Transformation optics
Encyclopedia
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 similar to the equations that describe how gravity warps space and time, in General Relativity
. However, instead of space and time, these equations show how light can be directed in a chosen manner, analogous to warping space. For example, one potential application is collecting sunlight
with novel solar cell
s by concentrating the light in one area. Hence, a wide array of conventional devices could be markedly enhanced by the transformation optical approach. Complex artificial materials, known as metamaterial
s, are part of this science's tool bag.
, 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 values of chosen parameters of materials "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.
Transformation optics can go beyond cloaking (mimic celestial mechanics) because its control of the trajectory and path of light is highly effective. Currently transformation optics is a field of optical and material engineering and science
embracing nanophotonics
, plasmon
ics, and optical metamaterials.
of transformation optics. Transformation optics is the foundation for exploring a diverse set of theoretical, numerical, and experimental developments, involving the perspectives of the physics
and engineering communities
. The multi-disciplinary perspectives for inquiry and designing of materials develop understanding of their behaviors, properties, and potential applications for this field.
If a coordinate transformation can be derived or described, a ray of light (in the optical limit) will follow lines of a constant coordinate. There are constraints on the transformations, as listed in the references. In general, however, a particular goal can be accomplished using more than one transformation. The classic cylindrical cloak (first both simulated and demonstrated experimentally) can be created with many transformations. The simplest, and most often used, is a linear coordinate mapping in the radial coordinate. There is significant ongoing research into determining advantages and disadvantages of particular types of transformations, and what attributes are desirable for realistic transformations. One example of this is the broadband carpet cloak: the transformation used was quasi-conformal. Such a transformation can yield a cloak that uses non-extreme values of permittivity
and permeability
, unlike the classic cylindrical cloak, which required some parameters to vary towards infinity at the inner radius of the cloak.
General coordinate transformations can be derived which compress or expand space, bend or twist space, or even change the topology (e.g. by mimicking a wormhole
). Much current interest involves designing invisibility
cloaks, event cloaks, field concentrators, or beam-bending waveguides.
and matter
with spacetime
, as predicted by general relativity
, can be studied using the new type of artificial optical materials
that feature extraordinary abilities to bend light. Light is also known as electromagnetic radiation
. This research creates a link between the newly emerging field of artificial optical metamaterials
to that of celestial mechanics
, thus opening a new possibility to investigate astronomical phenomena
in a laboratory setting. The recently introduced, new class, of specially designed optical media can mimic the periodic
, quasi-periodic and chaotic motions
observed in celestial objects that have been subjected to gravitational field
s.
Hence, a new class of metamaterials introduced with the nomenclature “continuous-index photon traps” (CIPTs). CIPTz have applications as optical cavities. As such, CIPTs can control, slow and trap light in a manner similar to celestial phenomena such as black hole
s, strange attractors, and gravitational lenses.
A composite of air and the dielectric Gallium Indium Arsenide Phosphide (GaInAsP), operated in the infrared
spectral range and featured a high refractive index
with low absorptions.
This opens an avenue to investigate light phenomena that imitates orbital motion, strange attractors and chaos
in a controlled laboratory environment by merging the study of optical metamaterial
s with classical celestial mechanics.
If a metamaterial
could be produced that did not have high intrinsic loss and a narrow frequency
range of operation then it could be employed as a type of media to simulate light motion in a curved spacetime vacuum
. Such a proposal is brought forward, and metamaterials become prospective media in this type of study. The classical optical-mechanical analogy renders the possibility for the study of light propagation in homogeneous
media as an accurate analogy to the motion of massive bodies, and light, in gravitational potentials. A direct mapping of the celestial phenomena is accomplished by observing photon
motion in a controlled laboratory environment. The materials could facilitate periodic, quasi-periodic and chaotic light motion inherent to celestial objects subjected to complex gravitational fields.
Twisting the optical metamaterial
effects its "space" into new coordinates. The light that travels in real space will be curved in the twisted space, as applied in transformational optics. This effect is analogous to starlight when it moves through a closer gravitational field
and experiences curved spacetime or a gravitational lensing effect. This analogue between classic electromagnetism
and general relativity, shows the potential of optical metamaterials to study relativity phenomena such as the gravitational lens.
Observations of such celestial phenomena by astronomers can sometimes take a century of waiting. Chaos in dynamic systems is observed in areas as diverse as molecular motion, population dynamics and optics. In particular, a planet around a star can undergo chaotic motion if a perturbation, such as another large planet, is present. However, owing to the large spatial distances between the celestial bodies, and the long periods involved in the study of their dynamics, the direct observation of chaotic planetary motion has been a challenge. The use of the optical-mechanical analogy may enable such studies to be accomplished in a bench-top laboratory setting at any prescribed time.
The study also points toward the design of novel optical cavities and photon traps for application in microscopic devices and lasers systems.
propagating in a curved spacetime
is similar to the electromagnetic
wave propagation in a curved space
and in an in homogeneous
metamaterial, as stated in the previous section. Hence a black hole
can possibly be simulated using electromagnetic fields and metamaterials. In July 2009 a metamaterial
structure forming an effective black hole was theorized, and numerical simulations showed a highly efficient light absorption
.
The first experimental demonstration of electromagnetic black hole at microwave
frequencies occurred in October 2009. The proposed black hole was composed of non-resonant, and resonant, metamaterial structures, which can absorb electromagnetic waves efficiently coming from all directions due to the local control of electromagnetic field
s. It was constructed of a thin cylinder
at 21.6 centimeters in diameter
comprising 60 concentric rings of metamaterials. This structure created a gradient index of refraction, necessary for bending light in this way. However, it was characterized as being artificially inferior substitute for a real black hole
. The characterization was justified by an abosorption of only 80% in the microwave range, and that it has no internal source of energy. It is singularly a light absorber. The light absorption capability could be beneficial if it could be adapted to technologies such as solar cells. However, presently the device is limited to the microwave range.
Also in 2009, transformation optics were employed to mimic a black hole of Schwarzschild form
. Similar properties of photon sphere were also found numerically for the metamaterial black hole. Several reduced versions of the black hole systems were proposed for easier implementations.
Conventional lenses are ultimately limited by geometry. Available design parameters are a single index of refraction (n) per lens element, variations in the element surface profile, including continuous surfaces (lens curvature) and/or discontinuous surfaces (diffractive optics). Light rays undergo refraction at the surfaces of each element, but travel in straight lines within the lens. Since the design space of conventional optics is limited to a combination of refractive index and surface structure, correcting for aberrations (for example through the use of achromatic or diffractive optics) leads to large, heavy, complex designs, and/or greater losses, lower image quality, and manufacturing difficulties.
For example, determining whether a cloud in the distance is harmless or an aerosol of enemy chemical or biological warfare is presently very difficult to quickly assess. However, with the new metamaterials being developed, the ability exists to see things smaller than the wavelength of light - something that has never been done before. Utilizing metamaterials in the creation of a new lens may allow soldiers to be able to see pathogens and viruses that are currently impossible to detect with any visual device.
Harnessing subwavelength capabilities then allow for other advancements which appear to be beyond the battlefied. All kinds of materials could be manufactured with nano-manufacturing, which could go into electronic and optical devices from night vision goggles to distance sensors to other kinds of sensors. Longer term views include the possibility for cloaking materials, which would provide "invisibility" by redirecting light around a cylindrical shape.
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
regime which allows for novel control 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...
, also known as electromagnetic waves. The mathematics underpinning transformation optics is similar to the equations that describe how gravity warps space and time, in General Relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. However, instead of space and time, these equations show how light can be directed in a chosen manner, analogous to warping space. For example, one potential application is collecting sunlight
Sunlight
Sunlight, in the broad sense, is the total frequency spectrum of electromagnetic radiation given off by the Sun. On Earth, sunlight is filtered through the Earth's atmosphere, and solar radiation is obvious as daylight when the Sun is above the horizon.When the direct solar radiation is not blocked...
with novel solar cell
Solar cell
A solar cell is a solid state electrical device that converts the energy of light directly into electricity by the photovoltaic effect....
s by concentrating the light in one area. Hence, a wide array of conventional devices could be markedly enhanced by the transformation optical approach. Complex artificial materials, known as 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, are part of this science's tool bag.
Coordinate transformations
Transformation optics has its beginnings in two research endeavors, and their conclusions. They were published on May 25, 2006, in the same issue of Science ExpressScience (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 values of chosen parameters of materials "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.
Transformation optics can go beyond cloaking (mimic celestial mechanics) because its control of the trajectory and path of light is highly effective. Currently transformation optics is a field of optical and material engineering and science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
embracing nanophotonics
Nanophotonics
Nanophotonics or Nano-optics is the study of the behavior of light on the nanometer scale. It is considered as a branch of optical engineering which deals with optics, or the interaction of light with particles or substances, at deeply subwavelength length scales...
, plasmon
Plasmon
In physics, a plasmon is a quantum of plasma oscillation. The plasmon is a quasiparticle resulting from the quantization of plasma oscillations just as photons and phonons are quantizations of light and mechanical vibrations, respectively...
ics, and optical metamaterials.
Developments of transformation optics
Developments in this field focus on advances in researchResearch
Research can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...
of transformation optics. Transformation optics is the foundation for exploring a diverse set of theoretical, numerical, and experimental developments, involving the perspectives of the 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...
and engineering communities
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
. The multi-disciplinary perspectives for inquiry and designing of materials develop understanding of their behaviors, properties, and potential applications for this field.
If a coordinate transformation can be derived or described, a ray of light (in the optical limit) will follow lines of a constant coordinate. There are constraints on the transformations, as listed in the references. In general, however, a particular goal can be accomplished using more than one transformation. The classic cylindrical cloak (first both simulated and demonstrated experimentally) can be created with many transformations. The simplest, and most often used, is a linear coordinate mapping in the radial coordinate. There is significant ongoing research into determining advantages and disadvantages of particular types of transformations, and what attributes are desirable for realistic transformations. One example of this is the broadband carpet cloak: the transformation used was quasi-conformal. Such a transformation can yield a cloak that uses non-extreme 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...
, unlike the classic cylindrical cloak, which required some parameters to vary towards infinity at the inner radius of the cloak.
General coordinate transformations can be derived which compress or expand space, bend or twist space, or even change the topology (e.g. by mimicking a wormhole
Wormhole
In physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional surface. If this surface is folded along a third dimension, it...
). Much current interest involves designing invisibility
Invisibility
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...
cloaks, event cloaks, field concentrators, or beam-bending waveguides.
Mimicking celestial mechanics
The interactions of lightLight
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...
and 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...
with spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
, as predicted by general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, can be studied using the new type of artificial optical materials
Metamaterial cloaking
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....
that feature extraordinary abilities to bend light. Light is also known as electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
. This research creates a link between the newly emerging field of artificial optical metamaterials
Photonic metamaterials
Photonic 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...
to that of celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
, thus opening a new possibility to investigate astronomical phenomena
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
in a laboratory setting. The recently introduced, new class, of specially designed optical media can mimic the periodic
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,...
, quasi-periodic and chaotic motions
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
observed in celestial objects that have been subjected to gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
s.
Hence, a new class of metamaterials introduced with the nomenclature “continuous-index photon traps” (CIPTs). CIPTz have applications as optical cavities. As such, CIPTs can control, slow and trap light in a manner similar to celestial phenomena such as black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
s, strange attractors, and gravitational lenses.
A composite of air and the dielectric Gallium Indium Arsenide Phosphide (GaInAsP), operated in the 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...
spectral range and featured a high 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....
with low absorptions.
This opens an avenue to investigate light phenomena that imitates orbital motion, strange attractors and chaos
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
in a controlled laboratory environment by merging the study of optical metamaterial
Photonic metamaterials
Photonic 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...
s with classical celestial mechanics.
If a 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....
could be produced that did not have high intrinsic loss and a narrow 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...
range of operation then it could be employed as a type of media to simulate light motion in a curved spacetime 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...
. Such a proposal is brought forward, and metamaterials become prospective media in this type of study. The classical optical-mechanical analogy renders the possibility for the study of light propagation in 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...
media as an accurate analogy to the motion of massive bodies, and light, in gravitational potentials. A direct mapping of the celestial phenomena is accomplished by observing photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
motion in a controlled laboratory environment. The materials could facilitate periodic, quasi-periodic and chaotic light motion inherent to celestial objects subjected to complex gravitational fields.
Twisting the optical metamaterial
Photonic metamaterials
Photonic 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...
effects its "space" into new coordinates. The light that travels in real space will be curved in the twisted space, as applied in transformational optics. This effect is analogous to starlight when it moves through a closer gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
and experiences curved spacetime or a gravitational lensing effect. This analogue between classic electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and general relativity, shows the potential of optical metamaterials to study relativity phenomena such as the gravitational lens.
Observations of such celestial phenomena by astronomers can sometimes take a century of waiting. Chaos in dynamic systems is observed in areas as diverse as molecular motion, population dynamics and optics. In particular, a planet around a star can undergo chaotic motion if a perturbation, such as another large planet, is present. However, owing to the large spatial distances between the celestial bodies, and the long periods involved in the study of their dynamics, the direct observation of chaotic planetary motion has been a challenge. The use of the optical-mechanical analogy may enable such studies to be accomplished in a bench-top laboratory setting at any prescribed time.
The study also points toward the design of novel optical cavities and photon traps for application in microscopic devices and lasers systems.
- For related information see:Chaos theoryChaos theoryChaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
and General relativityGeneral relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
Producing black holes with metamaterials
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...
propagating in a curved spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
is similar to the electromagnetic
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
wave propagation in a curved space
Curved space
Curved space often refers to a spatial geometry which is not “flat” where a flat space is described by Euclidean geometry. Curved spaces can generally be described by Riemannian geometry though some simple cases can be described in other ways. Curved spaces play an essential role in General...
and in an in 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...
metamaterial, as stated in the previous section. Hence a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
can possibly be simulated using electromagnetic fields and metamaterials. In July 2009 a 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....
structure forming an effective black hole was theorized, and numerical simulations showed a highly efficient light 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...
.
The first experimental demonstration of electromagnetic black hole at 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 occurred in October 2009. The proposed black hole was composed of non-resonant, and resonant, metamaterial structures, which can absorb electromagnetic waves efficiently coming from all directions due to the local control of 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. It was constructed of a thin cylinder
Cylinder (geometry)
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder...
at 21.6 centimeters in diameter
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
comprising 60 concentric rings of metamaterials. This structure created a gradient index of refraction, necessary for bending light in this way. However, it was characterized as being artificially inferior substitute for a real black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
. The characterization was justified by an abosorption of only 80% in the microwave range, and that it has no internal source of energy. It is singularly a light absorber. The light absorption capability could be beneficial if it could be adapted to technologies such as solar cells. However, presently the device is limited to the microwave range.
Also in 2009, transformation optics were employed to mimic a black hole of Schwarzschild form
Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...
. Similar properties of photon sphere were also found numerically for the metamaterial black hole. Several reduced versions of the black hole systems were proposed for easier implementations.
Multi-dimensional universe
Engineering optical space with metamaterials could be useful to reproduce an accurate laboratory model of the physical multiverse. "This ‘metamaterial landscape’ may include regions in which one or two spatial dimensions are compactified." Metamaterial models appear to be useful for non-trivial models such as 3D de Sitter space with one compactified dimension, 2D de Sitter space with two compactified dimensions, 4D de Sitter dS4, and anti-de Sitter AdS4 spaces.Gradient index lensing
Transformation optics is employed to increase capabilities of gradient index lenses.Conventional optical limitations
Optical elements (lenses) perform a variety of functions, ranging from image formation, to light projection or light collection. The performance of these systems is frequently limited by their optical elements, which dominate system weight and cost, and force tradeoffs between system parameters such as focal length, field of view (or acceptance angle), resolution, and range.Conventional lenses are ultimately limited by geometry. Available design parameters are a single index of refraction (n) per lens element, variations in the element surface profile, including continuous surfaces (lens curvature) and/or discontinuous surfaces (diffractive optics). Light rays undergo refraction at the surfaces of each element, but travel in straight lines within the lens. Since the design space of conventional optics is limited to a combination of refractive index and surface structure, correcting for aberrations (for example through the use of achromatic or diffractive optics) leads to large, heavy, complex designs, and/or greater losses, lower image quality, and manufacturing difficulties.
GRIN lenses
Gradient index lenses (or GRIN lenses) as the name implies, are optical elements whose index of refraction varies within the lens. Control of the internal refraction allows the steering of light in curved trajectories through the lens. GRIN optics thus increase the design space to include the entire volume of the optical elements, providing the potential for dramatically reduced size, weight, element count, and assembly cost, as well as opening up new space to trade between performance parameters. However, past efforts to make large aperture GRIN lenses have had limited success due to restricted refractive index change, poor control over index profiles, and/or severe limitations in lens diameter.Recent advances
Recent steps forward in material science have led to at least one method for developing large (>10 mm) GRIN lenses with 3-dimensional gradient indexes. There is a possibility of adding expanded deformation capabilities to the GRIN lenses. This translates into controlled expansion, contraction, and shear (for variable focus lenses or asymmetric optical variations). These capabilities have been demonstrated. Additionally, recent advances in transformation optics and computational power provide a unique opportunity to design, assemble and fabricate elements in order to advance the utility and availability of GRIN lenses across a wide range of optics-dependent systems, defined by needs. A possible future capability could be to further advance lens design methods and tools, which are coupled to enlarged fabrication processes.Battlefield applications
Transformation optics has potential applications for the battlefield. The versatile properties of metamaterials can be tailored to fit almost any practical need, and transformation optics shows that space for light can be bent in almost any arbitrary way. This is perceived as providing new capabilities to soldiers in the battlefield. For battlefield scenarios benefits from metamaterials have both short term and long term impacts.For example, determining whether a cloud in the distance is harmless or an aerosol of enemy chemical or biological warfare is presently very difficult to quickly assess. However, with the new metamaterials being developed, the ability exists to see things smaller than the wavelength of light - something that has never been done before. Utilizing metamaterials in the creation of a new lens may allow soldiers to be able to see pathogens and viruses that are currently impossible to detect with any visual device.
Harnessing subwavelength capabilities then allow for other advancements which appear to be beyond the battlefied. All kinds of materials could be manufactured with nano-manufacturing, which could go into electronic and optical devices from night vision goggles to distance sensors to other kinds of sensors. Longer term views include the possibility for cloaking materials, which would provide "invisibility" by redirecting light around a cylindrical shape.
See also
- 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...
- Chirality (electromagnetism)Chirality (electromagnetism)The term chiral describes an object, especially a molecule, which has or produces a non-superimposeable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism...
- 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....
- 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...
- 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...
- Metamaterial cloakingMetamaterial cloakingMetamaterial 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....
- Negative index metamaterialsNegative index metamaterialsNegative index metamaterials or negative index materials are artificial structures where the refractive index has a negative value over some frequency range. This does not occur in any known natural materials, and thus is only achievable with engineered structures known as metamaterials...
- 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 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...
- 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
- 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...
- 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...
- Theories of cloaking
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- 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
- Books
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