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Metamaterial cloaking is the usage of metamaterials 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 and transmission of specified parts of the
light spectrum The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
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 fr ...
. Metamaterial cloaking, based on transformation optics, describes the process of shielding something from view by controlling
electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
. 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 Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
, also known as the
electromagnetic spectrum The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
, in a manner that is difficult or impossible to achieve with
natural material * A ″ natural material a substance that comes from plants, animals, or the earth, and has not been made by humans.. Minerals and the metals that can be extracted from them (without further modification) are also considered to belong into this ...
s. In other words, these metamaterials can be further defined as artificially structured
composite material A composite or composite material (also composition material) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a ...
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 via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
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 design – a sequentially repeating network – of identical elements. Additionally, for
microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...
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 optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...
. Also, a metamaterial is composed of a sequence of elements and spacings, which are much smaller than the selected wavelength of light. 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 u ...
, microwave, or other radiations, now just beginning to reach into the
visible frequencies The visible spectrum is the band of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' (or simply light). The optical spectrum is sometimes consider ...
.
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 phenome ...
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 called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...
and a
magnetic field A magnetic field (sometimes called B-field) is a physical 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 ...
, 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 micros ...
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, such as ordinary
refraction In physics, refraction is the redirection of a wave as it passes from one transmission medium, 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 commo ...
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 light 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 (wave propagation), interference, diffraction, Polarization (waves), polarization, and other phenomena for which the ray approximation of geometric opti ...
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 th ...
. 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 spectral band, band 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). The optica ...
.
Dissipation In thermodynamics, dissipation is the result of an irreversible process that affects a thermodynamic system. In a dissipative process, energy ( internal, bulk flow kinetic, or system potential) transforms from an initial form to a final form, wh ...
, absorption, and dispersion are also current drawbacks, but this field is still in its optimistic infancy.


Metamaterials and transformation optics

The field of transformation optics 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 discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
'', a peer-reviewed journal. The two papers are tenable theories on bending or distorting
light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
to electromagnetically conceal an object. Both papers notably map the initial configuration of the
electromagnetic field An electromagnetic field (also EM field) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarde ...
s on to a Cartesian 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, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
, or
electromagnetic waves In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ran ...
and
energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
, 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, Electrical network, electr ...
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 and standardize the Position (geometry), position of the Point (geometry), points or other geometric elements on a manifold such as ...
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 (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
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 possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...
and
magnetic field A magnetic field (sometimes called B-field) is a physical 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 ...
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 the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
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 devices.


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 br ...
), 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 a type of material engineered to have a property, typically rarely observed in naturally occu ...
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 to ...
s employ metamaterials to create directed blind spots by deflecting certain parts of the
light spectrum The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
(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 modula ...
, 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 phenome ...
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 an optical phenomenon caused by refraction, internal reflection and dispersion of light in water droplets resulting in a continuous spectrum of light appearing in the sky. The rainbow takes the form of a multicoloured circular ...
. 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 system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
,
cell phone A mobile phone or cell phone is a portable telephone that allows users to make and receive calls over a radio frequency link while moving within a designated telephone service area, unlike fixed-location phones ( landline phones). This radio ...
s, and
wireless Internet Wireless communication (or just wireless, when the context allows) is the transfer of information (''telecommunication'') between two or more points without the use of an electrical conductor, optical fiber or other continuous guided mediu ...
. The infrared spectrum is used for
thermal imaging Infrared thermography (IRT), thermal video 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 im ...
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, also called a digicam, is a camera that captures photographs in digital memory. Most cameras produced today are digital, largely replacing those that capture images on photographic film or film stock. Digital cameras are now ...
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 v ...
. Astronomers employ the terahertz band for submillimeter observations to answer deep
cosmological Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe, the cosmos. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', with the meaning of "a speaking of the wo ...
questions. Furthermore, electromagnetic energy is light energy, but only a small part of it is
visible light Light, visible light, or visible radiation is electromagnetic radiation that can be perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400–700 nanometres (nm ...
. 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 that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...
, 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 particles that can ...
than longer waves, such as
microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...
s and
radio waves Radio waves (formerly called Hertzian waves) are a type of electromagnetic radiation with the lowest frequencies and the longest wavelengths in the electromagnetic spectrum, typically with frequencies below 300 gigahertz (GHz) and wavelengths ...
. For the
science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
s, the light spectrum is known as the
electromagnetic spectrum The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
.


The properties of optics and light

Prism PRISM is a code name for a program under which the United States National Security Agency (NSA) collects internet communications from various U.S. internet companies. The program is also known by the SIGAD . PRISM collects stored internet ...
s,
mirror A mirror, also known as a looking glass, is an object that Reflection (physics), reflects an image. Light that bounces off a mirror forms an image of whatever is in front of it, which is then focused through the lens of the eye or a camera ...
s, and
lens A lens is a transmissive optical device that 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 an amorphous (non-crystalline solid, non-crystalline) solid. Because it is often transparency and translucency, transparent and chemically inert, glass has found widespread practical, technological, and decorative use in window pane ...
. Hence, these familiar
technologies Technology is the application of Conceptual model, conceptual knowledge to achieve practical goals, especially in a reproducible way. The word ''technology'' can also mean the products resulting from such efforts, including both tangible too ...
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 full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
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 (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...
(AD 85 – 165). In his work entitled ''Optics'', he writes about the properties of
light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
, including reflection,
refraction In physics, refraction is the redirection of a wave as it passes from one transmission medium, 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 commo ...
, and
color Color (or colour in English in the Commonwealth of Nations, Commonwealth English; American and British English spelling differences#-our, -or, see spelling differences) is the visual perception based on the electromagnetic spectrum. Though co ...
. 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 the Snell–Descartes law, the 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 th ...
. He was followed by the most notable Islamic scientist,
Ibn Al-Haytham Ḥasan Ibn al-Haytham (Latinization of names, Latinized as Alhazen; ; full name ; ) was a medieval Mathematics in medieval Islam, mathematician, Astronomy in the medieval Islamic world, astronomer, and Physics in the medieval Islamic world, p ...
(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 scientific study of matter, its Elementary particle, 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 whi ...
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 optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...
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, commonly known as Snell. His name is usually associated with the law of refraction of light known as Snell's law. The ...
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) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
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 pa ...
. 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 a type of material engineered to have a property, typically rarely observed in naturally occu ...
s alter how objects interact with the
electromagnetic spectrum The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
. 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, 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. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
, or
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
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, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
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 f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase. The g ...
in the material properties. The associated report was published in the journal ''
Science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
''. 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 in the visual system that reacts to light, visible light allowing eyesight. Other functions include maintaining the circadian rhythm, and Balance (ability), keeping balance. The eye can be considered as a living ...
, which sees only within the
visible spectrum The visible spectrum is the spectral band, band 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). The optica ...
. This is because the
wavelengths In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same '' phase'' on ...
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; it has symbol Cu (from Latin ) 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 pinkish-orang ...
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 full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
, from radio frequencies to microwave to the
visible spectrum The visible spectrum is the spectral band, band 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). The optica ...
, and to
x-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
, is not available at this time. This is due to the dispersive nature of present-day metamaterials. The coordinate transformation ( transformation optics) requires extraordinary material parameters that are only approachable through the use of
resonant Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...
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 pa ...
. 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, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
. As stated earlier – the range of response has been known, and studied, going back to
Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...
– 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 the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
of a given optical material. Every
natural material * A ″ natural material a substance that comes from plants, animals, or the earth, and has not been made by humans.. Minerals and the metals that can be extracted from them (without further modification) are also considered to belong into this ...
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 full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
, is accomplished with common objects and materials which control and direct the
electromagnetic field An electromagnetic field (also EM field) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarde ...
s. For example, a glass
lens A lens is a transmissive optical device that 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-frequency engineering, an antenna (American English) or aerial (British English) is an electronic device that converts an alternating electric current into radio waves (transmitting), or radio waves into an electric current (receivi ...
s are designed to transmit and receive daily FM broadcasts.
Homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...
materials, which manipulate or modulate
electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
, such as glass lenses, are limited in the upper limit of refinements to correct for aberrations. Combinations of
inhomogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...
lens materials are able to employ gradient
refractive indices In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
, but the ranges tend to be limited. Metamaterials were introduced about a decade ago, and these expand control of parts of the
electromagnetic spectrum The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high ...
; from
microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...
, to terahertz, to
infrared Infrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...
. 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 modula ...
, will eventually expand control and direction of electromagnetic fields into the
visible spectrum The visible spectrum is the spectral band, band 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). The optica ...
. 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 (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
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 universe, natural world that can be or that has been reproducibility, repeatedly tested and has corroborating evidence in accordance with the scientific method, using accepted protocol (s ...
for cloaking of objects from electromagnetic detection. Each component responds independently to a radiated
electromagnetic wave In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ...
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 and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
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 phenome ...
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) ...
, 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 relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...
composite
metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is a type of material engineered to have a property, typically rarely observed in naturally occu ...
s which direct, at will,
conserved quantities A conserved quantity is a property or value that remains constant over time in a system even when changes occur in the system. In mathematics, a conserved quantity of a dynamical system is formally defined as a function of the dependent vari ...
of
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
. These quantities are specifically, the
electric displacement field In physics, the electric displacement field (denoted by D), also called electric flux density, is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, com ...
D, the
magnetic field intensity A magnetic field (sometimes called B-field) is a physical 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 ...
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 wat ...
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 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, Electrical network, electr ...
and are more than only ray approximation found in
geometrical optics Geometrical optics, or ray optics, is a model of optics that describes light Wave propagation, propagation in terms of ''ray (optics), rays''. The ray in geometrical optics is an abstract object, abstraction useful for approximating the paths along ...
. 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 (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
, ε, and
magnetic permeability In electromagnetism, permeability is the measure of magnetization produced in a material in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. It is the ratio of the magnetic ...
, μ. The sources are embedded in an arbitrarily 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 modula ...
with
dielectric In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...
and
magnetic Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, m ...
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 called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...
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 and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...
: :::::''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 structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit ver ...
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 arcs. 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 (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
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 In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. According to Fourier analysis, any physical signal can be decomposed int ...
capabilities. This is because the rays must curve around the "concealed"
sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, 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 (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...
, 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 mathematica ...
with the beginning radiated
light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
. 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, t ...
exceeds the
velocity of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
in a
vacuum A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...
, 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 (waves), envelope'' of the wave—propagates through space. For example, if a stone is thro ...
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, t ...
. 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. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
.


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 In physics, scattering is 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 particles and radiat ...
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 Wave propagation, propagation in terms of ''ray (optics), rays''. The ray in geometrical optics is an abstract object, abstraction useful for approximating the paths along ...
. Imperfections can be made arbitrarily, and exponentially 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 (: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word ''spectrum'' was first used scientifically in optics to describe the rainbow of co ...
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. The term covers a range of military technology, methods used to make personnel ...
, impedance matching could result in absorption of beamed electromagnetic waves rather than reflection, hence, evasion of detection by
radar Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
. 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 br ...
, 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 slow-moving or stationary electric charges. Since classical antiquity, classical times, it has been known that some materials, such as amber, attract lightweight particles after triboelectric e ...
,
fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...
,
classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...
, and quantum chaos. Mathematically, it can be shown that the
wave In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...
propagation is indistinguishable from empty space where light rays 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 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 the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
. 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 navigate, measure distances ( ranging), communicate with or detect objects 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 () is a structure whose visible surfaces are triangular in broad outline and converge toward the top, making the appearance roughly a pyramid in the geometric sense. The base of a pyramid can be of any polygon shape, such as trian ...
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 to quasi-
orthogonal coordinates In mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. ...
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, Electrical network, electr ...
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 (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
. 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 Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...
s, was used to construct a metamaterial consisting of thousands of elements, each with its own
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
. 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 the secondary sector of the economy. The term may refer to ...
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, event cloaking, dipolar scattering cancellation, tunneling light transmittance, sensors and active sources, and acoustic cloaking.


Institutional research

The research in the field of metamaterials 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 aeronaval 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 succe ...
,
US Air Force The United States Air Force (USAF) is the Air force, air service branch of the United States Department of Defense. It is one of the six United States Armed Forces and one of the eight uniformed services of the United States. Tracing its ori ...
, and
US Army The United States Army (USA) is the primary land service branch of the United States Department of Defense. It is designated as the Army of the United States in the United States Constitution.Article II, section 2, clause 1 of the United Stat ...
. Many scientific institutions are involved including: *
California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...
*
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
*
Colorado State University Colorado State University (Colorado State or CSU) is a Public university, public Land-grant university, land-grant research university in Fort Collins, Colorado, United States. It is the flagship university of the Colorado State University Syst ...
*
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 Pennsyl ...
*
Duke University Duke University is a Private university, private research university in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present-day city of Trinity, North Carolina, Trinity in 1838, the school moved to Durham in 1 ...
*
Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
*
Aalto University Aalto University (; ) is a public university, 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 Helsinki School of Economic ...
*
Imperial College London Imperial College London, also known as Imperial, is a Public university, public research university in London, England. Its history began with Prince Albert of Saxe-Coburg and Gotha, Prince Albert, husband of Queen Victoria, who envisioned a Al ...
*
Max Planck Society The Max Planck Society for the Advancement of Science (; abbreviated MPG) is a formally independent non-governmental and non-profit association of German research institutes. Founded in 1911 as the Kaiser Wilhelm Society, it was renamed to the M ...
*
MSU Faculty of Physics The Fizfak (Faculty of Physics) of Moscow State University is one of the most esteemed faculty (division), faculties of Moscow State University, widely regarded by students as one of the toughest faculties in the university. It was established in ...
*
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 Outline of p ...
*
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 o ...
*
University College London University College London (Trade name, branded as UCL) is a Public university, public research university in London, England. It is a Member institutions of the University of London, member institution of the Federal university, federal Uni ...
*
University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
*
University of California, Irvine The University of California, Irvine (UCI or UC Irvine) is a Public university, public Land-grant university, land-grant research university in Irvine, California, United States. One of the ten campuses of the University of California system, U ...
*
University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public university, public Land-grant university, land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school the ...
*
University of California, San Diego The University of California, San Diego (UC San Diego in communications material, formerly and colloquially UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California, United States. Es ...
*
University of Colorado The University of Colorado (CU) is a system of public universities in Colorado. It consists of four institutions: the University of Colorado Boulder, the University of Colorado Colorado Springs, the University of Colorado Denver, and the U ...
*
University of Delaware The University of Delaware (colloquially known as UD, UDel, or Delaware) is a Statutory college#Delaware, privately governed, state-assisted Land-grant university, land-grant research university in Newark, Delaware, United States. UD offers f ...
*
University of Rochester The University of Rochester is a private university, private research university in Rochester, New York, United States. It was founded in 1850 and moved into its current campus, next to the Genesee River in 1930. With approximately 30,000 full ...
Funding for research into this technology is provided by the following American agencies: *
Air Force Research Laboratory The Air Force Research Laboratory (AFRL) is a scientific research and development detachment of the United States Air Force Air Force Materiel Command, Materiel Command dedicated to leading the discovery, development, and integration of direct- ...
*
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 Adva ...
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Director of Central Intelligence The director of central intelligence (DCI) was the head of the American Central Intelligence Agency (CIA) from 1946 to 2004, acting as the principal intelligence advisor to the president of the United States and the United States National Se ...
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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) to support national se ...
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Naval Air Systems Command The Naval Air Systems Command (NAVAIR) provides materiel support for aeronaval 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 succe ...
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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 navigate, measure distances ( ranging), communicate with or detect objects o ...
technology, and to improve
communications Communication is commonly defined as the transmission of information. Its precise definition is disputed and there are disagreements about whether Intention, unintentional or failed transmissions are included and whether communication not onl ...
in the
microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...
range; that this method is relevant to superlens design and to the cloaking of objects within and from
electromagnetic fields In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
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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 not-for-profit organization, not-for-profit news agency headquartered in New York City. Founded in 1846, it operates as a cooperative, unincorporated association, and produces news reports that are dist ...
. 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 * Acoustic metamaterials *
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 fro ...
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Metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is a type of material engineered to have a property, typically rarely observed in naturally occu ...
* Metamaterial absorber * Metamaterial antennas * Nonlinear metamaterials *
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 * Plasmonic metamaterials * Seismic metamaterials * Split-ring resonator * Superlens * Terahertz metamaterials * Theories of cloaking * Transformation optics * Tunable metamaterials ::::Academic journals * ''Metamaterials'' (journal) ::::Metamaterials books *'' Metamaterials Handbook'' *'' 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

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Manipulating 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