Metamaterial cloaking
Encyclopedia
Metamaterial cloaking is the scientific application of metamaterials in order to achieve invisibility-cloaking. 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. and demonstrate the potential to render an object seemingly invisible. Metamaterial cloaking, based on transformation optics
, describes the process of shielding something from view by controlling electromagnetic radiation
. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself.
Other related concepts have been proposed in peer review
ed, scientific articles, but are discussed in a different article (see below). Hence, other theories of invisibility-cloaking, or electromagnetic cloaking, describe different methods of scattering and shielding.
, in a manner that is difficult or impossible to achieve with natural material
s. In other words, these metamaterials can be further defined as artificially structured composite material
s, which exhibit interaction with light usually not available in nature (electromagnetic interactions). 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 are a lattice
design – a sequentially repeating network – of identical elements. Additionally, for microwave
frequencies, these materials are analogous to crystal
s for optics
. 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
, microwave, or other radiations, now just beginning to reach into the visible frequencies. Macroscopic
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
and a magnetic field
, ordinary optical materials, such as optical microscope
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
with common diffraction limitations in lenses and imaging
.
Since the beginning of optical sciences
, centuries ago, the ability to control the 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
and optical physics
. 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
. Dissipation
, absorption
, and dispersion
are also current drawbacks, but this field is still in its optimistic infancy.
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
, a peer reviewed journal. The two papers are tenable theories on bending or distorting light
to electromagnetically
conceal an object. Both papers notably map the initial configuration of the electromagnetic field
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
, or electromagnetic waves and energy
, in any preferred or desired fashion, for a desired application. Maxwell's equations
do not vary even though coordinates
transform. Instead it is the values of the chosen parameters of the materials which "transform", or alter, during a certain time period. Transformation optics developed from the capability to choose which parameters for a given material, known as a metamaterial. Hence, since Maxwell's equations retain the same form, it is the successive values of permittivity
and permeability
that change, over time. Permittivity and permeability are in a sense responses to the electric
and magnetic field
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
of ordinary materials become independent spatial gradients, that can be controlled at will. Therefore, transformation optics is a new method for creating novel and unique optical devices.
isolated from passing electromagnetic fields (or sound waves
), as with Metamaterial cloaking.
Cloaking objects, or making them appear invisible with metamaterial
s, can be roughly analogous to the magician's sleight of hand, or his tricks with mirrors. The object or subject didn't really disappear; it is an illusion. With the same goal, researcher
s employ metamaterials to create directed blind spots by deflecting certain parts of the light spectrum (electromagnetic spectrum). It is the light spectrum, as the transmission medium
, that determines what the human eye can see.
In other words, light is refracted 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
. 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
, cell phones, and wireless Internet
. The infrared spectrum is used for thermal imaging technologies, which can detect a warm body amidst a cooler night time environment, and infrared illumination is combined with specialized digital cameras
for night vision. Astronomers employ the terahertz band for submillimeter observations to answer deep cosmological
questions.
Furthermore, electromagnetic energy is light energy, but only a small part of it is visible light. This energy travels in waves. Shorter wavelengths, such as visible light and infrared
, carry more energy than longer waves, such as microwave
s and radio waves
. For the science
s, the light spectrum is known as the electromagnetic spectrum
.
s, mirror
s, and lens
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
. Hence, these familiar technologies 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 in development. 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
could technologically advance. With these beginning steps a whole new class optics has been established.
(AD 85 – 165). In his work entitled Optics, he writes about the properties of light
, including reflection
, refraction
, and color
. He developed a simplified equation for refraction without trigonometric functions. About 800 years later, in AD 984, Ibn Sahl
discovered a law of refraction mathematically equivalent to Snell's law
. He was followed by the most notable Islamic scientist, Ibn Al-Haytham (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
in general, and optics
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
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.
and matter have a symbiotic relationship. Radiation does not simply act on a material, nor is it simply acted on upon by a given material. Radiation interacts with matter
. Cloaking applications which employ metamaterial
s alter how objects interact with the electromagnetic spectrum
. 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.
Yet, this is one aspect of how science
can move forward. Scientific theories are developed from such visions. Furthermore, this perfect working device is actually the goal of the sciences involved in researching cloaking capabilities, e.g. find ways to make invisibility a reality.
One challenge up to the present date has been the inability of metamaterials, and cloaking devices, to interact at frequencies, or wavelength
s, within the visible light spectrum.
on October 19, 2006. This demonstration used a small cloaking device. Its height was less than one half inch tall with a five inch diameter, and successfully steered microwaves around it. 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 flow around the cylinder inside with some 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
near it. There was reduced reflection of electromagnetic waves (microwaves), from the object. Unlike any natural material with its material properties being 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 the material properties, which is in contrast to natural materials. The associated report was published in the journal Science
.
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
, which sees only within the visible spectrum
. This is because the wavelengths 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
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
, from radio frequencies to microwave to the visible spectrum
, and to x-ray
, 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 elements, which are inherently narrow band
, and dispersive
at resonance.
. 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
. As stated earlier - the range of response has been known, and studied, going back to Ptolemy
- 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
of a given optical material. Every natural material
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, metamaerials demonstrate the capability to deliver chosen responses at will.
The exploitation of "light", the electromagnetic spectrum
, is accomplished with common objects and materials which control and direct the electromagnetic field
s. For example a glass lens
in a camera is used to produce an image, a metal cage may be used to screen sensitive equipment, and radio antennas are designed to transmit and receive daily FM broadcasts. Homogeneous
materials, which manipulate or modulate electromagnetic radiation
, such as glass lenses, are limited in the upper limit of refinements to correct for aberrations. Combinations of inhomogeneous lens materials are able to employ gradient refractive indices, but the ranges tend to be limited.
Metamaterials were introduced about a decade ago, and these expand control of parts of the electromagnetic spectrum
; from microwave
, to terahertz, to infrared
. Theoretically, metamaterials, as a transmission medium
, will eventually expand control and direction of electromagnetic fields into the visible spectrum
. 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
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
for cloaking of objects from electromagnetic detection.
Each component responds independently to a radiated electromagnetic wave 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
it is understood that a macroscopic
view includes an effective value for both permittivity and permeability. These materials obey the laws of physics, 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 composite metamaterial
s which direct, at will, conserved quantities
of electromagnetism
. These quantities are specifically, the electric displacement field D, the magnetic field intensity
B, and the Poynting vector
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
and are more than only ray approximation
found in geometrical optics
. 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
, ε, and magnetic permeability, μ. The sources are embedded in an arbitrarily selected transmission medium
with dielectric
and magnetic 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
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:
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. #.
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.
, is the anisotropic 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
s. This is due to rapid changes in the now shifting and transforming permittivity
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
capabilities. This is because the rays must curve around the "concealed" sphere
, and therefore have longer trajectories than traversing free space, or air. However, the rays must arrive around the other side of the sphere in phase
with the beginning radiated light
. If this is happening then the phase velocity exceeds the velocity of light in a vacuum
, 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
will be identical with phase velocity
. 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
.
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
. 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
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
, impedance matching could result in absorption of beamed electromagnetic waves rather than reflection, hence, evasion of detection by radar
. These general principles can also be applied to sound waves, 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
, fluid mechanics
, classical mechanics
, and quantum chaos
.
Mathematically, it can be shown that the wave
propagation is indistinguishable from empty space where light rays propagate along straight lines. The medium performs an optical conformal mapping to empty space.
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.
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, and each ring with acoustic circuits. It is intentionally designed to guide sound waves, in two dimensions. The first microwave metamaterial cloak guided electromagnetic waves in two dimensions.
Each ring has a different index of refraction. 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". This device has been described as an array of cavities which actually slow the speed of the propagating sound waves. An experimental cylinder was submerged in tank and then disappeared from sonar. Other objects of various shape and density were also hidden from the sonar. The acoustic cloak demonstrated effectiveness for the sound wavelengths of 40 kHz to 80 kHz.
is applied to Maxwell's equations
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
. 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
s, was used to construct a metamaterial consisting of thousands of elements, each with its own geometry
. Developing the algorithm allowed the manufacturing process 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.
, event cloaking, dipolar scattering cancellation, tunneling light transmittance, sensors and active sources, and acoustic cloaking
.
, US Air Force, and US Army. Many scientific institutions are involved including:
Funding for research into this technology is provided by the following American
agencies:
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
technology, and to improve communications in the microwave
range; that this method is relevant to superlens
design and to the cloaking of objects within and from electromagnetic fields.
. 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.
Metamaterials scientists
Metamaterials direct and control the propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
and transmission of specified parts of the light spectrum. and demonstrate the potential to render an object seemingly invisible. Metamaterial cloaking, based on transformation optics
Transformation optics
Transformation optics represents an advancement in the design of optical devices. It is the basis for conceptualizing complex tools in the electromagnetic regime which allows for novel control of light, also known as electromagnetic waves. The mathematics underpinning transformation optics is...
, describes the process of shielding something from view by controlling electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
. Objects in the defined location are still present, but incident waves are guided around them without being affected by the object itself.
Other related concepts have been proposed in peer review
Peer review
Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...
ed, scientific articles, but are discussed in a different article (see below). Hence, other theories of invisibility-cloaking, or electromagnetic cloaking, describe different methods of scattering and shielding.
Electromagnetic metamaterials
Electromagnetic metamaterials respond to chosen parts of radiated light, also known as the electromagnetic spectrumElectromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
, in a manner that is difficult or impossible to achieve with natural material
Natural material
A natural material is any product or physical matter that comes from plants, animals, or the ground. Minerals and the metals that can be extracted from them are also considered to belong into this category.* Biotic materials...
s. In other words, these metamaterials can be further defined as artificially structured composite material
Composite material
Composite materials, often shortened to composites or called composition materials, are engineered or naturally occurring materials made from two or more constituent materials with significantly different physical or chemical properties which remain separate and distinct at the macroscopic or...
s, which exhibit interaction with light usually not available in nature (electromagnetic interactions). 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 are a lattice
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
design – a sequentially repeating network – of identical elements. Additionally, for microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
frequencies, these materials are analogous to crystal
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
s for optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
. 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
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
, microwave, or other radiations, now just beginning to reach into the visible frequencies. Macroscopic
Macroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...
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
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
, ordinary optical materials, such as optical microscope
Optical microscope
The optical microscope, often referred to as the "light microscope", is a type of microscope which uses visible light and a system of lenses to magnify images of small samples. Optical microscopes are the oldest design of microscope and were possibly designed in their present compound form in the...
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
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
with common diffraction limitations in lenses and imaging
Optical resolution
Optical resolution describes the ability of an imaging system to resolve detail in the object that is being imaged.An imaging system may have many individual components including a lens and recording and display components...
.
Since the beginning of optical sciences
History of optics
Optics began with the development of lenses by the ancient Egyptians and Mesopotamians, followed by theories on light and vision developed by ancient Greek and Indian philosophers, and the development of geometrical optics in the Greco-Roman world. The word optics is derived from the Greek term τα...
, centuries ago, the ability to control the light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
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
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
is expanded beyond the ordinary optical limitations that are described by the sciences of physical optics
Physical optics
In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid...
and optical physics
Optical physics
Optical physics, or optical science, is a subfield of atomic, molecular, and optical physics. It is the study of the generation of electromagnetic radiation, the properties of that radiation, and the interaction of that radiation with matter, especially its manipulation and control...
. 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
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
, 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
Frequency spectrum
The frequency spectrum of a time-domain signal is a representation of that signal in the frequency domain. The frequency spectrum can be generated via a Fourier transform of the signal, and the resulting values are usually presented as amplitude and phase, both plotted versus frequency.Any signal...
has not been achieved, including the visible spectrum
Visible spectrum
The visible spectrum is the portion 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. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...
. Dissipation
Dissipation
In physics, dissipation embodies the concept of a dynamical system where important mechanical models, such as waves or oscillations, lose energy over time, typically from friction or turbulence. The lost energy converts into heat, which raises the temperature of the system. Such systems are called...
, absorption
Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...
, and dispersion
Dispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....
are also current drawbacks, but this field is still in its optimistic infancy.
Metamaterials and transformation optics
The field of transformation opticsTransformation optics
Transformation optics represents an advancement in the design of optical devices. It is the basis for conceptualizing complex tools in the electromagnetic regime which allows for novel control of light, also known as electromagnetic waves. The mathematics underpinning transformation optics is...
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 (journal)
Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....
, a peer reviewed journal. The two papers are tenable theories on bending or distorting light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
to electromagnetically
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
conceal an object. Both papers notably map the initial configuration of the electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
s on to a Cartesian
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...
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
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
, or electromagnetic waves and energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
, in any preferred or desired fashion, for a desired application. Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
do not vary even though coordinates
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...
transform. Instead it is the values of the chosen parameters of the materials which "transform", or alter, during a certain time period. Transformation optics developed from the capability to choose which parameters for a given material, known as a metamaterial. Hence, since Maxwell's equations retain the same form, it is the successive values of permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
and permeability
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
that change, over time. Permittivity and permeability are in a sense responses to the electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
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
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
of ordinary materials become independent spatial gradients, that can be controlled at will. Therefore, transformation optics is a new method for creating novel and unique optical devices.
-
- For further information see: Transformation opticsTransformation opticsTransformation optics represents an advancement in the design of optical devices. It is the basis for conceptualizing complex tools in the electromagnetic regime which allows for novel control of light, also known as electromagnetic waves. The mathematics underpinning transformation optics is...
- For further information see: Transformation optics
Science of cloaking devices
The purpose of a cloaking device is to hide something, so that a defined region of space is invisiblyInvisibility
Invisibility is the state of an object that cannot be seen. An object in this state is said to be invisible . The term is usually used as a fantasy/science fiction term, where objects are literally made unseeable by magical or technological means; however, its effects can also be seen in the real...
isolated from passing electromagnetic fields (or sound waves
Acoustic metamaterials
Acoustic metamaterials are artificially fabricated materials designed to control, direct, and manipulate sound in the form of sonic, infrasonic, or ultrasonic waves, as these might occur in gases, liquids, and solids. The hereditary line into acoustic metamaterials follows from theory and research...
), as with Metamaterial cloaking.
Cloaking objects, or making them appear invisible with metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
s, can be roughly analogous to the magician's sleight of hand, or his tricks with mirrors. The object or subject didn't really disappear; it is an illusion. With the same goal, researcher
Researcher
A researcher is somebody who performs research, the search for knowledge or in general any systematic investigation to establish facts. Researchers can work in academic, industrial, government, or private institutions.-Examples of research institutions:...
s employ metamaterials to create directed blind spots by deflecting certain parts of the light spectrum (electromagnetic spectrum). It is the light spectrum, as the transmission medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
, that determines what the human eye can see.
In other words, light is refracted or reflected determining the view, color, or illusion that is seen. The visible extent of light is seen in a chromatic spectrum
Visible spectrum
The visible spectrum is the portion 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. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...
such as the rainbow
Rainbow
A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc...
. 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
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
is employed by radar
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
, cell phones, and wireless Internet
Wireless
Wireless telecommunications is the transfer of information between two or more points that are not physically connected. Distances can be short, such as a few meters for television remote control, or as far as thousands or even millions of kilometers for deep-space radio communications...
. The infrared spectrum is used for thermal imaging technologies, which can detect a warm body amidst a cooler night time environment, and infrared illumination is combined with specialized digital cameras
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...
for night vision. Astronomers employ the terahertz band for submillimeter observations to answer deep cosmological
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
questions.
Furthermore, electromagnetic energy is light energy, but only a small part of it is visible light. This energy travels in waves. Shorter wavelengths, such as visible light and infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...
, carry more energy than longer waves, such as microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
s and radio waves
Radio waves
Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies from 300 GHz to as low as 3 kHz, and corresponding wavelengths from 1 millimeter to 100 kilometers. Like all other electromagnetic waves,...
. For the science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
s, the light spectrum is known as the electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
.
The properties of optics and light
PrismPrism (optics)
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...
s, mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...
s, and lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
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
Glass is an amorphous solid material. Glasses are typically brittle and optically transparent.The most familiar type of glass, used for centuries in windows and drinking vessels, is soda-lime glass, composed of about 75% silica plus Na2O, CaO, and several minor additives...
. Hence, these familiar technologies are constrained by the fundamental, physical laws of optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
. 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
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
. 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 in development. 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
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
could technologically advance. With these beginning steps a whole new class 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 PtolemyPtolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
(AD 85 – 165). In his work entitled Optics, he writes about the properties of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
, including reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
, refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
, and color
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...
. He developed a simplified equation for refraction without trigonometric functions. About 800 years later, in AD 984, Ibn Sahl
Ibn Sahl
This article is about the physicist. For the physician, see Ali ibn Sahl Rabban al-Tabari. For the poet, see Ibn Sahl of Sevilla.Ibn Sahl was a Muslim Persian mathematician, physicist and optics engineer of the Islamic Golden Age associated with the Abbasid court of Baghdad...
discovered a law of refraction mathematically equivalent to Snell's law
Snell's law
In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...
. He was followed by the most notable Islamic scientist, Ibn Al-Haytham (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
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
in general, and optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
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
Willebrord Snellius was a Dutch astronomer and mathematician. In the west, especially the English speaking countries, his name has been attached to the law of refraction of light for several centuries, but it is now known that this law was first discovered by Ibn Sahl in 984...
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.
Perfect cloak and theory
Electromagnetic radiationElectromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
and matter have a symbiotic relationship. Radiation does not simply act on a material, nor is it simply acted on upon by a given material. Radiation interacts with matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
. Cloaking applications which employ metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
s alter how objects interact with the electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
. 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 (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
, rendering the object invisible. In reality, the simple cloaking devices of the present are imperfect, and have limitations.
Yet, this is one aspect of how science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
can move forward. Scientific theories are developed from such visions. Furthermore, this perfect working device is actually the goal of the sciences involved in researching cloaking capabilities, e.g. find ways to make invisibility a reality.
One challenge up to the present date has been the inability of metamaterials, and cloaking devices, to interact at frequencies, or wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
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 bandMicrowave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
on October 19, 2006. This demonstration used a small cloaking device. Its height was less than one half inch tall with a five inch diameter, and successfully steered microwaves around it. The object to be hidden from view, a small cylinder, was placed in the center of the device. The invisibility cloak deflected microwave beams
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
so they flow around the cylinder inside with some 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
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
near it. There was reduced reflection of electromagnetic waves (microwaves), from the object. Unlike any natural material with its material properties being 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 the material properties, which is in contrast to natural materials. The associated report was published in the journal Science
Science (journal)
Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....
.
Although a successful demonstration, three notable limitations can be shown. First, since its effectiveness was only in the microwave spectrum
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
the small object is somewhat invisible only at microwave frequencies. This means invisibility had not been achieved for the human eye
Human eye
The human eye is an organ which reacts to light for several purposes. As a conscious sense organ, the eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth...
, which sees only within the visible spectrum
Visible spectrum
The visible spectrum is the portion 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. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...
. This is because the wavelengths 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
Nanotechnology
Nanotechnology is the study of manipulating matter on an atomic and molecular scale. Generally, nanotechnology deals with developing materials, devices, or other structures possessing at least one dimension sized from 1 to 100 nanometres...
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
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
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
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
, from radio frequencies to microwave to the visible spectrum
Visible spectrum
The visible spectrum is the portion 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. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...
, and to x-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
, is not available at this time. This is due to the dispersive nature
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
of present day metamaterials. The coordinate transformation (transformation optics
Transformation optics
Transformation optics represents an advancement in the design of optical devices. It is the basis for conceptualizing complex tools in the electromagnetic regime which allows for novel control of light, also known as electromagnetic waves. The mathematics underpinning transformation optics is...
) requires extraordinary material parameters that are only approachable through the use of resonant elements, which are inherently narrow band
Narrowband
In radio, narrowband describes a channel in which the bandwidth of the message does not significantly exceed the channel's coherence bandwidth. It is a common misconception that narrowband refers to a channel which occupies only a "small" amount of space on the radio spectrum.The opposite of...
, and dispersive
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
at resonance.
Why metamaterials are used
At the very beginning of the new millennium, metamaterials were established as an extraordinary new medium, which expanded control capabilities over matterMatter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
. 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
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
. As stated earlier - the range of response has been known, and studied, going back to Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
- 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
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
of a given optical material. Every natural material
Natural material
A natural material is any product or physical matter that comes from plants, animals, or the ground. Minerals and the metals that can be extracted from them are also considered to belong into this category.* Biotic materials...
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, metamaerials demonstrate the capability to deliver chosen responses at will.
Metamaterial cloaking 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
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
, is accomplished with common objects and materials which control and direct the electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
s. For example a glass lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
in a camera is used to produce an image, a metal cage may be used to screen sensitive equipment, and radio antennas are designed to transmit and receive daily FM broadcasts. Homogeneous
Homogeneity (physics)
In general, homogeneity is defined as the quality or state of being homogeneous . For instance, a uniform electric field would be compatible with homogeneity...
materials, which manipulate or modulate electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
, such as glass lenses, are limited in the upper limit of refinements to correct for aberrations. Combinations of inhomogeneous lens materials are able to employ gradient refractive indices, but the ranges tend to be limited.
Metamaterials were introduced about a decade ago, and these expand control of parts of the electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
; from microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
, to terahertz, to infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...
. Theoretically, metamaterials, as a transmission medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
, will eventually expand control and direction of electromagnetic fields into the visible spectrum
Visible spectrum
The visible spectrum is the portion 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. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...
. 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
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
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
Scientific theory
A scientific theory comprises a collection of concepts, including abstractions of observable phenomena expressed as quantifiable properties, together with rules that express relationships between observations of such concepts...
for cloaking of objects from electromagnetic detection.
Each component responds independently to a radiated electromagnetic wave 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
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
of the radiated source. Since these components are smaller than the radiated wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
it is understood that a macroscopic
Macroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...
view includes an effective value for both permittivity and permeability. These materials obey the laws of physics, 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
Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...
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 composite metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
s which direct, at will, conserved quantities
Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
of electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
. These quantities are specifically, the electric displacement field D, the magnetic field intensity
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
B, and the Poynting vector
Poynting vector
In physics, the Poynting vector can be thought of as representing the directional energy flux density of an electromagnetic field. It is named after its inventor John Henry Poynting. Oliver Heaviside and Nikolay Umov independently co-invented the Poynting vector...
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
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
and are more than only ray approximation
Ray (optics)
In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...
found in geometrical optics
Geometrical optics
Geometrical optics, or ray optics, describes light propagation in terms of "rays". The "ray" in geometric optics is an abstraction, or "instrument", which can be used to approximately model how light will propagate. Light rays are defined to propagate in a rectilinear path as far as they travel in...
. 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
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
, ε, and magnetic permeability, μ. The sources are embedded in an arbitrarily selected transmission medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
with dielectric
Dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
and magnetic 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
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
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:
-
-
-
-
- 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 tracingRay tracing (physics)
In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces,...
, is the anisotropic 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 (geometry)
In geometry, an arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of the circumference of a circle...
s. This is due to rapid changes in the now shifting and transforming permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
ε′ and permeability
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
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
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
capabilities. This is because the rays must curve around the "concealed" sphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
, and therefore have longer trajectories than traversing free space, or air. However, the rays must arrive around the other side of the sphere in phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
with the beginning radiated light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
. If this is happening then the phase velocity exceeds the velocity of light in a vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
, 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
Group velocity
The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....
will be identical with phase velocity
Phase velocity
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
. 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
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
.
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 scatteringScattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
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
Geometrical optics, or ray optics, describes light propagation in terms of "rays". The "ray" in geometric optics is an abstraction, or "instrument", which can be used to approximately model how light will propagate. Light rays are defined to propagate in a rectilinear path as far as they travel in...
. Imperfections can be made arbitrarily, and exponentially
Exponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
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
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...
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
Stealth technology also termed LO technology is a sub-discipline of military tactics and passive electronic countermeasures, which cover a range of techniques used with personnel, aircraft, ships, submarines, and missiles, to make them less visible to radar, infrared, sonar and other detection...
, impedance matching could result in absorption of beamed electromagnetic waves rather than reflection, hence, evasion of detection by radar
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
. These general principles can also be applied to sound waves, 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
Electrostatics is the branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges....
, fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
, classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
, and quantum chaos
Quantum chaos
Quantum chaos is a branch of physics which studies how 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 between quantum mechanics and classical chaos?" The correspondence principle...
.
Mathematically, it can be shown that the wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
propagation is indistinguishable from empty space where light rays propagate along straight lines. The medium performs an optical conformal mapping to empty space.
Invisiblity cloaking at 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.
Invisiblity cloaking at 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.Invisibility cloaking at sonic frequencies
A laboratory metamaterial device, applicable to ultra-sound waves has been demonstrated in January 2011. It can be applied to sound wavelengthsWavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
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, and each ring with acoustic circuits. It is intentionally designed to guide sound waves, in two dimensions. The first microwave metamaterial cloak guided electromagnetic waves in two dimensions.
Each ring has a different index of refraction. 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". This device has been described as an array of cavities which actually slow the speed of the propagating sound waves. An experimental cylinder was submerged in tank and then disappeared from sonar. Other objects of various shape and density were also hidden from the sonar. The acoustic cloak demonstrated effectiveness for the sound wavelengths of 40 kHz to 80 kHz.
Broadband ground-plane cloak
If a transformation to quasi-orthogonal coordinatesOrthogonal coordinates
In mathematics, orthogonal coordinates are defined as a set of d coordinates q = in which the coordinate surfaces all meet at right angles . A coordinate surface for a particular coordinate qk is the curve, surface, or hypersurface on which qk is a constant...
is applied to Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
in order to conceal a perturbation on a flat conducting plane
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
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
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
. 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
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
s, was used to construct a metamaterial consisting of thousands of elements, each with its own geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. Developing the algorithm allowed the manufacturing process 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 opticsTransformation optics
Transformation optics represents an advancement in the design of optical devices. It is the basis for conceptualizing complex tools in the electromagnetic regime which allows for novel control of light, also known as electromagnetic waves. The mathematics underpinning transformation optics is...
, event cloaking, dipolar scattering cancellation, tunneling light transmittance, sensors and active sources, and acoustic cloaking
Acoustic metamaterials
Acoustic metamaterials are artificially fabricated materials designed to control, direct, and manipulate sound in the form of sonic, infrasonic, or ultrasonic waves, as these might occur in gases, liquids, and solids. The hereditary line into acoustic metamaterials follows from theory and research...
.
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 CommandNaval Air Systems Command
The Naval Air Systems Command provides material support for aircraft and airborne weapon systems for the United States Navy. NAVAIR was established in 1966 as the successor to the Navy's Bureau of Naval Weapons . Current Commander, Naval Air Systems Command, is Vice Adm. David Architzel since May...
, US Air Force, and US Army. Many scientific institutions are involved including:
- California Institute of TechnologyCalifornia Institute of TechnologyThe California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
- Colorado State UniversityColorado State UniversityColorado State University is a public research university located in Fort Collins, Colorado. The university is the state's land grant university, and the flagship university of the Colorado State University System.The enrollment is approximately 29,932 students, including resident and...
- Duke UniversityDuke UniversityDuke University is a private research university located in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present day town of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco industrialist James B...
- Harvard UniversityHarvard UniversityHarvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
- Helsinki University of TechnologyHelsinki University of TechnologyAalto University School of Science and Technology , was the temporary name for Helsinki University of Technology during the process of forming the Aalto University...
- Imperial College LondonImperial College LondonImperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
- Max Planck SocietyMax Planck SocietyThe Max Planck Society for the Advancement of Science is a formally independent non-governmental and non-profit association of German research institutes publicly funded by the federal and the 16 state governments of Germany....
- MSU Faculty of PhysicsMSU Faculty of PhysicsThe Faculty of Physics of Moscow State University is the largest faculty of Moscow State University.-Nobel winners:*Igor Tamm *Ilya Frank *Lev Davidovich Landau...
- National Institute of Standards and TechnologyNational Institute of Standards and TechnologyThe National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...
- Nederlandse Organisatie voor Wetenschappelijk OnderzoekNederlandse Organisatie voor Wetenschappelijk OnderzoekThe Nederlandse Organisatie voor Wetenschappelijk Onderzoek is a scientific research organization in the Netherlands....
- University College LondonUniversity College LondonUniversity College London is a public research university located in London, United Kingdom and the oldest and largest constituent college of the federal University of London...
- University of California, BerkeleyUniversity of California, BerkeleyThe University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
- University of California, IrvineUniversity of California, IrvineThe University of California, Irvine , founded in 1965, is one of the ten campuses of the University of California, located in Irvine, California, USA...
- University of California, Los AngelesUniversity of California, Los AngelesThe University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
- University of California, San DiegoUniversity of California, San DiegoThe University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...
- University of ColoradoUniversity of Colorado SystemThe University of Colorado system is a system of public universities in Colorado consisting of three universities in four campuses: University of Colorado Boulder, University of Colorado Colorado Springs, and University of Colorado Denver in downtown Denver and at the Anschutz Medical Campus in...
- University of DelawareUniversity of DelawareThe university is organized into seven colleges:* College of Agriculture and Natural Resources* College of Arts and Sciences* Alfred Lerner College of Business and Economics* College of Earth, Ocean and Environment* College of Education and Human Development...
- University of RochesterUniversity of RochesterThe University of Rochester is a private, nonsectarian, research university in Rochester, New York, United States. The university grants undergraduate and graduate degrees, including doctoral and professional degrees. The university has six schools and various interdisciplinary programs.The...
Funding for research into this technology is provided by the following American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
agencies:
- Air Force Research LaboratoryAir Force Research LaboratoryThe Air Force Research Laboratory is a scientific research organization operated by the United States Air Force Materiel Command dedicated to leading the discovery, development, and integration of affordable aerospace warfighting technologies; planning and executing the Air Force science and...
- Defense Advanced Research Projects Agency
- Director of Central IntelligenceDirector of Central IntelligenceThe Office of United States Director of Central Intelligence was the head of the United States Central Intelligence Agency, the principal intelligence advisor to the President and the National Security Council, and the coordinator of intelligence activities among and between the various United...
- National Geospatial-Intelligence AgencyNational Geospatial-Intelligence AgencyThe National Geospatial-Intelligence Agency is an agency of the federal government of the United States with the primary mission of collecting, analyzing and distributing geospatial intelligence in support of national security. NGA was formerly known as the National Imagery and Mapping Agency ...
- Naval Air Systems CommandNaval Air Systems CommandThe Naval Air Systems Command provides material support for aircraft and airborne weapon systems for the United States Navy. NAVAIR was established in 1966 as the successor to the Navy's Bureau of Naval Weapons . Current Commander, Naval Air Systems Command, is Vice Adm. David Architzel since May...
- Office of Naval ResearchOffice of Naval ResearchThe Office of Naval Research , headquartered in Arlington, Virginia , is the office within the United States Department of the Navy that coordinates, executes, and promotes the science and technology programs of the U.S...
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
Sonar is a technique that uses sound propagation to navigate, communicate with or detect other vessels...
technology, and to improve communications in the microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
range; that this method is relevant to superlens
Superlens
A superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
design and to the cloaking of objects within and from electromagnetic fields.
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 PressAssociated Press
The Associated Press is an American news agency. The AP is a cooperative owned by its contributing newspapers, radio and television stations in the United States, which both contribute stories to the AP and use material written by its staff journalists...
. 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.
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"See also
- History of metamaterialsHistory of metamaterialsHistory of metamaterials shares a common history with artificial dielectrics in microwave engineering, as it developed just after World War II. However, there are seminal explorations of artificial materials for manipulating electromagnetic waves at the end of the 19th century...
- SuperlensSuperlensA superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
- Photonic metamaterialsPhotonic metamaterialsPhotonic metamaterials, also known as Optical metamaterials, are a type of electromagnetic metamaterial, which are designed to interact with optical frequencies which are terahertz , infrared , and eventually, visible wavelengths. As a type of metamaterial, the periodic structures are made up of...
- Metamaterial antennasMetamaterial antennasMetamaterial antennas are a class of antennas which use metamaterials to increase performance of miniaturized antenna systems. Their purpose, as with any electromagnetic antenna, is to launch energy into free space...
- Nonlinear metamaterialsNonlinear metamaterialsA 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 material permeability. The product of the permittivity and permeability results in the refractive...
- Photonic crystalPhotonic crystalPhotonic crystals are periodic optical nanostructures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons...
- Seismic metamaterialsSeismic metamaterialsSeismic metamaterials, are metamaterials which are designed to counteract the adverse effects of seismic waves on artificial structures, which exist on or near the surface of the earth...
- Split-ring resonator
- Acoustic metamaterialsAcoustic metamaterialsAcoustic metamaterials are artificially fabricated materials designed to control, direct, and manipulate sound in the form of sonic, infrasonic, or ultrasonic waves, as these might occur in gases, liquids, and solids. The hereditary line into acoustic metamaterials follows from theory and research...
- Metamaterial absorberMetamaterial absorberA metamaterial absorber manipulates the loss components of the complex effective parameters, permittivity and magnetic permeability of metamaterials, to create a material with particularly high absorption...
- MetamaterialMetamaterialMetamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
- ChiralityChiralityChirality is a property of asymmetry important in several branches of science. It may refer to:* Chirality , a property of molecules having a non-superimposable mirror image...
- Plasmonic metamaterialsPlasmonic metamaterialsPlasmonic metamaterials are negative index metamaterials that exploit surface plasmons, which are produced from the interaction of light with metal-dielectric materials. Under specific conditions, the incident light couples with the surface plasmons to create self-sustaining, propagating...
- Terahertz metamaterialsTerahertz metamaterialsTerahertz metamaterials are a new class of composite, artificial materials which interact at terahertz frequencies. The terahertz frequency range used in materials research is usually defined as 0.1 to 10 THz...
- Tunable metamaterialsTunable metamaterialsA tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave interacts with a metamaterial. This means the capablitity to determine whether the EM wave is transmitted, reflected, or...
- Transformation opticsTransformation opticsTransformation optics represents an advancement in the design of optical devices. It is the basis for conceptualizing complex tools in the electromagnetic regime which allows for novel control of light, also known as electromagnetic waves. The mathematics underpinning transformation optics is...
- Theories of cloaking
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- Academic journals
- Metamaterials (journal)Metamaterials (journal)Metamaterials is a peer-reviewed scientific journal that was established in March 2007. It is published by Elsevier in association with the Metamorphose Network of Excellence. The Coordinating Editor is Mikhail Lapine. The journal is published quarterly, with occasional special issues...
- Metamaterials (journal)
- Metamaterials books
- Metamaterials HandbookMetamaterials HandbookMetamaterials Handbook is a two-volume handbook on metamaterials edited by Filippo Capolino .The series is designed to cover all theory and application topics related to electromagnetic metamaterials. Disciplines have combined to study, and develop electromagnetic metamaterials...
- Metamaterials: Physics and Engineering ExplorationsMetamaterials: Physics and Engineering ExplorationsMetamaterials: Physics and Engineering Explorations is a book length introduction to the fundamental research and advancements in electromagnetic composite substances known as electromagnetic metamaterials. The discussion encompasses examination of the physics of metamaterial interactions, the...
- Metamaterials Handbook
- Academic journals
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Metamaterials scientists
- Richard W. ZiolkowskiRichard W. ZiolkowskiRichard W. Ziolkowski is a past president of the IEEE Antennas and Propagation Society , and a former vice president of this same society . In 2006 he was awarded OSA Fellow. He is also an IEEE Fellow....
- John PendryJohn PendrySir John Brian Pendry, FRS FInstP is an English theoretical physicist known for his research into refractive indexes and creation of the first practical "Invisibility Cloak"...
- David R. SmithDavid R. SmithDavid R. Smith is a renowned American physicist and professor of electrical and computer engineering at Duke University in North Carolina. Smith's research focuses on electromagnetic metamaterials, or materials with a negative index of refraction...
- Nader EnghetaNader EnghetaNader Engheta is an Iranian scientist and engineer. He has significantly contributed to novel artificial materials, photonics, nano-structured materials, novel graphene materials, and plasmonics....
External links
- Defining metamaterials
- Manipulating the Near Field with Metamaterials Slide show, with audio available, by Dr. John Pendry, Imperial College, London