamaterials. This gave an average effective refractive index, which results in assuming homogeneous metamaterial. Employing this technique for this experiment, spatial mapping of phases and amplitudes of the microwave radiations interacting with metamaterial samples was conducted. The performance of the cloak was confirmed by comparing the measured field maps to simulations. For this demonstration, the concealed object was a conducting cylinder at the inner radius of the cloak. As the largest possible object designed for this volume of space, it has the most substantial scattering properties. The conducting cylinder was effectively concealed in two dimensions.


Infrared frequencies

The definition optical frequency, in metamaterials literature, ranges from far infrared, to near infrared, through the visible spectrum, and includes at least a portion of ultra-violet. To date when literature refers optical frequencies these are almost always frequencies in the infrared, which is below the visible spectrum. In 2009 a group of researchers announced cloaking at optical frequencies. In this case the cloaking frequency was centered at 1500 nm or 1.5 micrometers – the infrared.


Sonic frequencies

A laboratory metamaterial device, applicable to
ultra-sound Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies fr ...
waves was demonstrated in January 2011. It can be applied to sound wavelengths corresponding to frequencies from 40 to 80 kHz. The metamaterial acoustic cloak is designed to hide objects submerged in water. The metamaterial cloaking mechanism bends and twists sound waves by intentional design. The cloaking mechanism consists of 16 concentric rings in a cylindrical configuration. Each ring has acoustic circuits. It is intentionally designed to guide sound waves in two dimensions. Each ring has a different
index of refraction In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
. This causes sound waves to vary their speed from ring to ring. "The sound waves propagate around the outer ring, guided by the channels in the circuits, which bend the waves to wrap them around the outer layers of the cloak". It forms an array of cavities that slow the speed of the propagating sound waves. An experimental cylinder was submerged and then disappeared from
sonar Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigation, navigate, measure distances (ranging), communicate with or detect o ...
. Other objects of various shape and density were also hidden from the sonar. The acoustic cloak demonstrated effectiveness for frequencies of 40 kHz to 80 kHz. In 2014 researchers created a 3D acoustic cloak from stacked plastic sheets dotted with repeating patterns of holes. The
pyramid A pyramid (from el, πυραμίς ') is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilat ...
al geometry of the stack and the hole placement provide the effect.


Invisibility in diffusive light scattering media

In 2014, scientists demonstrated good cloaking performance in murky water, demonstrating that an object shrouded in fog can disappear completely when appropriately coated with metamaterial. This is due to the random scattering of light, such as that which occurs in clouds, fog, milk, frosted glass, etc., combined with the properties of the metatmaterial coating. When light is diffused, a thin coat of metamaterial around an object can make it essentially invisible under a range of lighting conditions.


Cloaking attempts


Broadband ground-plane cloak

If a
transformation Transformation may refer to: Science and mathematics In biology and medicine * Metamorphosis, the biological process of changing physical form after birth or hatching * Malignant transformation, the process of cells becoming cancerous * Trans ...
to quasi-
orthogonal coordinates In mathematics, orthogonal coordinates are defined as a set of ''d'' coordinates q = (''q''1, ''q''2, ..., ''q'd'') in which the coordinate hypersurfaces all meet at right angles (note: superscripts are indices, not exponents). A coordinate su ...
is applied to
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
in order to conceal a perturbation on a flat conducting plane rather than a singular point, as in the first demonstration of a transformation optics-based cloak, then an object can be hidden underneath the perturbation. This is sometimes referred to as a "carpet" cloak. As noted above, the original cloak demonstrated utilized resonant metamaterial elements to meet the effective material constraints. Utilizing a quasi-conformal transformation in this case, rather than the non-conformal original transformation, changed the required material properties. Unlike the original (singular expansion) cloak, the "carpet" cloak required less extreme material values. The quasi-conformal carpet cloak required anisotropic, inhomogeneous materials which only varied in
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
. Moreover, the permittivity was always positive. This allowed the use of non-resonant metamaterial elements to create the cloak, significantly increasing the bandwidth. An automated process, guided by a set of
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...
s, was used to construct a metamaterial consisting of thousands of elements, each with its own
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
. Developing the algorithm allowed the
manufacturing process Manufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of secondary sector of the economy. The term may refer to a ran ...
to be automated, which resulted in fabrication of the metamaterial in nine days. The previous device used in 2006 was rudimentary in comparison, and the manufacturing process required four months in order to create the device. These differences are largely due to the different form of transformation: the original 2006 cloak transformed a singular point, while the ground-plane version transforms a plane, and the transformation in the carpet cloak was quasi-conformal, rather than non-conformal.


Other theories of cloaking

Other theories of cloaking discuss various science and research based theories for producing an electromagnetic cloak of invisibility. Theories presented employ
transformation optics Transformation optics is a branch of optics which applies metamaterials to produce spatial variations, derived from coordinate transformations, which can direct chosen bandwidths of electromagnetic radiation. This can allow for the construction ...
, event cloaking, dipolar scattering cancellation, tunneling light transmittance, sensors and active sources, and acoustic cloaking.


Institutional research

The research in the field of
metamaterials A metamaterial (from the Ancient Greek, Greek word Meta, μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally ...
has diffused out into the American government science research departments, including the US
Naval Air Systems Command The Naval Air Systems Command (NAVAIR) provides materiel support for aircraft and airborne weapon systems for the United States Navy. It is one of the Echelon II Navy systems commands (SYSCOM), and was established in 1966 as the successor to the ...
,
US Air Force The United States Air Force (USAF) is the air service branch of the United States Armed Forces, and is one of the eight uniformed services of the United States. Originally created on 1 August 1907, as a part of the United States Army Signal ...
, and
US Army The United States Army (USA) is the land service branch of the United States Armed Forces. It is one of the eight U.S. uniformed services, and is designated as the Army of the United States in the U.S. Constitution.Article II, section 2, cla ...
. Many scientific institutions are involved including: *
California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
*
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
*
Colorado State University Colorado State University (Colorado State or CSU) is a public land-grant research university in Fort Collins, Colorado. It is the flagship university of the Colorado State University System. Colorado State University is classified among "R1: ...
*
Pennsylvania State University The Pennsylvania State University (Penn State or PSU) is a Public university, public Commonwealth System of Higher Education, state-related Land-grant university, land-grant research university with campuses and facilities throughout Pennsylvan ...
*
Duke University Duke University is a private research university in Durham, North Carolina. Founded by Methodists and Quakers in the present-day city of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco and electric power industrialist James ...
*
Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
*
Aalto University Aalto University ( fi, Aalto-yliopisto; sv, Aalto-universitetet) is a public research university located in Espoo, Finland. It was established in 2010 as a merger of three major Finnish universities: the Helsinki University of Technology, the He ...
*
Imperial College London Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...
*
Max Planck Society The Max Planck Society for the Advancement of Science (german: Max-Planck-Gesellschaft zur Förderung der Wissenschaften e. V.; abbreviated MPG) is a formally independent non-governmental and non-profit association of German research institutes. ...
*
MSU Faculty of Physics The Fizfak (Faculty of Physics) of Moscow State University is one of the most esteemed faculties of Moscow State University, widely regarded by students as one of the toughest faculties in the university. It was established in 1933. The current de ...
*
National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
*
Nederlandse Organisatie voor Wetenschappelijk Onderzoek The Dutch Research Council (NWO, Dutch: Nederlandse Organisatie voor Wetenschappelijk Onderzoek) is the national research council of the Netherlands. NWO funds thousands of top researchers at universities and institutes and steers the course of ...
*
University College London , mottoeng = Let all come who by merit deserve the most reward , established = , type = Public research university , endowment = £143 million (2020) , budget = ...
*
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...
*
University of California, Irvine The University of California, Irvine (UCI or UC Irvine) is a public land-grant research university in Irvine, California. One of the ten campuses of the University of California system, UCI offers 87 undergraduate degrees and 129 graduate and pr ...
*
University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...
*
University of California, San Diego The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Insti ...
*
University of Colorado The University of Colorado (CU) is a system of public universities in Colorado. It consists of four institutions: University of Colorado Boulder, University of Colorado Colorado Springs, University of Colorado Denver, and the University of Co ...
*
University of Delaware The University of Delaware (colloquially UD or Delaware) is a public land-grant research university located in Newark, Delaware. UD is the largest university in Delaware. It offers three associate's programs, 148 bachelor's programs, 121 mas ...
*
University of Rochester The University of Rochester (U of R, UR, or U of Rochester) is a private research university in Rochester, New York. The university grants undergraduate and graduate degrees, including doctoral and professional degrees. The University of Roc ...
Funding for research into this technology is provided by the following
American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...
agencies: *
Air Force Research Laboratory The Air Force Research Laboratory (AFRL) is a scientific research organization operated by the United States Air Force Materiel Command dedicated to leading the discovery, development, and integration of aerospace warfighting technologies, pl ...
*
Defense Advanced Research Projects Agency The Defense Advanced Research Projects Agency (DARPA) is a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military. Originally known as the Adv ...
*
Director of Central Intelligence The director of central intelligence (DCI) was the head of the American Central Intelligence Agency from 1946 to 2005, acting as the principal intelligence advisor to the president of the United States and the United States National Security C ...
*
National Geospatial-Intelligence Agency The National Geospatial-Intelligence Agency (NGA) is a combat support agency within the United States Department of Defense whose primary mission is collecting, analyzing, and distributing geospatial intelligence (GEOINT) in support of national ...
*
Naval Air Systems Command The Naval Air Systems Command (NAVAIR) provides materiel support for aircraft and airborne weapon systems for the United States Navy. It is one of the Echelon II Navy systems commands (SYSCOM), and was established in 1966 as the successor to the ...
*
Office of Naval Research The Office of Naval Research (ONR) is an organization within the United States Department of the Navy responsible for the science and technology programs of the U.S. Navy and Marine Corps. Established by Congress in 1946, its mission is to plan ...
Through this research, it has been realized that developing a method for controlling electromagnetic fields can be applied to escape detection by radiated probing, or
sonar Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigation, navigate, measure distances (ranging), communicate with or detect o ...
technology, and to improve
communications Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...
in the
microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
range; that this method is relevant to
superlens A superlens, or super lens, is a lens (optics), lens which uses metamaterials to go beyond the diffraction limit. For example, in 1995, Guerra combined a transparent grating having 50nm lines and spaces (the "metamaterial") with a conventional micro ...
design and to the cloaking of objects within and from
electromagnetic fields An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical co ...
.


In the news

On October 20, 2006, the day after Duke University achieved enveloping and "disappearing" an object in the microwave range, the story was reported by
Associated Press The Associated Press (AP) is an American non-profit news agency headquartered in New York City. Founded in 1846, it operates as a cooperative, unincorporated association. It produces news reports that are distributed to its members, U.S. newspa ...
. Media outlets covering the story included USA Today, MSNBC's Countdown With Keith Olbermann: ''Sight Unseen'', The New York Times with ''Cloaking Copper, Scientists Take Step Toward Invisibility'', (London) The Times with ''Don't Look Now—Visible Gains in the Quest for Invisibility'', Christian Science Monitor with ''Disappear Into Thin Air? Scientists Take Step Toward Invisibility'', Australian Broadcasting, Reuters with ''Invisibility Cloak a Step Closer'', and the (Raleigh) News & Observer with Invisibility Cloak a Step Closer''. On November 6, 2006, the Duke University research and development team was selected as part of the Scientific American best 50 articles of 2006. In the month of November 2009, "research into designing and building unique 'metamaterials' has received a £4.9 million funding boost. Metamaterials can be used for invisibility 'cloaking' devices, sensitive security sensors that can detect tiny quantities of dangerous substances, and flat lenses that can be used to image tiny objects much smaller than the wavelength of light." In November 2010, scientists at the University of St Andrews in Scotland reported the creation of a flexible cloaking material they call "Metaflex", which may bring industrial applications significantly closer. In 2014, the world 's first 3D acoustic device was built by Duke engineers.


See also

*
History of metamaterials The history of metamaterials begins with artificial dielectrics in microwave engineering as it developed just after World War II. Yet, there are seminal explorations of artificial materials for manipulating electromagnetic waves at the end of the 1 ...
*
Acoustic metamaterials An acoustic metamaterial, sonic crystal, or phononic crystal, is a material designed to control, direct, and manipulate sound waves or phonons in gases, liquids, and solids (crystal lattices). Sound wave control is accomplished through manipulating ...
*
Chirality Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from ...
*
Metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...
*
Metamaterial absorber A metamaterial absorber is a type of metamaterial intended to efficiently absorb electromagnetic radiation such as light. Furthermore, metamaterials are an advance in materials science. Hence, those metamaterials that are designed to be absorbers ...
*
Metamaterial antennas Metamaterial antennas are a class of antennas which use metamaterials to increase performance of miniaturized ( electrically small) antenna systems. Their purpose, as with any electromagnetic antenna, is to launch energy into free space. However, ...
*
Nonlinear metamaterials A nonlinear metamaterial is an artificially constructed material that can exhibit properties not found in nature. Its response to electromagnetic radiation can be characterized by its permittivity and magnetic permeability, material permeability. Th ...
*
Photonic crystal A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of Crystal structure, natural crystals gives rise to X-ray crystallograp ...
*
Photonic metamaterials A photonic metamaterial (PM), also known as an optical metamaterial, is a type of electromagnetic metamaterial, that interacts with light, covering terahertz (Terahertz radiation, THz), infrared (IR) or visible wavelengths. The materials employ a ...
*
Plasmonic metamaterials A plasmonic metamaterial is a metamaterial that uses surface plasmons to achieve optical properties not seen in nature. Plasmons are produced from the interaction of light with metal-dielectric materials. Under specific conditions, the incident ligh ...
*
Seismic metamaterials A seismic metamaterial, is a metamaterial that is designed to counteract the adverse effects of seismic waves on artificial structures, which exist on or near the surface of the earth. Current designs of seismic metamaterials utilize configurations ...
*
Split-ring resonator A split-ring resonator (SRR) is an artificially produced structure common to metamaterials. Its purpose is to produce the desired magnetic susceptibility (magnetic response) in various types of metamaterials up to 200 terahertz. These media cre ...
*
Superlens A superlens, or super lens, is a lens (optics), lens which uses metamaterials to go beyond the diffraction limit. For example, in 1995, Guerra combined a transparent grating having 50nm lines and spaces (the "metamaterial") with a conventional micro ...
*
Terahertz metamaterials A terahertz metamaterial is a class of composite metamaterials designed to interact at Terahertz radiation, terahertz (THz) frequencies. The terahertz frequency range used in materials science, materials research is usually defined as 0.1 to 10 Ter ...
*
Theories of cloaking Theories of cloaking discusses various theories based on science and research, for producing an electromagnetic cloaking device. Theories presented employ transformation optics, event cloaking, dipolar scattering cancellation, tunneling light tran ...
*
Transformation optics Transformation optics is a branch of optics which applies metamaterials to produce spatial variations, derived from coordinate transformations, which can direct chosen bandwidths of electromagnetic radiation. This can allow for the construction ...
*
Tunable metamaterials A tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave (EM wave) interacts with a metamaterial. This translates into the capabi ...
::::Academic journals * ''Metamaterials'' (journal) ::::Metamaterials books *''
Metamaterials Handbook ''Metamaterials Handbook'' is a two-volume handbook on metamaterials edited by Filippo Capolino (University of California). The series is designed to cover all theory and application topics related to electromagnetic metamaterials. Disciplin ...
'' *'' Metamaterials: Physics and Engineering Explorations''


References


Further reading

* 148 pages. "''Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics in the Graduate School of Duke University 2009''"


External links


Defining metamaterialsManipulating the Near Field with Metamaterials
Slide show, with audio available, by Dr. John Pendry, Imperial College, London
Researchers propose mimicking the cosmos with metamaterials
{{emerging technologies, topics=yes, robotics=yes, manufacture=yes, materials=yes Electromagnetism Metamaterials Stealth technology