Photonic metamaterials
Encyclopedia
Photonic metamaterials, also known as Optical metamaterials, are a type of electromagnetic metamaterial, which are designed to interact with optical frequencies which are terahertz (THz), infrared (IR
), and eventually, visible wavelengths. As a type of metamaterial, the periodic structures
are made up of single units called cells. These single units are much smaller than the wavelength
of the radiated source. With photonic metamaterials the radiated source is at optical wavelengths. Furthermore, the subwavelength period distinguishes the photonic metamaterial from photonic band gap or photonic crystal
structures. This is because the special optical properties
do not arise from photonic bandgaps, but rather from a subwavelength interaction with the light spectrum, which mimics atom
s or ion
s. However, the periodic cells
(meta-atoms) are fabricated on a scale that is magnitudes larger than the atom, yet smaller than the radiated wavelength.
Electromagnetic metamaterials in general are designed to operate at different frequencies. For example, prior and current research
is in the microwave
domain with physical periodic cell structures on the scale of millimeters. Because the optical wavelengths (wavelengths of a few micrometres) are much shorter than microwave frequencies, photonic metamaterial cell structures are on the scale of nanometers.
In a naturally occurring, (conventional) material, the response to electric and magnetic fields, and hence to light
, is determined by the atom
s As a type of metamaterial, the photonic metamaterial is an artificially engineered structure
. Therefore, each periodic cell is designed with specific parameters by which it interacts with the radiated field at optical frequencies. At the same time, however, metamaterials in general, which includes photonic metamaterials, are described as homogeneous materials
, or in other words, utilizing an effective medium model.
Furthermore, demonstrating artificial magnetism at high frequencies, resulting in strong magnetic coupling, is contrasted with the usual or normal weak magnetic coupling of ordinary materials. This can then be applied to achieving negative index of refraction in the optical range, and developing approaches that show potential for application to optical cloaking
. In addition, photonic metamaterials are an emergent tool in transformation optics
.
Finally, regarding photonic crystal
s, the size and periodicity of the scattering elements are on the order of the wavelength
rather than subwavelength. A photonic crystal cannot be described as a homogeneous medium
so it is not possible to define values of ε or u. However, photonic crystal materials are typically composed of insulators and therefore can exhibit very low losses, even at optical frequencies.
s, came the awareness of possibilities that were once thought not possible before the mid-1990s such as Nanometer-scale imaging, an opposite refraction phenomenon, and cloaking objects
. These observable, scientific phenomena are possible because structural units of the metamaterials can be tailored in shape, size, and spacing
. Their composition, and their form or structure, can be finely adjusted. Inclusions are specifically designed, and then placed at desired locations. Each design alteration, and - or change-up in spacing, creates a new variation in the function of a metamaterial. As of 2009 these possibilities are occurring in the lab, and some related metamaterial technologies
are already in the commercial sector.
A basis for understanding metamaterials in general is the propagation
of light in conventional optical materials, such as glass or prisms
. Although light consists of an electric field
and a magnetic field
, ordinary optical materials have a vigorous interaction only with the electric field. In comparison, the corresponding faint, magnetic interaction is essentially nil. This results in only the most common optics
effects. These common optical effects include ordinary refraction
with common diffraction limitations in lenses and imaging
. In other words, this property limits the ability to control electromagnetic
waves, which includes visible light, propagating
through these materials. While researching whether or not matter
interacts with the magnetic component of light, Victor Veselago
(1967) envisioned the possibility of extraordinary refraction, occurring with a negative sign according to Maxwell's equations
. According to Veselago, and confirmed by researchers 30 years later, a refractive index
with a negative sign is the result of permittivity, ε < 0
(less than zero) and magnetic permeability, μ < 0
(also less than zero).
s, such as precious metal
s, can achieve permittivity
values of less than zero (ε < 0) up to the visible frequencies. However, at terahertz, infrared
, and visible
frequencies (optical range), natural materials have a very weak magnetic coupling component, or permeability. In other words, suceptibility to the magnetic component of the radiated light, or electromagnetic wave, can be considered negligible. Nevertheless, producing negative values for permeability (μ < 0) is necessary to produce the negative refractive index
of the photonic metamaterial.
Thirty years after Victor Veselago's analytical paper, an artificial negative value for permeability was achieved with the first repeating split-ring resonator (SRR) structure. The SRR achieved negative permeability (μ < 0) within a narrow range of frequency. This was then combined with a symmetrically positioned electric conducting
post, which created the first actual left-handed material LHM - a type of Metamaterial
- operating in the microwave
sector. A similarly structured left-handed material, with ehanced capabilities compared to the first, soon followed. This also was demonstrated at microwave frequencies. Although experiments and simulations on these left handed materials demonstrated the presence of a left-handed propagation band, the first experimental confirmation
of negative index of refraction occurred at a time shortly after the above, and once again at microwave frequencies.
The negative index metamaterial is a material, which behaves contrary to the conventional "right-handed" interaction of light found in conventional optical materials. Hence, these are dubbed left-handed materials or negative index materials
(NIMs), among other nomenclatures. Simply put, metamaterials, LHMs - or NIMs - have effectively expanded the material response.
To date (March 2010), only artificially fabricated LHMs have the distinction of exhibiting this capability; even when compared to photonic crystal
s. Photonic crystals, like many other known systems, can exhibit unusual propagation behavior such as reversal of phase
and group velocities. But, negative refraction does not occur in these systems, and not yet realistically in Photonic crystals.
Naturally occurring ferromagnetic
and antiferromagnetic materials can achieve magnetic resonance, but with significant losses. Furthermore, characteristic of natural materials such as natural magnets
, and ferrites
, resonance for the electric (coupling) response
and magnetic (coupling) response do not occur simultaneously, at the same frequencies. These constraints imply that Veselago’s theoretical analysis of a material with extraordinary properties might have remained in the background as an intriguing curiosity. However, explorations into the possibility of manufacturing materials which have the enlarged electric and magnetic response began in the mid-1990s. Although earlier research into artificial materials
dates back to the 1940s, and even the late 19th century, advances of the 1990s in fabrication and the computational science
s led to a resurgence in research for these unconventional materials
. Furthermore, Victor Veselago's seminal analysis has been cited in over 1500 peered reviewed articles, including a number of books on the subject of artificial materials
that have a negative index, and variations thereof.
and nanolithography
techniques. One type of nanoscale SRR cell has three very small metallic rods which are physically connected. This is configured into a U type of a shape, which then functions as a nano-inductor
. The gap between the tips of the U-shape function as a nano-capacitor
. Hence, it is then a nano-LC resonator
, with resonance
occurring at optical frequencies. These are the actual "inclusions" mentioned in the metamaterial literature, which create local electric
and magnetic field
s when externally excited. A notable characteristic occurs at optical frequencies; these inclusions are usually ten times smaller than the vacuum wavelength
of the light
c0, at resonance frequency. The fabrication of the inclusions in this way can then be evaluated by using an effective medium approximation.
Finally, photonic metamaterials open up a way to overcome the constraints (stated above) set by ordinary materials. The proper design of the inclusions (meta-atoms), which are elementary building blocks, now allow for a magnetic response with sufficient magnitude at optical frequencies. This includes negative permeability, μ < 0, despite the fact that these are constructed from non-magnetic materials. Furthermore, analogous to ordinary optical material, such a photonic metamaterial can be treated as an effective medium that is characterized by effective medium parameters ε(ω) and μ(ω), or similarly, εeff and μeff.
approximation means that the combined overall effect of the inclusions, when reacting to an external excitation, is approximated to evaluate the metamaterial slab (the medium) as "effectively" homogeneous
. The slab also has effective parameters, which include effective ε and µ. These are also approximated over the entire medium. Separate inclusions may have different values, but the overall effect results in an approximated effect for each parameter, hence, effective ε, effective µ.
Among other properties, metamaterials can be described in terms of macroscopic quantities: permittivity, permeability, and index of refraction.
Metamaterials are most often intentionally fabricated as composite structures. These contain numerous elements that are identical in size, shape, capability, and electromagnetic parameters. These elements are engineered to be smaller than the propagating electromagnetic waves. Each element can be purposely designed to have a unique or similar value relative to the other components. However, due to the subwavelength structure of the elements, the entire composite material can be viewed and measured as homogeneous and isotropic. This then gives approximated electromagnetic values for the composite structure. These approximated values are effective permittivity, effective permeability, and an effective index of refraction. In other words, metamaterials from the microwave domain, into the infrared and optical ranges can be described in terms of macroscopic properties - rather than the varying values of each individual element. Hence, metamaterials can be constructed to exhibit properties not available in nature.
Furthermore, although these materials are artificially constructed they are behaving as "real" materials, because real materials also have a periodic structure, but at atom
ic scales. Real materials have a refractive index
, just like these artificial materials. However, these artificial materials are able to create the overall effect of negative refractive index. So there is no qualitative difference between a metamaterial and a natural dielectric
material. There is only a quantitative difference - the unit sizes interacting with light (EM radiation) are magnitudes larger with left-handed metamaterials.
surface, it is relatively difficult to stack these bulk structures due to the tight alignment tolerance requirements. However, a layer by layer stacking technique for SRRs was published in 2007. It uses dielectric spacers to apply a planarization procedure to flatten the SRR layer. As a result it appears that any number of layers can be made this way, including any chosen number of unit cells as well as intentional designing of the spatial arrangements of subsequent layers.
) at microwave
frequencies by using arrays of split-ring resonators, to demonstrate experimental verification of a negative index of refraction. In most natural occurring materials, the magnetically coupled response starts to taper off at frequencies in the gigahertz range, which also means significant magnetism does not occur at optical frequencies
. This creates a state where the effective permeability of the material is unity, μeff = 1. Hence, the magnetic component of a radiated electromagnetic field
has virtually no effect on natural occurring materials at optical frequencies
.
As metamaterials evolve, a new domain of optical materials has been developed, and magnetic permeability μeff no longer equals unity for materials at optical frequencies. For metamaterials μeff ≠ 1, and much research
and experimentation has been accomplished for permeability less than 0 (negative values); μeff < 0.
Reviewing the characteristics of predetermined, engineered, periodic structures
such as SRRs
leads to an understanding of the physics
of a periodic metamaterial. Meta-atoms
are used to create conditions where a normally weak magnetic effect on materials is now strengthened in the new artificial materials. A meta-atom could be an SRR
cell, the arrayed wire component of a YIG tuner
, or any other artificial material designed to be periodic, and responsive at a fraction of the radiated wavelength.
In such a design, the meta-atom becomes a larger scale
, millimeter or nanometer-sized-magnetic dipole
, when compared to the picometer sized atom. A meta-atom creates a magnetic dipole moment
analogous to the magnetic dipole moment of natural atoms. For meta-atom constructed from the precious metal
, gold
the condition of μ < 0 can be achieved at telecommunication
frequencies but, still not across the range of the visible frequencies. The visible frequency has been elusive because the plasma frequency of any metal is the ultimate limiting condition.
Researchers are earnestly engaged in combining negative "magnetic" permeability μ < 0 with negative "electric" permittivity ε < 0, which can occur in each meta-atom when engineered to do so.
In 2006, researchers from various groups agreed to state the following: "Possibly, the real potential of the photonic metamaterials lies in other unexplored areas, for example, in chiral metamaterials or in nonlinear metamaterials. In any case, given today’s possibilities regarding the nanofabrication of tailored “atoms,” only our own imagination and creativity set the limits."
ic and non-plasmonic nanoparticle
s, lumped circuit element nanocircuits at infrared
and optical frequencies appear to be possible. Designing subwavelength lumped circuit element structures at infrared and optical frequencies has special challenges when compared to lower frequency domains. Conventional lumped circuit elements are not available in a conventional way.
The concept and implementation of lumped circuit
elements in the microwave
and radio frequency
(RF) domain for metamaterial
design has proved to be effective. These are subwavelength
structures. The lumped element concept has allowed for element simplification and circuit modularization. A similar concept applicable to materials that respond at terahertz (THz), infrared
(IR), and visible wavelengths can be employed. However these lumped circuit elements must also be smaller than terahertz (THz), infrared
(IR), and visible wavelengths. Nanoscale fabrication techniques do exist to accomplish this. Therefore, size reduction as an obstacle, may in time, be overcome.
The response of metals at smaller wavelegnths is, however, a more pronounced limitation. Metals such as gold
, silver
, aluminum, and copper
easily conduct current
s at RF and microwave frequencies. Hence, these have been more easily integrated as materials employed in these regimes. At optical frequencies characteristics of some noble metals are altered. Rather than normal current flow, plasmonic resonance
s occur as the real part of the complex permittivity of these metal
s become negative. Therefore, the main current flow
is actually the electric displacement current density
∂D / ∂t, and can be termed as the “flowing optical current". Solving this problem, then, becomes more than scaling down the element size.
Being smaller than the wavelength
, the impedance
of the particle becomes dependent several factors. The particle's shape, size
, material, along with the optical frequency illumination all contribute to determine the nanoparticle's impedance. The particle's orientation with the optical electric field may also help determine the impedance. The choice of material actually results in the type of impedance the nanoparticle will exhibit. If the material is a conventional silicon
dielectric, with real permittivity εreal > 0 at optical frequencies, the nanoparticle will act as a capacitive impedance or, in other words - nanocapacitor. Conversely, if the material is a noble metal
such as gold
(Au) or silver
(Ag), with a real permittivity less than zero, εreal < 0, then it takes on inductive
characteristics. Hence, it becomes a nanoinductor. Finally, material loss is represented as a nano-resistor.
s are much longer than terahertz and infrared
wavelengths, photonic metamaterials are more difficult to realize. Metamaterials in the microwave domain
can be fabricated from circuit board materials. In contrast lithography
techniques must be employed to produce the rudimentary elements, nano-resonators, that can create photonic metamaterials. The earlier type of nano-resonators were based on the split-ring resonator in the microwave domain. These can be considered as simplified LC circuits. Inductance is achieved because the ring is split, and capacitance occurs across the gap.
Other types of subwavelength photonic materials soon followed. In one instance, a periodic arrangement of short wires, and in another instance metallic pieces with varied shapes successfully interact at shorter wavelengths. In a different study, rather than the isolated nano-resonator structure, the whole metamaterial can be electrically connected for desired photonic subwavelength result.
In the following sections, some of the fabrication techniques are discussed.
Focused ion beam nanostructuring is a convenient tool for rapid prototyping of photonic metamaterials. The FIB is used as a micro-machining tool, to modify or machine materials at the micro- and nanoscale. FIB micro machining has become a broad field of its own, but nano machining with FIB is a field that still needs developing. The common smallest beam size is around 2.5 to 2.6 nanometers.
Ions are positive, large, heavy and slow, whereas electrons (electron beam lithography) are negative, small, light and fast. The most important consequence of these properties is that ion beams will remove atoms from the substrate and because the beam position, dwell time, and size are so well controlled it can be applied to remove material locally in a highly controlled manner, down to the nanometer scale.
Moreover, unlike an electron microscope
, FIB is inherently destructive to the specimen. When the high-energy gallium ions strike the sample, they will sputter atoms from the surface. Gallium atoms
will also be implanted into the top few nanometers of the surface, and the surface will be made amorphous.
FIB tools are designed to etch or machine surfaces, an ideal FIB might machine away one atom layer without any disruption of the atoms in the next layer, or any residual disruptions above the surface. Yet currently because of the sputter the machining typically roughens surfaces at the submicrometre length scales.
An FIB can also be used to deposit material via ion beam induced deposition. FIB-assisted chemical vapor deposition
occurs when a gas, such as tungsten hexacarbonyl
(W(CO)6) is introduced to the vacuum chamber and allowed to chemisorb
onto the sample. By scanning an area with the beam, the precursor gas will be decomposed into volatile and non-volatile components; the non-volatile component, such as tungsten, remains on the surface as a deposition. This is useful, as the deposited metal can be used as a sacrificial layer, to protect the underlying sample from the destructive sputtering of the beam. From nanometers to hundred of micrometers in length, tungsten metal deposition allows to put metal lines right where needed. Other materials such as platinum
, cobalt, carbon, gold, etc., can also be locally deposited. Gas assisted deposition and FIB etching processes are shown to the right.
and Nonlinear metamaterials
articles. However, a brief overview is given in this section.
As discussed throughout the article, some photonic applications are the purview of nanostructured metamaterials, which exhibit unique physical and optical properties. Areas of active research in optical materials are metamaterials that are capable of negative values for index of refraction (NIMs), and metamaterials that are capable of zero index of refraction (ZIMs). Complicated steps required to fabricate these nano-scale metamaterials have led to the desire for fabricated, tunable structures capable of the prescribed spectral ranges or resonances.
The most commonly applied scheme to achieve these effects is electro-optical tuning. Here the change in refractive index is proportional to either the applied electric field, or is proportional to the square modulus of the electric field. These are the Pockels effect
and Kerr effect
, respectively.
An alternative is to employ a nonlinear optical material as one of the constituents of this system, and depend on the optical field intensity to modify the refractive index, or magnetic parameters.
, and the unit cell of metamaterials is much smaller than the wavelength
of light. As of December 2007, the physical characteristics of metamaterials, which include negative permeability
and negative refraction
, had been limited to demonstrations in two-dimension
s. However, a group of researchers at the Physikalisches Institut - Universität Stuttgart perceived that the practical applications of these physical characteristics require three-dimensional bulk like structures. Up to this time, fabrication techniques were most compatible in the GHz range for microwave applications.
By simply stacking printed circuit board
s applications were available at GHz
frequencies in the microwave range. This fabrication technique of metal–dielectric stacks is successful in this frequency range. However, a stacking technique in the optical (infrared
) domain encountered technical problems which limited the number of stacked layers. So, an alternative to the unsuccessful stacking attempt was presented. The selected alternative is the split-ring resonator (SRR) structure. The SRR structure is widely used, and has induced negative values for permeability, for certain frequency ranges. SRR have been used in metamaterials since the 2001 demonstration.
The completed SRR metamaterial layers cannot be stacked, as it is not a flat (or planar) surface. This design prevents stacking. So, the SRR layers were flattened with dielectric spacers.
Suitable photonic metamaterial structures can support lossless surface waves of the form envisaged by Dyakonov. Surface waves are a special type of waves that are confined at the very boundary between two different media. By their very nature, surface waves are unique tools to explore the properties of material interfaces. This includes not only intrinsic properties but also extrinsic effects, thus making surface waves ideal tools for sensing physical, chemical,
and biological agents. They feature genuine physical phenomena as well as prospects for far-reaching applications.
operation wavelength (gamma) is ideally much larger than the lattice constant a for the polarization configuration shown in the metamaterial can be viewed as composed of two sets of sub-circuits or “atoms”: A coil with inductance L in series with two capacitors with net capacitance C as an LC circuit, providing a magnetic resonance at the LC resonance frequency. Long metallic wires, acting like a diluted metal below the effective plasma frequency of the arrangement. Negative magnetic permeability and the negative electric permittivity are created, which leads to lead to a negative index of refraction. Silver was used as constituent material because it is known to introduce significantly lower losses than gold and other noble metals at visible frequencies.
of 3.5. This metamaterial is made of cascaded ‘fishnet’ structures, with a negative index existing over a broad spectral range. Moreover, it can readily be probed from free space, making it functional for optical devices. Constructed as a 21-layer fishnet structure with a unit cell parameters of a = 5.860 µm, b = 5.565 µm and c = 5.265 µm.
dispersion relation is a nonlinear function of frequency.
Since the invention of the superheterodyne receiver by Edwin Armstrong in 1918 and, later,
the development of harmonic signal generators, most radio communication systems have
been narrow-band in nature. However, the explosion of needs for high data-rate wireless links
is currently producing a paradigmatic shift of radio toward broadband and ultra-wideband spectrum operation. In this context, the unprecedented and tailorable dispersive properties of
metamaterials may provide solutions to several new challenges. While the past decades have focused on magnitude engineering and filter design we predict that the forthcoming decades will
experience major interest in phase engineering (where the term "phase engineering" is intended to represent both "dispersion and nonlinearity" engineering) along with phase-engineered devices. In this case, metamaterials are expected to play an important role.
Metamaterials scientists
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...
), and eventually, visible wavelengths. As a type of metamaterial, the periodic structures
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,...
are made up of single units called cells. These single units are much smaller than the 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...
of the radiated source. With photonic metamaterials the radiated source is at optical wavelengths. Furthermore, the subwavelength period distinguishes the photonic metamaterial from photonic band gap or photonic crystal
Photonic crystal
Photonic 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...
structures. This is because the special optical properties
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....
do not arise from photonic bandgaps, but rather from a subwavelength interaction with the light spectrum, which mimics atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
s or ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
s. However, the periodic cells
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,...
(meta-atoms) are fabricated on a scale that is magnitudes larger than the atom, yet smaller than the radiated wavelength.
Electromagnetic metamaterials in general are designed to operate at different frequencies. For example, prior and current research
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....
is 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...
domain with physical periodic cell structures on the scale of millimeters. Because the optical wavelengths (wavelengths of a few micrometres) are much shorter than microwave frequencies, photonic metamaterial cell structures are on the scale of nanometers.
In a naturally occurring, (conventional) material, the response to electric and magnetic fields, and hence 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...
, is determined by the atom
Dipole
In physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...
s As a type of metamaterial, the photonic metamaterial is an artificially engineered structure
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...
. Therefore, each periodic cell is designed with specific parameters by which it interacts with the radiated field at optical frequencies. At the same time, however, metamaterials in general, which includes photonic metamaterials, are described as homogeneous materials
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...
, or in other words, utilizing an effective medium model.
Furthermore, demonstrating artificial magnetism at high frequencies, resulting in strong magnetic coupling, is contrasted with the usual or normal weak magnetic coupling of ordinary materials. This can then be applied to achieving negative index of refraction in the optical range, and developing approaches that show potential for application to optical cloaking
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....
. In addition, photonic metamaterials are an emergent tool in 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...
.
Finally, regarding photonic crystal
Photonic crystal
Photonic 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...
s, the size and periodicity of the scattering elements are on the order of the 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...
rather than subwavelength. A photonic crystal cannot be described as a homogeneous medium
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...
so it is not possible to define values of ε or u. However, photonic crystal materials are typically composed of insulators and therefore can exhibit very low losses, even at optical frequencies.
The development of photonic metamaterials
Artificial composite structures – metamaterials
In tandem with the assemblage of the first metamaterialMetamaterial
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, came the awareness of possibilities that were once thought not possible before the mid-1990s such as Nanometer-scale imaging, an opposite refraction phenomenon, and cloaking objects
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....
. These observable, scientific phenomena are possible because structural units of the metamaterials can be tailored in shape, size, and spacing
Lattice constant
The lattice constant [or lattice parameter] refers to the constant distance between unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice constants, referred to as a, b, and c. However, in the special case of cubic crystal structures, all of the constants are...
. Their composition, and their form or structure, can be finely adjusted. Inclusions are specifically designed, and then placed at desired locations. Each design alteration, and - or change-up in spacing, creates a new variation in the function of a metamaterial. As of 2009 these possibilities are occurring in the lab, and some related metamaterial technologies
Metamaterial antennas
Metamaterial 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...
are already in the commercial sector.
A basis for understanding metamaterials in general is 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....
of light in conventional optical materials, such as glass or prisms
Prism (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...
. 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 have a vigorous interaction only with the electric field. In comparison, the corresponding faint, magnetic interaction is essentially nil. This results in only the most common 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...
effects. These common optical effects include 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...
. In other words, this property limits the ability to control electromagnetic
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....
waves, which includes visible light, propagating
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 these materials. While researching whether or not 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...
interacts with the magnetic component of light, Victor Veselago
Victor Veselago
Victor Georgievich Veselago is a Russian physicist. In 1967, he was the first to publish a theoretical analysis of materials with negative permittivity, ε, and permeability μ....
(1967) envisioned the possibility of extraordinary refraction, occurring with a negative sign according 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...
. According to Veselago, and confirmed by researchers 30 years later, a 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 a negative sign is the result of permittivity, ε < 0
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...
(less than zero) and magnetic permeability, μ < 0
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...
(also less than zero).
Negative permeability and negative refractive index
Natural materialNatural 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, such as precious metal
Precious metal
A precious metal is a rare, naturally occurring metallic chemical element of high economic value.Chemically, the precious metals are less reactive than most elements, have high lustre, are softer or more ductile, and have higher melting points than other metals...
s, can achieve 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...
values of less than zero (ε < 0) up to the visible frequencies. However, at terahertz, 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...
, and visible
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...
frequencies (optical range), natural materials have a very weak magnetic coupling component, or permeability. In other words, suceptibility to the magnetic component of the radiated light, or electromagnetic wave, can be considered negligible. Nevertheless, producing negative values for permeability (μ < 0) is necessary to produce the negative 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 the photonic metamaterial.
Thirty years after Victor Veselago's analytical paper, an artificial negative value for permeability was achieved with the first repeating split-ring resonator (SRR) structure. The SRR achieved negative permeability (μ < 0) within a narrow range of frequency. This was then combined with a symmetrically positioned electric conducting
Electrical conductor
In physics and electrical engineering, a conductor is a material which contains movable electric charges. In metallic conductors such as copper or aluminum, the movable charged particles are electrons...
post, which created the first actual left-handed material LHM - a type of 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....
- operating 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...
sector. A similarly structured left-handed material, with ehanced capabilities compared to the first, soon followed. This also was demonstrated at microwave frequencies. Although experiments and simulations on these left handed materials demonstrated the presence of a left-handed propagation band, the first experimental confirmation
Negative index metamaterials
Negative 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...
of negative index of refraction occurred at a time shortly after the above, and once again at microwave frequencies.
The negative index metamaterial is a material, which behaves contrary to the conventional "right-handed" interaction of light found in conventional optical materials. Hence, these are dubbed left-handed materials or negative index materials
Negative index metamaterials
Negative 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...
(NIMs), among other nomenclatures. Simply put, metamaterials, LHMs - or NIMs - have effectively expanded the material response.
To date (March 2010), only artificially fabricated LHMs have the distinction of exhibiting this capability; even when compared to photonic crystal
Photonic crystal
Photonic 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...
s. Photonic crystals, like many other known systems, can exhibit unusual propagation behavior such as reversal of phase
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...
and group velocities. But, negative refraction does not occur in these systems, and not yet realistically in Photonic crystals.
Naturally occurring ferromagnetic
Ferromagnetism
Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished...
and antiferromagnetic materials can achieve magnetic resonance, but with significant losses. Furthermore, characteristic of natural materials such as natural magnets
Ferrite (magnet)
Ferrites are chemical compounds consisting of ceramic materials with iron oxide as their principal component. Many of them are magnetic materials and they are used to make permanent magnets, ferrite cores for transformers, and in various other applications.Many ferrites are spinels with the...
, and ferrites
Ferrite (iron)
Ferrite or alpha iron is a materials science term for iron, or a solid solution with iron as the main constituent, with a body centred cubic crystal structure. It is the component which gives steel and cast iron their magnetic properties, and is the classic example of a ferromagnetic material...
, resonance for the electric (coupling) response
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 magnetic (coupling) response do not occur simultaneously, at the same frequencies. These constraints imply that Veselago’s theoretical analysis of a material with extraordinary properties might have remained in the background as an intriguing curiosity. However, explorations into the possibility of manufacturing materials which have the enlarged electric and magnetic response began in the mid-1990s. Although earlier research into artificial materials
History of metamaterials
History 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...
dates back to the 1940s, and even the late 19th century, advances of the 1990s in fabrication and the computational science
Computational science
Computational science is the field of study concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems...
s led to a resurgence in research for these unconventional materials
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....
. Furthermore, Victor Veselago's seminal analysis has been cited in over 1500 peered reviewed articles, including a number of books on the subject of artificial materials
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....
that have a negative index, and variations thereof.
Optical frequency metamaterials
Within a only a few years the structures were scaled down for optical frquencies with nano-scale metamaterials. Photonic metamaterial SRRs have now reached scales below 100 nanometers, with special electron beamElectron beam lithography
Electron beam lithography is the practice of emitting a beam of electrons in a patterned fashion across a surface covered with a film , and of selectively removing either exposed or non-exposed regions of the resist...
and nanolithography
Nanolithography
Nanolithography is the branch of nanotechnology concerned with the study and application of fabricating nanometer-scale structures, meaning patterns with at least one lateral dimension between the size of an individual atom and approximately 100 nm...
techniques. One type of nanoscale SRR cell has three very small metallic rods which are physically connected. This is configured into a U type of a shape, which then functions as a nano-inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...
. The gap between the tips of the U-shape function as a nano-capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
. Hence, it is then a nano-LC resonator
LC circuit
An LC circuit, also called a resonant circuit or tuned circuit, consists of an inductor, represented by the letter L, and a capacitor, represented by the letter C...
, with resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
occurring at optical frequencies. These are the actual "inclusions" mentioned in the metamaterial literature, which create local 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 when externally excited. A notable characteristic occurs at optical frequencies; these inclusions are usually ten times smaller than the vacuum 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...
of the light
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....
c0, at resonance frequency. The fabrication of the inclusions in this way can then be evaluated by using an effective medium approximation.
Finally, photonic metamaterials open up a way to overcome the constraints (stated above) set by ordinary materials. The proper design of the inclusions (meta-atoms), which are elementary building blocks, now allow for a magnetic response with sufficient magnitude at optical frequencies. This includes negative permeability, μ < 0, despite the fact that these are constructed from non-magnetic materials. Furthermore, analogous to ordinary optical material, such a photonic metamaterial can be treated as an effective medium that is characterized by effective medium parameters ε(ω) and μ(ω), or similarly, εeff and μeff.
Effective medium model
An effective (transmission) mediumTransmission medium
A transmission medium is a material substance that can propagate energy waves...
approximation means that the combined overall effect of the inclusions, when reacting to an external excitation, is approximated to evaluate the metamaterial slab (the medium) as "effectively" 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...
. The slab also has effective parameters, which include effective ε and µ. These are also approximated over the entire medium. Separate inclusions may have different values, but the overall effect results in an approximated effect for each parameter, hence, effective ε, effective µ.
Among other properties, metamaterials can be described in terms of macroscopic quantities: permittivity, permeability, and index of refraction.
Metamaterials are most often intentionally fabricated as composite structures. These contain numerous elements that are identical in size, shape, capability, and electromagnetic parameters. These elements are engineered to be smaller than the propagating electromagnetic waves. Each element can be purposely designed to have a unique or similar value relative to the other components. However, due to the subwavelength structure of the elements, the entire composite material can be viewed and measured as homogeneous and isotropic. This then gives approximated electromagnetic values for the composite structure. These approximated values are effective permittivity, effective permeability, and an effective index of refraction. In other words, metamaterials from the microwave domain, into the infrared and optical ranges can be described in terms of macroscopic properties - rather than the varying values of each individual element. Hence, metamaterials can be constructed to exhibit properties not available in nature.
Furthermore, although these materials are artificially constructed they are behaving as "real" materials, because real materials also have a periodic structure, but at atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
ic scales. Real materials have a 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....
, just like these artificial materials. However, these artificial materials are able to create the overall effect of negative refractive index. So there is no qualitative difference between a metamaterial and a natural 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...
material. There is only a quantitative difference - the unit sizes interacting with light (EM radiation) are magnitudes larger with left-handed metamaterials.
The mechanics of optical frequency metamaterials
Stacking layers is important to achieve the desired results at optical frequencies. However, the surface configuration (non-planar, bulk) of the SRR metamaterial layers normally prevents stacking. Although a single-layer SRR structure can easily be constructed on a dielectricDielectric
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...
surface, it is relatively difficult to stack these bulk structures due to the tight alignment tolerance requirements. However, a layer by layer stacking technique for SRRs was published in 2007. It uses dielectric spacers to apply a planarization procedure to flatten the SRR layer. As a result it appears that any number of layers can be made this way, including any chosen number of unit cells as well as intentional designing of the spatial arrangements of subsequent layers.
Photonic metamaterials: coupling magnetism at optical frequencies
To be characterized as a left-handed material there is a requirement for negative magnetic permeability μ. This was originally achieved in a left-handed medium (metamaterialMetamaterial
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....
) 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 by using arrays of split-ring resonators, to demonstrate experimental verification of a negative index of refraction. In most natural occurring materials, the magnetically coupled response starts to taper off at frequencies in the gigahertz range, which also means significant magnetism does not occur at optical frequencies
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...
. This creates a state where the effective permeability of the material is unity, μeff = 1. Hence, the magnetic component of a radiated 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...
has virtually no effect on natural occurring materials at optical frequencies
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...
.
As metamaterials evolve, a new domain of optical materials has been developed, and magnetic permeability μeff no longer equals unity for materials at optical frequencies. For metamaterials μeff ≠ 1, and much research
Research
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...
and experimentation has been accomplished for permeability less than 0 (negative values); μeff < 0.
Reviewing the characteristics of predetermined, engineered, periodic structures
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,...
such as SRRs
Split Ring Resonator
A split-ring resonator is a component of a Negative index metamaterial , also known as Double negative metamaterials or Left-handed medium . It also component of other types of metamaterial such as Single Negative metamaterial . SRRs are also used for research in Terahertz metamaterials,...
leads to an understanding 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...
of a periodic metamaterial. Meta-atoms
Dipole
In physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...
are used to create conditions where a normally weak magnetic effect on materials is now strengthened in the new artificial materials. A meta-atom could be an SRR
Split Ring Resonator
A split-ring resonator is a component of a Negative index metamaterial , also known as Double negative metamaterials or Left-handed medium . It also component of other types of metamaterial such as Single Negative metamaterial . SRRs are also used for research in Terahertz metamaterials,...
cell, the arrayed wire component of a YIG tuner
Tunable metamaterials
A tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave interacts with a metamaterial. This means the capablitity to determine whether the EM wave is transmitted, reflected, or...
, or any other artificial material designed to be periodic, and responsive at a fraction of the radiated wavelength.
In such a design, the meta-atom becomes a larger scale
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...
, millimeter or nanometer-sized-magnetic dipole
Dipole
In physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...
, when compared to the picometer sized atom. A meta-atom creates a magnetic dipole moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
analogous to the magnetic dipole moment of natural atoms. For meta-atom constructed from the precious metal
Precious metal
A precious metal is a rare, naturally occurring metallic chemical element of high economic value.Chemically, the precious metals are less reactive than most elements, have high lustre, are softer or more ductile, and have higher melting points than other metals...
, gold
Gold
Gold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...
the condition of μ < 0 can be achieved at telecommunication
Telecommunication
Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...
frequencies but, still not across the range of the visible frequencies. The visible frequency has been elusive because the plasma frequency of any metal is the ultimate limiting condition.
Researchers are earnestly engaged in combining negative "magnetic" permeability μ < 0 with negative "electric" permittivity ε < 0, which can occur in each meta-atom when engineered to do so.
In 2006, researchers from various groups agreed to state the following: "Possibly, the real potential of the photonic metamaterials lies in other unexplored areas, for example, in chiral metamaterials or in nonlinear metamaterials. In any case, given today’s possibilities regarding the nanofabrication of tailored “atoms,” only our own imagination and creativity set the limits."
Proposal for metamaterials with optical frequencies response
By employing a combination of plasmonPlasmon
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...
ic and non-plasmonic nanoparticle
Nanoparticle
In nanotechnology, a particle is defined as a small object that behaves as a whole unit in terms of its transport and properties. Particles are further classified according to size : in terms of diameter, coarse particles cover a range between 10,000 and 2,500 nanometers. Fine particles are sized...
s, lumped circuit element nanocircuits at 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...
and optical frequencies appear to be possible. Designing subwavelength lumped circuit element structures at infrared and optical frequencies has special challenges when compared to lower frequency domains. Conventional lumped circuit elements are not available in a conventional way.
The concept and implementation of lumped circuit
Lumped element model
The lumped element model simplifies the description of the behaviour of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions...
elements 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...
and 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...
(RF) domain for 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....
design has proved to be effective. These are subwavelength
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....
structures. The lumped element concept has allowed for element simplification and circuit modularization. A similar concept applicable to materials that respond at terahertz (THz), 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...
(IR), and visible wavelengths can be employed. However these lumped circuit elements must also be smaller than terahertz (THz), 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...
(IR), and visible wavelengths. Nanoscale fabrication techniques do exist to accomplish this. Therefore, size reduction as an obstacle, may in time, be overcome.
The response of metals at smaller wavelegnths is, however, a more pronounced limitation. Metals such as gold
Gold
Gold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...
, silver
Silver
Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...
, aluminum, and 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...
easily conduct current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
s at RF and microwave frequencies. Hence, these have been more easily integrated as materials employed in these regimes. At optical frequencies characteristics of some noble metals are altered. Rather than normal current flow, plasmonic resonance
Surface plasmon resonance
The excitation of surface plasmons by light is denoted as a surface plasmon resonance for planar surfaces or localized surface plasmon resonance for nanometer-sized metallic structures....
s occur as the real part of the complex permittivity of these metal
Metal
A metal , is an element, compound, or alloy that is a good conductor of both electricity and heat. Metals are usually malleable and shiny, that is they reflect most of incident light...
s become negative. Therefore, the main current flow
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
is actually the electric displacement current density
Current density
Current density is a measure of the density of flow of a conserved charge. Usually the charge is the electric charge, in which case the associated current density is the electric current per unit area of cross section, but the term current density can also be applied to other conserved...
∂D / ∂t, and can be termed as the “flowing optical current". Solving this problem, then, becomes more than scaling down the element size.
Being smaller than the 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...
, the impedance
Wave impedance
The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields . For a transverse-electric-magnetic plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium...
of the particle becomes dependent several factors. The particle's shape, size
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 ....
, material, along with the optical frequency illumination all contribute to determine the nanoparticle's impedance. The particle's orientation with the optical electric field may also help determine the impedance. The choice of material actually results in the type of impedance the nanoparticle will exhibit. If the material is a conventional silicon
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...
dielectric, with real permittivity εreal > 0 at optical frequencies, the nanoparticle will act as a capacitive impedance or, in other words - nanocapacitor. Conversely, if the material is a noble metal
Noble metal
Noble metals are metals that are resistant to corrosion and oxidation in moist air, unlike most base metals. They tend to be precious, often due to their rarity in the Earth's crust...
such as gold
Gold
Gold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...
(Au) or silver
Silver
Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...
(Ag), with a real permittivity less than zero, εreal < 0, then it takes on inductive
Electromagnetic induction
Electromagnetic induction is the production of an electric current across a conductor moving through a magnetic field. It underlies the operation of generators, transformers, induction motors, electric motors, synchronous motors, and solenoids....
characteristics. Hence, it becomes a nanoinductor. Finally, material loss is represented as a nano-resistor.
Fabrication techniques
Because microwaveMicrowave
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 are much longer than terahertz 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...
wavelengths, photonic metamaterials are more difficult to realize. Metamaterials in the microwave domain
Negative index metamaterials
Negative 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...
can be fabricated from circuit board materials. In contrast lithography
Nanolithography
Nanolithography is the branch of nanotechnology concerned with the study and application of fabricating nanometer-scale structures, meaning patterns with at least one lateral dimension between the size of an individual atom and approximately 100 nm...
techniques must be employed to produce the rudimentary elements, nano-resonators, that can create photonic metamaterials. The earlier type of nano-resonators were based on the split-ring resonator in the microwave domain. These can be considered as simplified LC circuits. Inductance is achieved because the ring is split, and capacitance occurs across the gap.
Other types of subwavelength photonic materials soon followed. In one instance, a periodic arrangement of short wires, and in another instance metallic pieces with varied shapes successfully interact at shorter wavelengths. In a different study, rather than the isolated nano-resonator structure, the whole metamaterial can be electrically connected for desired photonic subwavelength result.
In the following sections, some of the fabrication techniques are discussed.
Electron beam lithography
Because state-of-the-art photolithography is limited by the diffraction limit, electron beam lithography (EBL) shows an advantage. The unit sizes that make up the photonic metamaterial are beyond the resolution limit of photolithography. Instead, EBL is usually employed at this frequency range to construct a single layer of metamaterial atop a transparent substrate (2 dimensional). With nanometer beamwidths, EBL generates chosen patterns on the surface of materials at nanoscale resolution. Practical first and second generation structures were constructed with this technique, and experimentally demonstrated. The second generation showed improvement. There are still limitations using this writing technique including the high cost of fabrication. Furthermore, only small areas can be fabricated within a reasonable time and at acceptable cost.Focused ion beam nanostructuring
Ions are positive, large, heavy and slow, whereas electrons (electron beam lithography) are negative, small, light and fast. The most important consequence of these properties is that ion beams will remove atoms from the substrate and because the beam position, dwell time, and size are so well controlled it can be applied to remove material locally in a highly controlled manner, down to the nanometer scale.
Moreover, unlike an electron microscope
Electron microscope
An electron microscope is a type of microscope that uses a beam of electrons to illuminate the specimen and produce a magnified image. Electron microscopes have a greater resolving power than a light-powered optical microscope, because electrons have wavelengths about 100,000 times shorter than...
, FIB is inherently destructive to the specimen. When the high-energy gallium ions strike the sample, they will sputter atoms from the surface. Gallium atoms
Gallium
Gallium is a chemical element that has the symbol Ga and atomic number 31. Elemental gallium does not occur in nature, but as the gallium salt in trace amounts in bauxite and zinc ores. A soft silvery metallic poor metal, elemental gallium is a brittle solid at low temperatures. As it liquefies...
will also be implanted into the top few nanometers of the surface, and the surface will be made amorphous.
FIB tools are designed to etch or machine surfaces, an ideal FIB might machine away one atom layer without any disruption of the atoms in the next layer, or any residual disruptions above the surface. Yet currently because of the sputter the machining typically roughens surfaces at the submicrometre length scales.
An FIB can also be used to deposit material via ion beam induced deposition. FIB-assisted chemical vapor deposition
Chemical vapor deposition
Chemical vapor deposition is a chemical process used to produce high-purity, high-performance solid materials. The process is often used in the semiconductor industry to produce thin films. In a typical CVD process, the wafer is exposed to one or more volatile precursors, which react and/or...
occurs when a gas, such as tungsten hexacarbonyl
Tungsten hexacarbonyl
Tungsten hexacarbonyl is the chemical compound with the formula W6. This complex gave rise to the first example of a dihydrogen complex....
(W(CO)6) is introduced to the vacuum chamber and allowed to chemisorb
Chemisorption
Chemisorption is a sub-class of adsorption, driven by a chemical reaction occurring at the exposed surface. A new chemical species is generated at the adsorbant surface...
onto the sample. By scanning an area with the beam, the precursor gas will be decomposed into volatile and non-volatile components; the non-volatile component, such as tungsten, remains on the surface as a deposition. This is useful, as the deposited metal can be used as a sacrificial layer, to protect the underlying sample from the destructive sputtering of the beam. From nanometers to hundred of micrometers in length, tungsten metal deposition allows to put metal lines right where needed. Other materials such as platinum
Platinum
Platinum is a chemical element with the chemical symbol Pt and an atomic number of 78. Its name is derived from the Spanish term platina del Pinto, which is literally translated into "little silver of the Pinto River." It is a dense, malleable, ductile, precious, gray-white transition metal...
, cobalt, carbon, gold, etc., can also be locally deposited. Gas assisted deposition and FIB etching processes are shown to the right.
Interference lithography
Interference lithography is comparatively inexpensive and is versatile.Tunable metamaterials at optical frequencies
Photonic metamaterials have become part of the pantheon of tunable and non-linear metamaterials. These are discussed in the Tunable metamaterialsTunable metamaterials
A tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave interacts with a metamaterial. This means the capablitity to determine whether the EM wave is transmitted, reflected, or...
and Nonlinear metamaterials
Nonlinear metamaterials
A nonlinear metamaterial is an artificially constructed material that can exhibit properties not found in nature. Its response to electromagnetic radiation can be characterized by its permittivity and material permeability. The product of the permittivity and permeability results in the refractive...
articles. However, a brief overview is given in this section.
As discussed throughout the article, some photonic applications are the purview of nanostructured metamaterials, which exhibit unique physical and optical properties. Areas of active research in optical materials are metamaterials that are capable of negative values for index of refraction (NIMs), and metamaterials that are capable of zero index of refraction (ZIMs). Complicated steps required to fabricate these nano-scale metamaterials have led to the desire for fabricated, tunable structures capable of the prescribed spectral ranges or resonances.
The most commonly applied scheme to achieve these effects is electro-optical tuning. Here the change in refractive index is proportional to either the applied electric field, or is proportional to the square modulus of the electric field. These are the Pockels effect
Pockels effect
The Pockels effect , or Pockels electro-optic effect, produces birefringence in an optical medium induced by a constant or varying electric field. It is distinguished from the Kerr effect by the fact that the birefringence is proportional to the electric field, whereas in the Kerr effect it is...
and Kerr effect
Kerr effect
The Kerr effect, also called the quadratic electro-optic effect , is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index change is directly proportional to the square of the electric...
, respectively.
An alternative is to employ a nonlinear optical material as one of the constituents of this system, and depend on the optical field intensity to modify the refractive index, or magnetic parameters.
Three-dimensional photonic metamaterials at optical frequencies
As has been already established, metamaterials are artificial mediaTransmission medium
A transmission medium is a material substance that can propagate energy waves...
, and the unit cell of metamaterials is much smaller than the 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...
of light. As of December 2007, the physical characteristics of metamaterials, which include negative 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...
and negative refraction
Negative refraction
Negative refraction is the name for an electromagnetic phenomenon where light rays are refracted at an interface in the reverse sense to that normally expected...
, had been limited to demonstrations in two-dimension
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
s. However, a group of researchers at the Physikalisches Institut - Universität Stuttgart perceived that the practical applications of these physical characteristics require three-dimensional bulk like structures. Up to this time, fabrication techniques were most compatible in the GHz range for microwave applications.
By simply stacking printed circuit board
Printed circuit board
A printed circuit board, or PCB, is used to mechanically support and electrically connect electronic components using conductive pathways, tracks or signal traces etched from copper sheets laminated onto a non-conductive substrate. It is also referred to as printed wiring board or etched wiring...
s applications were available at GHz
GHZ
GHZ or GHz may refer to:# Gigahertz .# Greenberger-Horne-Zeilinger state — a quantum entanglement of three particles.# Galactic Habitable Zone — the region of a galaxy that is favorable to the formation of life....
frequencies in the microwave range. This fabrication technique of metal–dielectric stacks is successful in this frequency range. However, a stacking technique in the optical (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...
) domain encountered technical problems which limited the number of stacked layers. So, an alternative to the unsuccessful stacking attempt was presented. The selected alternative is the split-ring resonator (SRR) structure. The SRR structure is widely used, and has induced negative values for permeability, for certain frequency ranges. SRR have been used in metamaterials since the 2001 demonstration.
The completed SRR metamaterial layers cannot be stacked, as it is not a flat (or planar) surface. This design prevents stacking. So, the SRR layers were flattened with dielectric spacers.
Dyakonov surface waves in photonic metamaterials
An idea for a type of photonic metamaterial is derived from the birefringent properties of photonic crystals. By utilizing metamaterial anisotropy, resonance conditions at which Dyakonov surface waves exist is met.Suitable photonic metamaterial structures can support lossless surface waves of the form envisaged by Dyakonov. Surface waves are a special type of waves that are confined at the very boundary between two different media. By their very nature, surface waves are unique tools to explore the properties of material interfaces. This includes not only intrinsic properties but also extrinsic effects, thus making surface waves ideal tools for sensing physical, chemical,
and biological agents. They feature genuine physical phenomena as well as prospects for far-reaching applications.
Negative-index photonic metamaterial at 780 nm wavelength
Photonic metamaterials are tailored artificial optical materials composed of sub-wavelength metallic building blocks that can be viewed as nano-scale electronic circuits. These building blocks or “photonic atoms” are densely packed into an effective material such that theoperation wavelength (gamma) is ideally much larger than the lattice constant a for the polarization configuration shown in the metamaterial can be viewed as composed of two sets of sub-circuits or “atoms”: A coil with inductance L in series with two capacitors with net capacitance C as an LC circuit, providing a magnetic resonance at the LC resonance frequency. Long metallic wires, acting like a diluted metal below the effective plasma frequency of the arrangement. Negative magnetic permeability and the negative electric permittivity are created, which leads to lead to a negative index of refraction. Silver was used as constituent material because it is known to introduce significantly lower losses than gold and other noble metals at visible frequencies.
Optical negative-index metamaterials
Describing the recent progress (in 2006) made in creating nanostructured metamaterials with a negative index at optical wavelengths, and discusses some of the devices that could result from these new materials.Experimental demonstration of near-infrared NIMs
Received 7 March 2005 and published in September of that year was the first fabrication and experimental verification of a transversely structured metal-dielectric-metal multilayer exhibiting a negative refractive index around 2 μm. Both the amplitude and the phase of the transmission and reflection were measured experimentally, and are in good agreement with a rigorous coupled wave analysis.Three-dimensional optical metamaterial
Here is a 3D optical metamaterial having negative refractive index with a very high figure of meritFigure of merit
A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives. In engineering, figures of merit are often defined for particular materials or devices in order to determine their relative utility for an application...
of 3.5. This metamaterial is made of cascaded ‘fishnet’ structures, with a negative index existing over a broad spectral range. Moreover, it can readily be probed from free space, making it functional for optical devices. Constructed as a 21-layer fishnet structure with a unit cell parameters of a = 5.860 µm, b = 5.565 µm and c = 5.265 µm.
Negative refraction at 813 nm and 772 nm
Wavelengths of 813 nm and 772 nm approach the red end of the visible spectrum. A double negative refraction occurs at 813 nm and single negative refraction occurs at 772 nm.Phase-engineered metamaterial structures and devices
Electromagnetic metamaterials are inherently dispersive: their constitutive parameters (permittivity and permeability) are functions of frequency or, equivalently, theirdispersion relation is a nonlinear function of frequency.
Since the invention of the superheterodyne receiver by Edwin Armstrong in 1918 and, later,
the development of harmonic signal generators, most radio communication systems have
been narrow-band in nature. However, the explosion of needs for high data-rate wireless links
is currently producing a paradigmatic shift of radio toward broadband and ultra-wideband spectrum operation. In this context, the unprecedented and tailorable dispersive properties of
metamaterials may provide solutions to several new challenges. While the past decades have focused on magnitude engineering and filter design we predict that the forthcoming decades will
experience major interest in phase engineering (where the term "phase engineering" is intended to represent both "dispersion and nonlinearity" engineering) along with phase-engineered devices. In this case, metamaterials are expected to play an important role.
See also
- 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...
- 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...
- 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....
- 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...
- 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 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...
- 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....
- Ulf LeonhardtUlf LeonhardtUlf Leonhardt is a German scientist, born in Schlema, Germany . In 2006, he published the first scientific paper on invisibility cloaking with metamaterials at the same time Pendry's group published their paper in the journal Science...
- Vladimir ShalaevVladimir ShalaevVladimir M. Shalaev , the Robert and Anne Burnett Professor of Electrical and Computer Engineering and Professor of Biomedical Engineering at Purdue University, specializes in metamaterials, transformation optics, nanophotonics and plasmonics...
External links
- Effective metamaterial parameter extraction algorithm developed by Zsolt Szabo
- Optics and photonics: Physics enhancing our lives
- Metamaterial Publications from Metagroup Duke Uinversity - a list of all publications by D. R. Smith and co-researchers up to 2009.
- Metamaterial articles in the mainstream media. Page hosted by Duke U. Metagroup
- Google scholar List of Papers by JB Pendry
- Imperial College, Department of Physics, Condensed Matter Theory Group
- OPAL: A Computational Tool For Photonics
- Experimental Verification of Reversed Cherenkov Radiation...
- Oriented Assembly of Metamaterials Particle self-assembly suggested for assembly of metamaterials at optical wavelengths.
- Subpicosecond Optical Switching with a Negative Index Metamaterial
General references
- Shalaev, Vladimir M., et al. Negative Index of Refraction in Optical Metamaterials arXiv.org. 17 pages.
- Shalaev, Vladimir M., et al. Negative index of refraction in optical metamaterials Opt. Lett. Vol. 30. 2005-12-30. 3 pages