Metamaterial antennas
Encyclopedia
Metamaterial antennas are a class of antenna
s which use metamaterials to increase performance of miniaturized (electrically small) antenna system
s. Their purpose, as with any electromagnetic antenna, is to launch energy
into free space. However, these incorporate metamaterials, which are materials engineered with novel, often microscopic
, structures to produce unusual physical properties. Antenna designs incorporating metamaterials can step-up the radiated power
of an antenna. Novel components such as compact resonators, and metamaterial loaded waveguides offer the possiblity of previously unavailable applications.
With conventional antennas that are very small compared to the wavelength, most of the signal is reflected back to the source. The metamaterial, on the other hand, makes the antenna behave as if it were much larger than it really is, because the novel antenna structure stores energy, and re-radiates it.
These novel antennas appear to be useful for wireless
systems that continue to decrease in size, such as emergency communications devices, micro-sensors
and portable ground-penetrating radars
to search for tunnels, caverns and other geophysical features.
of an antenna. The newest metamaterial antennas radiate as much as 95 percent of an input radio signal. Standard antennas need to be at least half the size of the signal wavelength
to operate efficiently. At 300 MHz, for instance, an antenna would need to be half a meter long. In contrast, the experimental antennas are as small as one-fiftieth of a wavelength, and could have further decreases in size.
Metamaterials are a basis for further minaturation of microwave antennas, with efficient power and acceptable bandwidth. Novel antennas employing metamaterials offer the possibility of overcoming restrictive efficiency-bandwidth limitations for conventionally constructed, miniature antennas.
In contrast, metamaterials permit smaller antenna elements that cover a wider frequency range, thus making better use of available space for small platforms, or spaces. Some applications for metamaterial antennas are wireless communication, space communications
, GPS, satellite
s, space vehicle navigation, and airplanes. In these instances, miniature antennas with high gain are significantly relevant because the radiating elements are combined into large antenna arrays for these functions, and vehicles. Furthermore, negative refractive index
, produced by metamaterials, results in electromagnetic radiation
being focused by a flat lens versus being dispersed.
This configuration analytically and numerically appears to produce an order of magnitude increase in power. At the same time, the reactance appears to have a corresponding decrease. Furthermore, the DNG shell becomes a natural impedance matching network for this dipole antenna system.
s surrounding antennas offers improved isolation between radio frequency
, or microwave
channels of (multiple-input multiple-output) (MIMO) antenna arrays
. Metamaterial, high-impedance groundplanes
can also be used to improve the radiation
efficiency, and axial radio performance of low-profile antennas located close to the ground plane surface
. Metamaterials have also been used to increase the beam scanning
range by using both the forward and backward waves in leaky wave antennas. Various metamaterial antenna systems can be employed to support surveillance sensors, communication links, navigation systems, command and control systems.
.
with DNG slabs, or epsilon-negative (ENG) slabs with mu-negative (MNG) slabs are employed in the subsystems. The antenna subsystems that are currently being researched are cavity resonators
, waveguides, scatters, and antennas (radiators). In addition, metamaterial antennas are already (2009) commercially available.
et al. were able to show that a three-dimension
al array of intersecting, thin wires could be used to create negative values of permittivity
ε, and that a periodic array of copper split ring resonators could produce an effective negative magnetic permeability μ.
Then in the year 2000, the group of researchers, Smith et al.
were the first to successfully combine the split-ring resonator, often designated as SRR, with thin wire conducting posts and produce a left-handed material, which had negative values of ε and μ for frequencies in the gigahertz or microwave
range.
Then, in 2002, a different class of Negative refractive index (NRI) metamaterials was introduced. This employs periodic reactive loading of a 2-D transmission line
as the host medium
. This configuration actually used positive index material with negative index material. It employed a small, planar, negative-refractive-lens
interfaced with a positive index, parallel-plate waveguide
. This was experimentally verified soon after, in a subsequent demonstration.
Although some inefficiencies with split-ring resonances were stated during and after the introduction of this combined negative and positive index material, split-ring resonators are still effectively employed as of 2009 for research. SRRs have been involved in wide ranging metamaterial
research, including research on metamaterial antennas.
A more recent view is that by using split-ring resonators (SRRs) as typical metamaterial building blocks, the designed and desired electromagnetic response and associated flexibility is highly desirable.
. This is due to their negative index of refraction. This is accomplished by combining a slab of conventional lossless DPS material with a slab of lossless DNG metamaterial.
The DPS has a conventional or ordinary index of refraction, while the DNG has the opposite, negative refractive index. Both of these slabs are impedance matched to the outside region (e.g., free space). The desired monochromatic plane wave
is radiated on this configuration. As this wave propagates through the first slab there is a phase difference
between the exit face and entrance face. As the wave propagates
through the second slab the phase difference is decreased and even compensated for. Therefore as the wave exits the second slab the total phase difference is equal to zero. This is discussed in more detail in a section below.
With this system a phase-compensated, waveguiding system could be produced. By using multiple stacks of this configuration, the phase compensation (beam translation effects) would occur throughout the entire system. Furthermore, by changing the index of any of the DPS-DNG pairs, the speed at which the beam enters the front face, and exits the back face of the entire stack-system changes. In this manner, a volumetric, low loss, time delay transmission line
could be realized for a Gaussian beam
system.
Furthermore, this phase compensation can lead to a set of applications, which are miniaturized, subwavelength, cavity resonators, and waveguides with applications below diffraction limits.
of the DNG metamaterial as a transmission medium, it could be useful as an effective dispersion compensation device for time-domain applications
. The dispersion produces a variance of the group speed of the wave components of the signal, as they propagate in the DNG medium. Hence, volumetric (stacked) DNG metamaterials could be useful for the modification of the propagation of signals along a microstrip transmission line
. At the same time, dispersion leads to distortion. However, if the dispersion could be compensated for along the microstrip line, RF
or microwave
signals propagating
along them would not be distorted. This could create an environment where components for attenuating distortion are less critical, and could lead to simplification of components in many systems. Dispersion along the microstrip can be eliminated by correcting for the frequency dependence of the effective permittivity associated with this type of transmission line. It is possible to do this with metamaterials.
The strategy is to design a length of metamaterial
-loaded transmission line that can be introduced, in some manner, with the original length of microstrip
line to make the paired system dispersionless
. In other words, create a dispersion-compensating segment of transmission line
. This could be accomplished by introducing a metamaterial with a certain relative permittivity and a certain magnetic permeability, which then effects the overall relative permittivity and permeability of the microstrip line. At the same time it is introduced in such a manner that the wave impedance in the metamaterial remains the same as it is in the original conventional microstrip line. Then the index of refraction in the medium compensates for the dispersion effects associated with the microstrip geometry itself; that is the effective index of the pair becomes that of free space.
Part of the design strategy is that the effective permittivity and permeability of such a metamaterial should be negative - a DNG material must be introduced for this purpose.
The conventional Leaky Wave antenna has had limited commercial success because it lacks complete backfire-to-endfire frequency scanning capability. The CRLH configuration allows the innovation over half-space scanning (broadside-to-endfire). The CRLH now allows for complete backfire-to-endfire frequency scanning, including broadside.
antenna systems, is used as an efficient coupler to the external radiation, focusing radiation along or from a microstrip
transmission line into transmitting and receiving components. Hence, it can be designed as an input device
. In addition, it can enhance the amplitude of evanescent waves, as well as correct the phase of propagating waves.
lic mesh of thin wire
s - with wires in the three directions of space, and slices of foam. Interestingly the permittivity
of this material, above the plasma frequency can be positive and less than one. This means that the refractive index
is less than one, but hardly above zero. In this case, the relevant parameter is often the contrast between the permittivities rather than the value of the overall permittivity itself, at desired frequencies. This occurs because the equivalent (effective) permittivity has a behavior governed by a plasma frequency in the microwave domain. This low optical index material then becomes a good candidate for creation of extremely convergent microlens
es. Methods that have been developed theoretically using dielectric photonic crystals are applied in the microwave domain to realize a directive emitter using metallic grids.
In this instance, arrayed wires in a cubic, crystal lattice structure can be analyzed as an array of aerials (antenna array
). Therefore, as a lattice structure it has a lattice constant. The lattice constant
, or lattice parameter, refers to the constant distance between unit cells in a crystal lattice.
The earlier discovery of plasmon
s created the view that metal at plasmon frequency fp is a composite material. The effect of plasmons on any metal sample is to create properties in the metal such that it can behave as a dielectric
, independent of the wave vector of the EM excitation (radiation) field. Furthermore, there is a minute-fractionally small amount of plasmon energy that is absorbed into the system denoted as γ. For aluminium fp = 15 eV, and γ = 0.1 eV. Perhaps the most important result of the interaction of metal and the plasma frequency is that permittivity is negative below the plasma frequency, all the way to the minute value of γ.
These facts ultimately result in the arrayed wire structure as being effectively a homogenous medium.
This metamaterial allows for control of the direction of emission of an electromagnetic radiation source located inside the material in order to collect all the energy
in a small angular
domain around the normal
. By using a slab of a of a metamaterial, diverging electromagnetic waves are focused into a narrow cone. Dimensions of its component are small in comparison to the wavelength, and thus the slab behaves as a homogeneous material with a low plasma frequency.
A transmission line
is the material medium
or structure that forms all or part of a path
from one place to another for directing the transmission
of energy, such as electromagnetic waves as well as electric power transmission
.
Types of transmission line include wire
s, coaxial cable
s, dielectric slabs, stripline
s, optical fiber
s, electric power lines
, and waveguide
s.
A microstrip
is a type of electrical transmission line which can be fabricated using printed circuit board
technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane
by a dielectric layer known as the substrate. Microwave components such as antennas
, couplers, filter
s, power dividers etc. can be formed from microstrip.
From the simplified schematics to the right it can be seen that total impedance, conductance, reactance (capacitance and inductance), and the transmission medium (transmission line) can be represented by single components, which give the overall value.
With transmission line mediums it is important to match the load impedance ZL to the characteristic impedance
Z0 as closely as possible, because it is usually desirable that as much power as possible will be absorbed by the load.
is the resistance
per unit length,
is the inductance
per unit length,
is the conductance of the dielectric per unit length,
is the capacitance
per unit length,
is the imaginary unit
, and
is the angular frequency
.
, or distributed LC networks
, are often included in the research. Lumped circuit elements are actually microscopic elements that effectively approximate, their larger component counterpart. For example circuit capacitance and inductance can be created with spilt rings, which are on the scale of nanometers at optical frequencies. The distributed LC model is related to the lumped LC model, however the distributed element model
is more accurate but more complex than the lumped element model
.
s employ negative refractive index transmission-line metamaterials (NRI-TLM). These include lense
s that can overcome the diffraction
limit, small band and broadband phase shifting lines, small antennas, low profile antennas, antenna feed networks, and novel power architectures, and high directivity couplers.
A novel approach for implementing NRI-TLM is loading a planar metamaterial network of TLs with series capacitors and shunt inductors, which has a higher performance than standard TLs. This results in a large operating bandwidth while the refractive index is negative.
Because superlens
es can overcome the diffraction limit, this allows for a more efficient coupling to the external radiation, and enables the availability for a broader band of frequency. For example the superlens can be applied to the TLM architecture
. In conventional lenses, the imaging is limited by the diffraction limit. With John Pendry
's superlens the details of the near field
images are not lost. Growing evanescent waves are supported in the metamaterial (n < 1), which restores the decaying evanescent waves from the source. This results in a diffraction-limited resolution of λ/6, after some small losses. This compares with λ/2, from normal diffraction limit for conventional lenses.
By combining right-handed materials (RHM) with left-handed materials (LHM) as a composite material (CRLH) construction for the transmission line, both a backward to forward scanning capability is obtained.
Metamaterials were first used for antenna technology around 2005. This type of antenna used the established capability of SNGs to couple with external radiation
. Resonant coupling
allowed for a wavelength
larger than the antenna. At microwave frequencies this allowed for an electrically small antenna.
A metamaterial-loaded transmission line has stated advantages, which are significant over conventional or standard delay transmission lines. It is more compact in size, it can achieve positive or negative phase shift while occupying the same short physical length and it exhibits a linear, flatter phase response
with frequency
, leading to shorter group delays. It can work in lower frequency because of high series distributed-capacitors, it has smaller plane dimensions than its equivalent coplanar structure.
as a consequence.
It has long been known that transmission lines periodically
loaded with capacitive and inductive elements in a high-pass configuration support certain types of backward waves. In addition, planar transmission lines are a natural match for 2-D wave propagation. Furthermore, with lumped circuit elements they retain a compact configuration, and can still support the lower RF range. With this in mind, periodically loaded, two-dimensional LC transmission line networks, designed with a high pass and cutoff, were proposed. The LC networks can be designed to support backward waves, without bulky SRR/ wire structure. This was the first such proposal which veered away from bulk media for a negative refractive effect (result). A notable property of this type of networks is that there is no reliance on resonance, and instead it is the ability to support backward waves which defines negative refraction.
The principles behind focusing are derived from Veselago's well-known paper, “The electrodynamics of substances with simultaneously negative values of ε and μ” and Sir Pendry's Perfect lens proposal. To give an overview of how this works - by combining a conventional, flat, (planar) DPS slab, M-1, with a left-handed medium, M-2, a propagating electromagnetic wave with a wave vector
k1 in M-1, results in a refracted wave with a wave vector k2 in M-2. Since, M-2 supports backward wave propagation k2 is refracted to the opposite side of the normal, while the Poynting vector of M-2 is anti-parallel with k2. Under such conditions, power is refracted through an effectively negative angle, which indeed implies an effectively negative index of refraction.
Electromagnetic waves from a point source located inside a conventional DPS can be focused inside an LHM using a planar interface of the two media. These conditions can be modeled by exciting a single node inside the DPS, and observing the magnitude and phase of the voltages to ground at all points in the LHM. A focusing effect should manifest itself as a “spot” distribution of voltage at a predictable location in the LHM.
Negative refraction and focusing of electromagnetic waves can be accomplished without employing resonances or directly synthesizing the permittivity and permeability. In addition, this media can be practically fabricated by appropriately loading a host transmission line medium. Furthermore, the resulting planar topology permits LHM structures to be readily integrated with conventional planar microwave circuits and devices.
When transverse electromagnetic propagation occurs with a transmission line medium, the analogy for permittivity and permeability is ε = L, and μ = C. Since this analogy was developed with positive values for these parameters, then the next logic step was realizing that negative values could be achieved. In order to synthesize a left-handed medium (ε < 0 and μ < 0) the series reactance and shunt susceptibility should become negative, because the material parameters are directly proportional to these circuit quantities.
A transmission line which has lumped circuit elements that synthesize a left-handed medium is referred to as a "dual transmission line" as compared to "conventional transmission line". The dual transmission line structure can be implemented in practice by loading a host transmission
line with lumped element series capacitors (C) and shunt inductors (L). In this periodic
structure, the loading is strong such that the lumped elements dominate the propagation characteristics.
. In addition, to utilize SRRs at RF frequencies
, as with wireless devices, the split-ring resonators have to be scaled to larger dimensions. This worked against making the (wireless) devices themselves more and more compact. In contrast, LC network configurations could be scaled in both microwave and RF frequencies.
Therefore, it appeared that LC loaded transmission lines were enabling the design of a new class of metamaterials to synthesize a negative refractive index. In addition, by relying on LC networks to emulate electrical permittivity
and magnetic permeability this resulted in a substantial increase in operating bandwidths.
Moreover, their unit cells are connected through a transmission-line network and they may,
therefore, be equipped with lumped circuit elements, which permit them to be compact at frequencies where the SRR
cannot be compact. The flexibility gained through the use of either discrete or printed elements enables the proposed planar metamaterials to be scalable from the megahertz to the tens of gigahertz range. In addition, by utilizing varactors instead of capacitors, the effective material properties can be dynamically tuned. Furthermore, the proposed media are planar and inherently support two-dimensional (2-D) wave propagation, and are well suited for RF/microwave device and circuit applications.
As a negative refractive index medium, a dual TL structure is not simply a phase compensator. It can enhance the amplitude of evanescent waves, as well as correct the phase of propagating waves. Evanescent waves actually grow within the dual TL structure.
Anticipated future applications are new enabling RF/microwave devices can be implemented based on these proposed planar negative refractive index media for applications in wireless communications, surveillance, and radars.
Proposed designs of a new class of metamaterials to synthesize a negative refractive index. The proposed structures go beyond the wire/SRR composites in that they do not rely on SRRs to synthesize the material parameters, thus leading to dramatically increased operating bandwidths. Moreover, their unit cells are connected through a transmission-line network and they may, therefore, be equipped with lumped elements, which permit them to be compact at frequencies where the SRR cannot be compact. The flexibility gained through the use of either discrete or printed elements enables the proposed planar metamaterials to be scalable from the megahertz to the tens of gigahertz range. In addition, by utilizing varactors instead of capacitors, the effective material properties can be dynamically tuned. Furthermore, the proposed media are planar and inherently support two-dimensional (2-D) wave propagation. Therefore, these new metamaterials are well suited for RF/microwave device and circuit applications.
In the long-wavelength regime, the permittivity and permeability of conventional materials
can be artificially synthesized using periodic LC networks arranged in a low-pass
configuration. In the dual (high-pass) configuration, these equivalent material parameters
assume simultaneously negative values, and may therefore be used to synthesize a negative
refractive index.
An antenna (or aerial) is a transducer
designed to transmit
or receive
electromagnetic wave
s. In other words, antennas convert electromagnetic waves into electrical currents and vice versa.
An antenna as a radiator or receiver of electromagnetic
energy can also be defined as the transition region between free space and the guiding electromagnetic structure such as the transmission line.
Antenna theory is based on classical electromagnetic theory
as described by Maxwell's equations. Physically, an antenna is an arrangement of one or more conductor
s, usually called elements in this context. In transmission, an alternating current
is created in the elements by applying a voltage at the antenna terminals, causing the elements to radiate an electromagnetic field. In reception, the inverse occurs: an electromagnetic field from another source induces an alternating current in the elements and a corresponding voltage at the antenna's terminals. Some receiving antennas (such as parabolic and horn types) incorporate shaped reflective surfaces to collect EM waves from free space and direct or focus them onto the actual conductive elements.
An antenna creates sufficiently strong electromagnetic fields at large distances. Reciprocally, it is sensitive to the electromagnetic fields impressed upon it externally. The actual coupling between a transmitting and receiving antenna is so small that amplifier circuits are required at both the transmitting and receiving stations. Antennas are usually created by modifying ordinary circuitry into transmission line configurations.
The required antenna for any given application is dependent on the bandwidth employed, and range (power) requirements. In the microwave to millimeter-wave range – wavelengths from a few meters to millimeters – the following antennas are usually employed:
Dipole antennas, short antennas, parabolic and other reflector antennas, horn antennas, periscope antennas, helical antennas, spiral antennas, surface-wave and leaky wave antennas. Leaky wave antennas include dielectric and dielectric loaded antennas, and the variety of microstrip antennas.
s As a nonmagnetic conducting unit, it comprises an array of units which yield an enhanced negative effective magnetic permeability, when the frequency of the incident electromagnetic field is close to the SRR resonance frequency. The resonant frequency of the SRR simply depends on its shape and physical design. In addition, resonance can occur at wavelengths much larger than it size.
by electrically
small dipole
antennas can be notably increased. This could be accomplished by surrounding an antenna
with a shell of double negative (DNG) material. At the time (late 2003) this was investigated both analytically and numerically. When the electric dipole is embedded in a homogeneous
DNG medium, the analysis shows that the antenna acts inductively rather than capacitively, as it would in free space without the interaction of the DNG material. In addition, the dipole-DNG shell combination increases the real power radiated by more than an order of magnitude
over a free space antenna. A notable decrease in the reactance of the dipole antenna corresponds to the increase in radiated power.
Analysis also shows that the reactive power within this dipole-DNG shell system indicates that the DNG shell acts as a natural matching network for the dipole. The DNG material matches the intrinsic reactance of this antenna system to free space, hence the impedance of DNG material matches free space. It provides a natural matching circuit to the antenna.
was shown to increase by more than an order of magnitude
over a comparable free space antenna. Electrically
small antennas, high directivity
, and tunable operational frequency are produced with negative magnetic permeability
. When combining a right-handed material
(RHM) with a Veselago-left-handed material (LHM) other novel properties
are obtained. Finally, a single negative material
resonator, obtained with an SRR, can produce an electrically small antenna when operating at microwave frequencies, as follows:
The configuration of a split-ring resonator used was two concentric annular
rings with relative opposite gaps in the inner and outer ring. Its geometrical parameters were R = 3.6 mm, r = 2.5 mm, w = 0.2 mm, t = 0.9 mm. R and r are used in annular
parameters, w is the spacing between the rings and t = the width of the outer ring. The material had a thickness of 1.6 mm. Permittivity was 3.85 at 4 GHz. The SRR was fabricated with an etching technique onto a 30 μm thick copper
. The SRR was excited by using a monopole antenna
. The monopole antenna
was composed of a coaxial cable
, ground plane
, and radiating components. The ground plane material was aluminium
. The operation frequency of the antenna was 3.52 GHz, which was determined by considering the geometrical parameters of SRR.
A length of wire of 8.32 mm was placed above the ground plane, connected to the antenna, which was one quarter of the operation wavelength. Therefore, this makes the antenna work with a feed wavelength was 33.28 mm and feed frequency was 7.8 GHz. The resonant frequency of the SRR turned out to be smaller than the monopole operation frequency.
The monopole-SRR (metamaterial) antenna was found to operate efficiently at (λ/10) using the SRR-wire configuration. It demonstrated good coupling efficiency, and enough radiation efficiency. Its operation was found to be comparable to a conventional antenna at λ/2, which is recommended as an antenna size for efficient coupling and radiation for a conventional antenna. Therefore, the monopole-SRR antenna becomes an acceptable electrically small antenna, at the resonance frequency of the SRR. This antenna can be used wherever (planar) patch antenna
s are used.
When the SRR
is made part of this configuration the characteristics, such as radiation pattern of the antenna are entirely changed. This is noticed with comparison to a conventional monopole antenna. With modifications to the SRR structure (the metamaterial) the antenna size could reach (λ/40). Furthermore, by coupling 2, 3, and 4 SRRs side by side, there is a slight shift radiation patterns.
, with a metamaterial cover, which resulted in enhanced directivity
was proposed. According to the numerical results, the metamaterial patch antenna showed significant improvement in directivity, compared to the conventional patch antenna. This was cited in 2007 for an efficient design of directive patch antennas in mobile communications using metamaterial
s. This design was based on the left-handed material (LHM) transmission line model, with the circuit elements L and C of the LHM equivalent circuit
model. This study developed formula
e to determine the L and C values of the LHM equivalent circuit model for desirable characteristics of directive patch antennas. Design examples derived from actual frequency
bands in mobile communications were performed, which illustrates the efficiency of this patch antenna.
At the interface between two media, the concept of the continuity of the tangential electric and magnetic field components can be applied. If either the permeability or permittivity of two media has opposite signs then the normal components of the tangential field, on both sides of the interface, will be discontinuous (at the boundary). This implies a concentrated resonant phenomenon at the interface. This appears to be similar to the current and voltage distributions at the junction between an inductor and capacitor, at the resonance of an L-C circuit. This can be cause for notable characteristics of wave interaction in metamaterial-based devices and components. This "interface resonance" is essentially independent of the total thickness of the paired layers. This is because it occurs along the discontinuity between two such conjugate materials.
The real component values for negative permittivity and permeability results in a real component values for negative refraction n. In a loss less medium, all that would exist is real values. This concept can then be used to map out phase compensation when a conventional lossless material, DPS, is matched with a lossless NIM (DNG).
In phase compensation, the DPS of thickness d1 has ε > 0 and µ > 0. Conversely, the NIM of thickness d2 has ε < 0 and µ < 0. Assume that the intrinsic impedance of the DPS dielectric material (d1) is the same as that of the outside region, and responding to a normally incident plane wave. The wave travels through the medium without any reflection because the DPS impedance and the outside impedance are equal. However, the plane wave at the end of DPS slab it is out of phase with the plane wave at the beginning of the material.
The plane wave then enters the lossless NIM (d2). At certain frequencies ε < 0 and µ < 0 and n < 0. Like the DPS, the NIM has intrinsic impedance which is equal to the outside, and, therefore, is lossless as well. The direction of power flow (i.e., the Poynting vector) in the first slab should be the same as that in the second one, because the power of the incident wave enters the first slab (without any reflection at the first interface), traverses the first slab, exits the second interface, enters the second slab and traverses it, and finally leaves the second slab. However, as stated earlier, the direction of power is anti-parallel to the direction of phase velocity. Therefore, the wave vector k2 is in the opposite direction of k1. Furthermore, whatever phase difference is developed by traversing the first slab, it can be decreased and even cancelled by traversing the second slab. If the ratio of the two thicknesses is d1 / d 2 = n2 / n1, then total phase difference between the front face, and the back face, of the matched DPS - NIM slabs, is zero. This demonstrates how the NIM slab at chosen frequencies acts as a phase compensator. It is important to note that this phase compensation process is not dependent on the thickness of d1 + d1 but only on the ratio of d1 / d 2. Therefore, d1 + d1 can be any value, as long as this ratio satisfies the above condition. Finally, even though this two-layer structure is present, the wave traversing this structure would not experience the phase difference.
Following this, the next step is the subwavelength cavity resonator.
Compact subwavelength 1-D cavity resonators using metamaterials:
The phase compensator described above can be used to conceptualize the possibility of designing a compact 1-D cavity resonator. The above two-layer structure is applied as two perfect
reflectors, or in other words, two perfect conducting plates.
Conceptually, what is constrained in the resonator is d1 / d2, not d1 + d2. Therefore, in principle, one can have a thin subwavelength cavity resonator for a given frequency, if at this frequency the second layer acts a metamaterial with negative permittivity and permeability and the ratio correlates to the correct values.
The cavity can conceptually be thin and can still be resonant, as long as the ratio of thicknesses is satisfied in the special dispersion relation. This can, in principle, provide possibility for having subwavelength thin compact cavity resonators.
resonant frequency, and also lowers the cut-off frequency along with other benefits, and smooth transition from a fast-wave to a slow-wave in a waveguide configuration.
s. On some of these patents the researcher
s of metamaterials and metamaterial antenna system components in the lab now have patents.
Phased array systems and antennas for use in such systems are well known in areas such as telecommunications and other radar applications. In general phased array systems work by coherently reassembling signals over the entire array by using circuit elements to compensate for relative phase differences and time delays.
(NIMs) as a biconcave lens to focus the microwaves transmitted by the antenna the sidelobes of the antenna are reduced. This equates to a reduction in radiated energy loss, and a relatively wider, useful bandwidth. Overall, because of the strategies implemented, this is an efficient (low-loss, reduced sidelobes), dynamically ranged phased array radar antenna system.
In addition, the signal amplitude is increased across the microstrip
transmission lines (TL) by suspending the microstrip TLs above the ground plane at a predetermined distance. In other words, they are not in contact with a solid substrate. By suspending the microstrip transmission lines in this manner, dielectric signal loss is reduced significantly, thus resulting in a less-attenuated signal at its destination.
In addition, this phased array
antenna system was designed to boost the performance of the Monolithic microwave integrated circuit
(MMIC), among other benefits. A transmission line (microstrip) is created with photolithography. A metamaterial lens, consisting of a thin wire array (see section above), focuses the transmitted or received signals between the microstrip TL and the emitter / receiver elements.
The metamaterial lens also functions as an input device and consists of a number of periodic unit-cells disposed along the microstrip line. Furthermore, the metamaterial lens consists of multiple microstrip lines of the same make up; a plurality of periodic unit-cells. The periodic unit-cells are constructed of a plurality of electrical components; capacitors and inductors as components of multiple distributed circuits
.
The metamaterial of the phased array antenna system incorporates a conducting transmission element, a substrate comprising at least a first ground plane for grounding the transmission element, a plurality of unit-cell circuits composed periodically along the transmission element, at least one via
for electrically connecting the transmission element
to at least the first ground plane. It also includes a means for suspending this conducting transmission element predetermined distance away from the substrate in a way such that the transmission element is located at a second predetermined distance away from the ground plane.
(RFID) tags have broad applications. The possible uses now range from electronic key fobs that remotely turn over engines, work-related swipe cards, and are placed inside shoes so manufactureres may match separate components. Other wireless technologies are light switches, printers and microwave ovens. Such broad expansion leads to interference from competing signals. Metamaterials, fucnctional at miniature sizes can allow signals in, but keep them from getting out. Rather than the conventional absorbers at three inches thick, metamterials can be the size of thin films, two millimetres thick (78/1000 or .078 inches).
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
s which use metamaterials to increase performance of miniaturized (electrically small) antenna system
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
s. Their purpose, as with any electromagnetic antenna, is to launch energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
into free space. However, these incorporate metamaterials, which are materials engineered with novel, often microscopic
Microscopic
The microscopic scale is the scale of size or length used to describe objects smaller than those that can easily be seen by the naked eye and which require a lens or microscope to see them clearly.-History:...
, structures to produce unusual physical properties. Antenna designs incorporating metamaterials can step-up the radiated power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
of an antenna. Novel components such as compact resonators, and metamaterial loaded waveguides offer the possiblity of previously unavailable applications.
With conventional antennas that are very small compared to the wavelength, most of the signal is reflected back to the source. The metamaterial, on the other hand, makes the antenna behave as if it were much larger than it really is, because the novel antenna structure stores energy, and re-radiates it.
These novel antennas appear to be useful for wireless
Wireless
Wireless telecommunications is the transfer of information between two or more points that are not physically connected. Distances can be short, such as a few meters for television remote control, or as far as thousands or even millions of kilometers for deep-space radio communications...
systems that continue to decrease in size, such as emergency communications devices, micro-sensors
Sensor
A sensor is a device that measures a physical quantity and converts it into a signal which can be read by an observer or by an instrument. For example, a mercury-in-glass thermometer converts the measured temperature into expansion and contraction of a liquid which can be read on a calibrated...
and portable ground-penetrating radars
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
to search for tunnels, caverns and other geophysical features.
Novel antennas
Antenna designs incorporating metamaterials can step-up the radiated powerPower (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
of an antenna. The newest metamaterial antennas radiate as much as 95 percent of an input radio signal. Standard antennas need to be at least half the size of the signal 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...
to operate efficiently. At 300 MHz, for instance, an antenna would need to be half a meter long. In contrast, the experimental antennas are as small as one-fiftieth of a wavelength, and could have further decreases in size.
Metamaterials are a basis for further minaturation of microwave antennas, with efficient power and acceptable bandwidth. Novel antennas employing metamaterials offer the possibility of overcoming restrictive efficiency-bandwidth limitations for conventionally constructed, miniature antennas.
In contrast, metamaterials permit smaller antenna elements that cover a wider frequency range, thus making better use of available space for small platforms, or spaces. Some applications for metamaterial antennas are wireless communication, space communications
Space Communications and Navigation Program
The Space Communications and Navigation program places the three prime NASA space communications networks, Space Network , Near Earth Network , and the Deep Space Network , under one Management and Systems Engineering umbrella. It was established in 2006...
, GPS, satellite
Satellite
In the context of spaceflight, a satellite is an object which has been placed into orbit by human endeavour. Such objects are sometimes called artificial satellites to distinguish them from natural satellites such as the Moon....
s, space vehicle navigation, and airplanes. In these instances, miniature antennas with high gain are significantly relevant because the radiating elements are combined into large antenna arrays for these functions, and vehicles. Furthermore, 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....
, produced by metamaterials, results in electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
being focused by a flat lens versus being dispersed.
The DNG shell
The earliest research in metamaterial based antennas was an analytical study of surrounding a miniature dipole antenna with material that produces a negative index of refraction. This material has an interchangeable nomenclature of negative index metamaterial (NIM) or double negative metamaterial (DNG) among other names.This configuration analytically and numerically appears to produce an order of magnitude increase in power. At the same time, the reactance appears to have a corresponding decrease. Furthermore, the DNG shell becomes a natural impedance matching network for this dipole antenna system.
Ground plane applications
Metamaterials employed in the ground planeGround plane
In electrical engineering, a ground plane is an electrically conductive surface.-Radio antenna theory :In telecommunication, a ground plane structure or relationship exists between the antenna and another object, where the only structure of the object is a structure which permits the antenna to...
s surrounding antennas offers improved isolation between 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...
, or 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...
channels of (multiple-input multiple-output) (MIMO) antenna arrays
Phased array
In wave theory, a phased array is an array of antennas in which the relative phases of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern of the array is reinforced in a desired direction and suppressed in undesired directions.An antenna array...
. Metamaterial, high-impedance groundplanes
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...
can also be used to improve the radiation
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...
efficiency, and axial radio performance of low-profile antennas located close to the ground plane surface
Ground plane
In electrical engineering, a ground plane is an electrically conductive surface.-Radio antenna theory :In telecommunication, a ground plane structure or relationship exists between the antenna and another object, where the only structure of the object is a structure which permits the antenna to...
. Metamaterials have also been used to increase the beam scanning
Microwave Scanning Beam Landing System
The Microwave Scanning Beam Landing System is a Ku band approach and landing navigation aid formerly used by NASA's space shuttle. It provides precise elevation, directional and distance data which was used to guide the orbiter for the last two minutes of flight until touchdown...
range by using both the forward and backward waves in leaky wave antennas. Various metamaterial antenna systems can be employed to support surveillance sensors, communication links, navigation systems, command and control systems.
.
Novel configurations
Besides antenna miniaturization, the novel configurations have potential applications ranging from radio frequecy devices to optical devices. Other combinations, for other devices in metamaterial antenna subsystems are being researched. Either double negative metamaterial slabs are used exclusively or combinations of double positive (DPS)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....
with DNG slabs, or epsilon-negative (ENG) slabs with mu-negative (MNG) slabs are employed in the subsystems. The antenna subsystems that are currently being researched are cavity resonators
Resonator
A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical...
, waveguides, scatters, and antennas (radiators). In addition, metamaterial antennas are already (2009) commercially available.
Negative refraction for novel antennas
PendryPendry
Pendry is the surname of :*Professor John Pendry, English theoretical physicist*Tom Pendry, Baron Pendry, English politician*Jan-Simon Pendry, the original creator of the Berkeley Automounter...
et al. were able to show that a three-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...
al array of intersecting, thin wires could be used to create negative values of permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
ε, and that a periodic array of copper split ring resonators could produce an effective negative magnetic permeability μ.
Then in the year 2000, the group of researchers, Smith et al.
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...
were the first to successfully combine the split-ring resonator, often designated as SRR, with thin wire conducting posts and produce a left-handed material, which had negative values of ε and μ for frequencies in the gigahertz or microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
range.
Then, in 2002, a different class of Negative refractive index (NRI) metamaterials was introduced. This employs periodic reactive loading of a 2-D transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...
as the host medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
. This configuration actually used positive index material with negative index material. It employed a small, planar, negative-refractive-lens
Superlens
A superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
interfaced with a positive index, parallel-plate waveguide
Waveguide
A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguides for each type of wave...
. This was experimentally verified soon after, in a subsequent demonstration.
Although some inefficiencies with split-ring resonances were stated during and after the introduction of this combined negative and positive index material, split-ring resonators are still effectively employed as of 2009 for research. SRRs have been involved in wide ranging 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....
research, including research on metamaterial antennas.
A more recent view is that by using split-ring resonators (SRRs) as typical metamaterial building blocks, the designed and desired electromagnetic response and associated flexibility is highly desirable.
Phase compensation due to negative refraction
DNG media can provide phase compensationPhase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
. This is due to their negative index of refraction. This is accomplished by combining a slab of conventional lossless DPS material with a slab of lossless DNG metamaterial.
The DPS has a conventional or ordinary index of refraction, while the DNG has the opposite, negative refractive index. Both of these slabs are impedance matched to the outside region (e.g., free space). The desired monochromatic plane wave
Plane wave
In the physics of wave propagation, a plane wave is a constant-frequency wave whose wavefronts are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector....
is radiated on this configuration. As this wave propagates through the first slab there is a phase difference
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
between the exit face and entrance face. As the wave propagates
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
through the second slab the phase difference is decreased and even compensated for. Therefore as the wave exits the second slab the total phase difference is equal to zero. This is discussed in more detail in a section below.
With this system a phase-compensated, waveguiding system could be produced. By using multiple stacks of this configuration, the phase compensation (beam translation effects) would occur throughout the entire system. Furthermore, by changing the index of any of the DPS-DNG pairs, the speed at which the beam enters the front face, and exits the back face of the entire stack-system changes. In this manner, a volumetric, low loss, time delay transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...
could be realized for a Gaussian beam
Gaussian beam
In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity distributions are well approximated by Gaussian functions. Many lasers emit beams that approximate a Gaussian profile, in which case the laser is said to be operating on the fundamental...
system.
Furthermore, this phase compensation can lead to a set of applications, which are miniaturized, subwavelength, cavity resonators, and waveguides with applications below diffraction limits.
Dispersion compensation in a transmission line using negative refraction
Because of the dispersive natureDispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....
of the DNG metamaterial as a transmission medium, it could be useful as an effective dispersion compensation device for time-domain applications
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
. The dispersion produces a variance of the group speed of the wave components of the signal, as they propagate in the DNG medium. Hence, volumetric (stacked) DNG metamaterials could be useful for the modification of the propagation of signals along a microstrip transmission line
Microstrip
Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components...
. At the same time, dispersion leads to distortion. However, if the dispersion could be compensated for along the microstrip line, RF
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...
or 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...
signals 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....
along them would not be distorted. This could create an environment where components for attenuating distortion are less critical, and could lead to simplification of components in many systems. Dispersion along the microstrip can be eliminated by correcting for the frequency dependence of the effective permittivity associated with this type of transmission line. It is possible to do this with metamaterials.
The strategy is to design a length 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....
-loaded transmission line that can be introduced, in some manner, with the original length of microstrip
Microstrip
Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components...
line to make the paired system dispersionless
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
. In other words, create a dispersion-compensating segment of transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...
. This could be accomplished by introducing a metamaterial with a certain relative permittivity and a certain magnetic permeability, which then effects the overall relative permittivity and permeability of the microstrip line. At the same time it is introduced in such a manner that the wave impedance in the metamaterial remains the same as it is in the original conventional microstrip line. Then the index of refraction in the medium compensates for the dispersion effects associated with the microstrip geometry itself; that is the effective index of the pair becomes that of free space.
Part of the design strategy is that the effective permittivity and permeability of such a metamaterial should be negative - a DNG material must be introduced for this purpose.
Innovation
A circuit design which has a broader range of material parameters resulting in negative refractive index has resulted in antennas that are notable and innovative. Combining a left-handed transmission line with a conventional (right-handed) transmission line results in novel configurations with advantages over conventional antenna designs. The left-handed transmission lines are essentially a high-pass filter with phase advance. Conversely, the right-handed transmission lines are a low-pass filter with phase lag. This configuration is designated composite right/left-handed (CRLH) metamaterial.The conventional Leaky Wave antenna has had limited commercial success because it lacks complete backfire-to-endfire frequency scanning capability. The CRLH configuration allows the innovation over half-space scanning (broadside-to-endfire). The CRLH now allows for complete backfire-to-endfire frequency scanning, including broadside.
Metamaterial microwave lens
The metamaterial lens, found in 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....
antenna systems, is used as an efficient coupler to the external radiation, focusing radiation along or from a microstrip
Microstrip
Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components...
transmission line into transmitting and receiving components. Hence, it can be designed as an input device
Input device
In computing, an input device is any peripheral used to provide data and control signals to an information processing system such as a computer or other information appliance...
. In addition, it can enhance the amplitude of evanescent waves, as well as correct the phase of propagating waves.
A metamaterial (lens) for directing radiation
The metamaterial for research in many instances is the SRR and wire configuration. However in this instance it is several layers of a metalMetal
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...
lic mesh of thin wire
Wire
A wire is a single, usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads and to carry electricity and telecommunications signals. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Standard sizes are determined by various...
s - with wires in the three directions of space, and slices of foam. Interestingly the 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...
of this material, above the plasma frequency can be positive and less than one. This means that the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
is less than one, but hardly above zero. In this case, the relevant parameter is often the contrast between the permittivities rather than the value of the overall permittivity itself, at desired frequencies. This occurs because the equivalent (effective) permittivity has a behavior governed by a plasma frequency in the microwave domain. This low optical index material then becomes a good candidate for creation of extremely convergent microlens
Microlens
A microlens is a small lens, generally with a diameter less than a millimetre and often as small as 10 micrometres . The small sizes of the lenses means that a simple design can give good optical quality but sometimes unwanted effects arise due to optical diffraction at the small features...
es. Methods that have been developed theoretically using dielectric photonic crystals are applied in the microwave domain to realize a directive emitter using metallic grids.
In this instance, arrayed wires in a cubic, crystal lattice structure can be analyzed as an array of aerials (antenna array
Phased array
In wave theory, a phased array is an array of antennas in which the relative phases of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern of the array is reinforced in a desired direction and suppressed in undesired directions.An antenna array...
). Therefore, as a lattice structure it has a lattice constant. The lattice constant
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...
, or lattice parameter, refers to the constant distance between unit cells in a crystal lattice.
The earlier discovery of plasmon
Plasmon
In physics, a plasmon is a quantum of plasma oscillation. The plasmon is a quasiparticle resulting from the quantization of plasma oscillations just as photons and phonons are quantizations of light and mechanical vibrations, respectively...
s created the view that metal at plasmon frequency fp is a composite material. The effect of plasmons on any metal sample is to create properties in the metal such that it can behave as a 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...
, independent of the wave vector of the EM excitation (radiation) field. Furthermore, there is a minute-fractionally small amount of plasmon energy that is absorbed into the system denoted as γ. For aluminium fp = 15 eV, and γ = 0.1 eV. Perhaps the most important result of the interaction of metal and the plasma frequency is that permittivity is negative below the plasma frequency, all the way to the minute value of γ.
These facts ultimately result in the arrayed wire structure as being effectively a homogenous medium.
This metamaterial allows for control of the direction of emission of an electromagnetic radiation source located inside the material in order to collect all the energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
in a small angular
Angular
The angular is a large bone in the lower jaw of amphibians and reptiles , which is connected to all other lower jaw bones: the dentary , the splenial, the suprangular, and the articular...
domain around the normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...
. By using a slab of a of a metamaterial, diverging electromagnetic waves are focused into a narrow cone. Dimensions of its component are small in comparison to the wavelength, and thus the slab behaves as a homogeneous material with a low plasma frequency.
Conventional transmission lines
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...
is the material medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
or structure that forms all or part of a path
Course (navigation)
In navigation, a vehicle's course is the angle that the intended path of the vehicle makes with a fixed reference object . Typically course is measured in degrees from 0° clockwise to 360° in compass convention . Course is customarily expressed in three digits, using preliminary zeros if needed,...
from one place to another for directing the transmission
Transmission (telecommunications)
Transmission, in telecommunications, is the process of sending, propagating and receiving an analogue or digital information signal over a physical point-to-point or point-to-multipoint transmission medium, either wired, optical fiber or wireless...
of energy, such as electromagnetic waves as well as electric power transmission
Electric power transmission
Electric-power transmission is the bulk transfer of electrical energy, from generating power plants to Electrical substations located near demand centers...
.
Types of transmission line include wire
Wire
A wire is a single, usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads and to carry electricity and telecommunications signals. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Standard sizes are determined by various...
s, coaxial cable
Coaxial cable
Coaxial cable, or coax, has an inner conductor surrounded by a flexible, tubular insulating layer, surrounded by a tubular conducting shield. The term coaxial comes from the inner conductor and the outer shield sharing the same geometric axis...
s, dielectric slabs, stripline
Stripline
Stripline is a transverse electromagnetic transmission line medium, that was invented by Robert M. Barrett of the Air Force Cambridge Research Centre in the 1950s.- Description :...
s, optical fiber
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...
s, electric power lines
Power Line
Power Line is an American political blog, providing news and commentary from a conservative point-of-view. It was originally written by three lawyers who attended Dartmouth College together: John H. Hinderaker, Scott W. Johnson, and Paul Mirengoff...
, and waveguide
Waveguide
A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguides for each type of wave...
s.
A microstrip
Microstrip
Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components...
is a type of electrical transmission line which can be fabricated using 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...
technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane
Ground plane
In electrical engineering, a ground plane is an electrically conductive surface.-Radio antenna theory :In telecommunication, a ground plane structure or relationship exists between the antenna and another object, where the only structure of the object is a structure which permits the antenna to...
by a dielectric layer known as the substrate. Microwave components such as antennas
Microstrip antenna
In telecommunication, there are several types of microstrip antennas the most common of which is the microstrip patch antenna or patch antenna...
, couplers, filter
Electronic filter
Electronic filters are electronic circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both...
s, power dividers etc. can be formed from microstrip.
From the simplified schematics to the right it can be seen that total impedance, conductance, reactance (capacitance and inductance), and the transmission medium (transmission line) can be represented by single components, which give the overall value.
With transmission line mediums it is important to match the load impedance ZL to the characteristic impedance
Characteristic impedance
The characteristic impedance or surge impedance of a uniform transmission line, usually written Z_0, is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. The SI unit of characteristic impedance is the ohm...
Z0 as closely as possible, because it is usually desirable that as much power as possible will be absorbed by the load.
is the resistanceElectrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
per unit length,
is the inductanceInductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
per unit length,
is the conductance of the dielectric per unit length, is the capacitanceCapacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
per unit length,
is the imaginary unitImaginary unit
In mathematics, the imaginary unit allows the real number system ℝ to be extended to the complex number system ℂ, which in turn provides at least one root for every polynomial . The imaginary unit is denoted by , , or the Greek...
, and
is the angular frequencyAngular frequency
In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...
.
Lumped circuit elements
Often, because of the goal which moves physical metamaterial inclusions (or cells) to smaller sizes, discussion and implementation of lumped LC circuitsLumped 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...
, or distributed LC networks
Distributed element model
In electrical engineering, the distributed element model or transmission line model of electrical circuits assumes that the attributes of the circuit are distributed continuously throughout the material of the circuit...
, are often included in the research. Lumped circuit elements are actually microscopic elements that effectively approximate, their larger component counterpart. For example circuit capacitance and inductance can be created with spilt rings, which are on the scale of nanometers at optical frequencies. The distributed LC model is related to the lumped LC model, however the distributed element model
Distributed element model
In electrical engineering, the distributed element model or transmission line model of electrical circuits assumes that the attributes of the circuit are distributed continuously throughout the material of the circuit...
is more accurate but more complex than the lumped element model
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...
.
Metamaterial - loaded transmission line configurations
Some noted metamaterial antennaAntenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
s employ negative refractive index transmission-line metamaterials (NRI-TLM). These include lense
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
s that can overcome the diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
limit, small band and broadband phase shifting lines, small antennas, low profile antennas, antenna feed networks, and novel power architectures, and high directivity couplers.
A novel approach for implementing NRI-TLM is loading a planar metamaterial network of TLs with series capacitors and shunt inductors, which has a higher performance than standard TLs. This results in a large operating bandwidth while the refractive index is negative.
Because superlens
Superlens
A superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
es can overcome the diffraction limit, this allows for a more efficient coupling to the external radiation, and enables the availability for a broader band of frequency. For example the superlens can be applied to the TLM architecture
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...
. In conventional lenses, the imaging is limited by the diffraction limit. With John Pendry
John Pendry
Sir 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"...
's superlens the details of the near field
Near and far field
The near field and far field and the transition zone are regions of the electromagnetic radiation field that emanates from a transmitting antenna, or as a result of radiation scattering off an object...
images are not lost. Growing evanescent waves are supported in the metamaterial (n < 1), which restores the decaying evanescent waves from the source. This results in a diffraction-limited resolution of λ/6, after some small losses. This compares with λ/2, from normal diffraction limit for conventional lenses.
By combining right-handed materials (RHM) with left-handed materials (LHM) as a composite material (CRLH) construction for the transmission line, both a backward to forward scanning capability is obtained.
Metamaterials were first used for antenna technology around 2005. This type of antenna used the established capability of SNGs to couple with external radiation
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...
. Resonant coupling
Coupling
A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. Couplings do not normally allow disconnection of shafts during operation, however there are torque limiting couplings which can slip or disconnect when some torque limit is exceeded.The...
allowed for a 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...
larger than the antenna. At microwave frequencies this allowed for an electrically small antenna.
A metamaterial-loaded transmission line has stated advantages, which are significant over conventional or standard delay transmission lines. It is more compact in size, it can achieve positive or negative phase shift while occupying the same short physical length and it exhibits a linear, flatter phase response
Phase response
In signal processing and electrical engineering, phase response is the relationship between the phase of a sinusoidal input and the output signal passing through any device that accepts input and produces an output signal, such as an amplifier or a filter....
with frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
, leading to shorter group delays. It can work in lower frequency because of high series distributed-capacitors, it has smaller plane dimensions than its equivalent coplanar structure.
Negative refractive index metamaterials supporting 2-D waves
In 2002, rather than using split-ring-resonator-wire configuration, or other 3-D media, researchers looked at planar configurations that supported backward wave propagation, thus demonstrating negative refractive index and focusingSuperlens
A superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
as a consequence.
It has long been known that transmission lines periodically
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,...
loaded with capacitive and inductive elements in a high-pass configuration support certain types of backward waves. In addition, planar transmission lines are a natural match for 2-D wave propagation. Furthermore, with lumped circuit elements they retain a compact configuration, and can still support the lower RF range. With this in mind, periodically loaded, two-dimensional LC transmission line networks, designed with a high pass and cutoff, were proposed. The LC networks can be designed to support backward waves, without bulky SRR/ wire structure. This was the first such proposal which veered away from bulk media for a negative refractive effect (result). A notable property of this type of networks is that there is no reliance on resonance, and instead it is the ability to support backward waves which defines negative refraction.
The principles behind focusing are derived from Veselago's well-known paper, “The electrodynamics of substances with simultaneously negative values of ε and μ” and Sir Pendry's Perfect lens proposal. To give an overview of how this works - by combining a conventional, flat, (planar) DPS slab, M-1, with a left-handed medium, M-2, a propagating electromagnetic wave with a wave vector
Wave vector
In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave , and its direction is ordinarily the direction of wave propagation In...
k1 in M-1, results in a refracted wave with a wave vector k2 in M-2. Since, M-2 supports backward wave propagation k2 is refracted to the opposite side of the normal, while the Poynting vector of M-2 is anti-parallel with k2. Under such conditions, power is refracted through an effectively negative angle, which indeed implies an effectively negative index of refraction.
Electromagnetic waves from a point source located inside a conventional DPS can be focused inside an LHM using a planar interface of the two media. These conditions can be modeled by exciting a single node inside the DPS, and observing the magnitude and phase of the voltages to ground at all points in the LHM. A focusing effect should manifest itself as a “spot” distribution of voltage at a predictable location in the LHM.
Negative refraction and focusing of electromagnetic waves can be accomplished without employing resonances or directly synthesizing the permittivity and permeability. In addition, this media can be practically fabricated by appropriately loading a host transmission line medium. Furthermore, the resulting planar topology permits LHM structures to be readily integrated with conventional planar microwave circuits and devices.
When transverse electromagnetic propagation occurs with a transmission line medium, the analogy for permittivity and permeability is ε = L, and μ = C. Since this analogy was developed with positive values for these parameters, then the next logic step was realizing that negative values could be achieved. In order to synthesize a left-handed medium (ε < 0 and μ < 0) the series reactance and shunt susceptibility should become negative, because the material parameters are directly proportional to these circuit quantities.
A transmission line which has lumped circuit elements that synthesize a left-handed medium is referred to as a "dual transmission line" as compared to "conventional transmission line". The dual transmission line structure can be implemented in practice by loading a host transmission
line with lumped element series capacitors (C) and shunt inductors (L). In this periodic
structure, the loading is strong such that the lumped elements dominate the propagation characteristics.
Left-handed behavior in LC loaded transmission lines
At the very end of 2002, some researchers noticed that split-ring resonators (SRRs) were restricted to narrow bandwidths, and this was mostly due to the SRRs reliance on resonanceResonance
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...
. In addition, to utilize SRRs at RF frequencies
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...
, as with wireless devices, the split-ring resonators have to be scaled to larger dimensions. This worked against making the (wireless) devices themselves more and more compact. In contrast, LC network configurations could be scaled in both microwave and RF frequencies.
Therefore, it appeared that LC loaded transmission lines were enabling the design of a new class of metamaterials to synthesize a negative refractive index. In addition, by relying on LC networks to emulate electrical permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
and magnetic permeability this resulted in a substantial increase in operating bandwidths.
Moreover, their unit cells are connected through a transmission-line network and they may,
therefore, be equipped with lumped circuit elements, which permit them to be compact at frequencies where the 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,...
cannot be compact. The flexibility gained through the use of either discrete or printed elements enables the proposed planar metamaterials to be scalable from the megahertz to the tens of gigahertz range. In addition, by utilizing varactors instead of capacitors, the effective material properties can be dynamically tuned. Furthermore, the proposed media are planar and inherently support two-dimensional (2-D) wave propagation, and are well suited for RF/microwave device and circuit applications.
Growing evanescent waves in negative-refractive-index transmission-line media
The periodic 2-D LC loaded transmission-line (TL) was shown to exhibit NRI properties over a broad frequency range. This network will be referred to as a dual TL structure since it is of a high-pass configuration, as opposed to the low-pass representation of a conventional TL structure. Dual TL structures have been used to experimentally demonstrate backward-wave radiation and focusing at microwave frequencies.As a negative refractive index medium, a dual TL structure is not simply a phase compensator. It can enhance the amplitude of evanescent waves, as well as correct the phase of propagating waves. Evanescent waves actually grow within the dual TL structure.
Backward wave antenna using an NRI loaded transmission line
Grbic et al. used one-dimensional LC loaded transmission line network, which supports fast backward-wave propagation to demonstrate characteristics analogous to "reversed Cherenkov radiation". Their proposed backward-wave radiating structure was inspired by negative refractive index LC materials. The simulated E-plane pattern at 15 GHz showed radiation towards the backfire direction in the far-field pattern, clearly indicating the excitation of a backward wave. Since the transverse dimension of the array is electrically short, the structure is backed by a long metallic trough. The trough acts as a waveguide below cut-off and recovers the back radiation, resulting in unidirectional far-field patternsPlanar NIMs with periodic loaded transmission lines
A technique has been presented for implementing planar media with an effective negative refractive index. The underlying concept is based on appropriately loading a printed network of transmission lines periodically with inductors and capacitors. This technique results in effective permittivity and permeability material parameters that are both inherently and simultaneously negative, obviating the need to synthesize these parameters separately, or by separate means. The proposed media possess several other desirable features including very wide bandwidth over which the refractive index. remains negative, the ability to guide 2-D TM waves, scalability from RF to millimeter-wave frequencies, low transmission losses, as well as the potential for tunability by inserting varactors and/or switches in the unit cell. The proposed concept has been verified with circuit and full-wave simulations. Moreover, a prototype focusing device has been implemented and tested experimentally. The experimental results demonstrated focusing of an incident cylindrical wave within an octave bandwidth and over an electrically short area; a phenomenon suggestive of near-field focusing.Anticipated future applications are new enabling RF/microwave devices can be implemented based on these proposed planar negative refractive index media for applications in wireless communications, surveillance, and radars.
Larger NRI transmission lines
According to some researchers SRR/wire configured metamaterials are bulky 3-D constructions, which are difficult to adapt for RF/microwave device and circuit applications. These structures can achieve a negative index of refraction only within a narrow bandwidth. Furthermore, when applied to wireless devices at RF frequencies the split ring-resonators have to be scaled to larger dimensions, which, in turn would make such devices less compact.Proposed designs of a new class of metamaterials to synthesize a negative refractive index. The proposed structures go beyond the wire/SRR composites in that they do not rely on SRRs to synthesize the material parameters, thus leading to dramatically increased operating bandwidths. Moreover, their unit cells are connected through a transmission-line network and they may, therefore, be equipped with lumped elements, which permit them to be compact at frequencies where the SRR cannot be compact. The flexibility gained through the use of either discrete or printed elements enables the proposed planar metamaterials to be scalable from the megahertz to the tens of gigahertz range. In addition, by utilizing varactors instead of capacitors, the effective material properties can be dynamically tuned. Furthermore, the proposed media are planar and inherently support two-dimensional (2-D) wave propagation. Therefore, these new metamaterials are well suited for RF/microwave device and circuit applications.
In the long-wavelength regime, the permittivity and permeability of conventional materials
can be artificially synthesized using periodic LC networks arranged in a low-pass
configuration. In the dual (high-pass) configuration, these equivalent material parameters
assume simultaneously negative values, and may therefore be used to synthesize a negative
refractive index.
Metamaterial antenna configurations
Over longer distances than human hearing, or which the unaided eye can see, electromagnetic waves are transmitted over wire or via aerial devices (antennas).An antenna (or aerial) is a transducer
Transducer
A transducer is a device that converts one type of energy to another. Energy types include electrical, mechanical, electromagnetic , chemical, acoustic or thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a...
designed to transmit
Transmitter
In electronics and telecommunications a transmitter or radio transmitter is an electronic device which, with the aid of an antenna, produces radio waves. The transmitter itself generates a radio frequency alternating current, which is applied to the antenna. When excited by this alternating...
or receive
Receiver (radio)
A radio receiver converts signals from a radio antenna to a usable form. It uses electronic filters to separate a wanted radio frequency signal from all other signals, the electronic amplifier increases the level suitable for further processing, and finally recovers the desired information through...
electromagnetic wave
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
s. In other words, antennas convert electromagnetic waves into electrical currents and vice versa.
An antenna as a radiator or receiver of electromagnetic
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
energy can also be defined as the transition region between free space and the guiding electromagnetic structure such as the transmission line.
Antenna theory is based on classical electromagnetic theory
Classical electromagnetism
Classical electromagnetism is a branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents...
as described by Maxwell's equations. Physically, an antenna is an arrangement of one or more conductor
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...
s, usually called elements in this context. In transmission, an alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....
is created in the elements by applying a voltage at the antenna terminals, causing the elements to radiate an electromagnetic field. In reception, the inverse occurs: an electromagnetic field from another source induces an alternating current in the elements and a corresponding voltage at the antenna's terminals. Some receiving antennas (such as parabolic and horn types) incorporate shaped reflective surfaces to collect EM waves from free space and direct or focus them onto the actual conductive elements.
An antenna creates sufficiently strong electromagnetic fields at large distances. Reciprocally, it is sensitive to the electromagnetic fields impressed upon it externally. The actual coupling between a transmitting and receiving antenna is so small that amplifier circuits are required at both the transmitting and receiving stations. Antennas are usually created by modifying ordinary circuitry into transmission line configurations.
The required antenna for any given application is dependent on the bandwidth employed, and range (power) requirements. In the microwave to millimeter-wave range – wavelengths from a few meters to millimeters – the following antennas are usually employed:
Dipole antennas, short antennas, parabolic and other reflector antennas, horn antennas, periscope antennas, helical antennas, spiral antennas, surface-wave and leaky wave antennas. Leaky wave antennas include dielectric and dielectric loaded antennas, and the variety of microstrip antennas.
Radiation properties antennas with SRRs
The split ring resonator (SRR) was introduced by Pendry in 1999, and is one of the most common elements of 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 As a nonmagnetic conducting unit, it comprises an array of units which yield an enhanced negative effective magnetic permeability, when the frequency of the incident electromagnetic field is close to the SRR resonance frequency. The resonant frequency of the SRR simply depends on its shape and physical design. In addition, resonance can occur at wavelengths much larger than it size.
Double negative metamaterials increase radiated power of antennas
Through the application of double negative metamaterials (DNG), the power radiatedPower (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
by electrically
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
small 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...
antennas can be notably increased. This could be accomplished by surrounding an antenna
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
with a shell of double negative (DNG) material. At the time (late 2003) this was investigated both analytically and numerically. When the electric dipole is embedded in a 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...
DNG medium, the analysis shows that the antenna acts inductively rather than capacitively, as it would in free space without the interaction of the DNG material. In addition, the dipole-DNG shell combination increases the real power radiated by more than an order of magnitude
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
over a free space antenna. A notable decrease in the reactance of the dipole antenna corresponds to the increase in radiated power.
Analysis also shows that the reactive power within this dipole-DNG shell system indicates that the DNG shell acts as a natural matching network for the dipole. The DNG material matches the intrinsic reactance of this antenna system to free space, hence the impedance of DNG material matches free space. It provides a natural matching circuit to the antenna.
Single negative SRR and monopole composite
There is interest in the use of metamaterials to increase antenna performance. With the addition of an SRR-DNG metamaterial the radiated powerPower (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
was shown to increase by more than an order of magnitude
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
over a comparable free space antenna. Electrically
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
small antennas, high directivity
Directivity
In electromagnetics, directivity is a figure of merit for an antenna. It measures the power density the antenna radiates in the direction of its strongest emission, versus the power density radiated by an ideal isotropic radiator radiating the same total power.An antenna's directivity is a...
, and tunable operational frequency are produced with negative magnetic permeability
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....
. When combining a right-handed material
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....
(RHM) with a Veselago-left-handed material (LHM) other novel 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....
are obtained. Finally, a single negative material
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....
resonator, obtained with an SRR, can produce an electrically small antenna when operating at microwave frequencies, as follows:
The configuration of a split-ring resonator used was two concentric annular
Annulus (mathematics)
In mathematics, an annulus is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. Or, it is the area between two concentric circles...
rings with relative opposite gaps in the inner and outer ring. Its geometrical parameters were R = 3.6 mm, r = 2.5 mm, w = 0.2 mm, t = 0.9 mm. R and r are used in annular
Annulus (mathematics)
In mathematics, an annulus is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. Or, it is the area between two concentric circles...
parameters, w is the spacing between the rings and t = the width of the outer ring. The material had a thickness of 1.6 mm. Permittivity was 3.85 at 4 GHz. The SRR was fabricated with an etching technique onto a 30 μm thick 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...
. The SRR was excited by using a monopole antenna
Monopole antenna
A monopole antenna is a class of radio antenna consisting of a straight rod-shaped conductor, often mounted perpendicularly over some type of conductive surface, called a ground plane. The driving signal from the transmitter is applied, or for receiving antennas the output voltage is taken,...
. The monopole antenna
Monopole antenna
A monopole antenna is a class of radio antenna consisting of a straight rod-shaped conductor, often mounted perpendicularly over some type of conductive surface, called a ground plane. The driving signal from the transmitter is applied, or for receiving antennas the output voltage is taken,...
was composed of a coaxial cable
Coaxial cable
Coaxial cable, or coax, has an inner conductor surrounded by a flexible, tubular insulating layer, surrounded by a tubular conducting shield. The term coaxial comes from the inner conductor and the outer shield sharing the same geometric axis...
, ground plane
Ground plane
In electrical engineering, a ground plane is an electrically conductive surface.-Radio antenna theory :In telecommunication, a ground plane structure or relationship exists between the antenna and another object, where the only structure of the object is a structure which permits the antenna to...
, and radiating components. The ground plane material was aluminium
Aluminium
Aluminium or aluminum is a silvery white member of the boron group of chemical elements. It has the symbol Al, and its atomic number is 13. It is not soluble in water under normal circumstances....
. The operation frequency of the antenna was 3.52 GHz, which was determined by considering the geometrical parameters of SRR.
A length of wire of 8.32 mm was placed above the ground plane, connected to the antenna, which was one quarter of the operation wavelength. Therefore, this makes the antenna work with a feed wavelength was 33.28 mm and feed frequency was 7.8 GHz. The resonant frequency of the SRR turned out to be smaller than the monopole operation frequency.
The monopole-SRR (metamaterial) antenna was found to operate efficiently at (λ/10) using the SRR-wire configuration. It demonstrated good coupling efficiency, and enough radiation efficiency. Its operation was found to be comparable to a conventional antenna at λ/2, which is recommended as an antenna size for efficient coupling and radiation for a conventional antenna. Therefore, the monopole-SRR antenna becomes an acceptable electrically small antenna, at the resonance frequency of the SRR. This antenna can be used wherever (planar) patch antenna
Patch antenna
A patch antenna is a type of radio antenna with a low profile, which can be mounted on a flat surface. It consists of a flat rectangular sheet or "patch" of metal, mounted over a larger sheet of metal called a ground plane. The assembly is usually contained inside a plastic radome, which...
s are used.
When the 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,...
is made part of this configuration the characteristics, such as radiation pattern of the antenna are entirely changed. This is noticed with comparison to a conventional monopole antenna. With modifications to the SRR structure (the metamaterial) the antenna size could reach (λ/40). Furthermore, by coupling 2, 3, and 4 SRRs side by side, there is a slight shift radiation patterns.
Patch antennas with a metamaterial
In 2005, a new, patch antennaPatch antenna
A patch antenna is a type of radio antenna with a low profile, which can be mounted on a flat surface. It consists of a flat rectangular sheet or "patch" of metal, mounted over a larger sheet of metal called a ground plane. The assembly is usually contained inside a plastic radome, which...
, with a metamaterial cover, which resulted in enhanced directivity
Directivity
In electromagnetics, directivity is a figure of merit for an antenna. It measures the power density the antenna radiates in the direction of its strongest emission, versus the power density radiated by an ideal isotropic radiator radiating the same total power.An antenna's directivity is a...
was proposed. According to the numerical results, the metamaterial patch antenna showed significant improvement in directivity, compared to the conventional patch antenna. This was cited in 2007 for an efficient design of directive patch antennas in mobile communications using metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
s. This design was based on the left-handed material (LHM) transmission line model, with the circuit elements L and C of the LHM equivalent circuit
Equivalent circuit
In electrical engineering and science, an equivalent circuit refers to a theoretical circuit that retains all of the electrical characteristics of a given circuit. Often, an equivalent circuit is sought that is the simplest form of a more complex circuit in order to aid analysis. In its most common...
model. This study developed formula
Formula
In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language....
e to determine the L and C values of the LHM equivalent circuit model for desirable characteristics of directive patch antennas. Design examples derived from actual frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
bands in mobile communications were performed, which illustrates the efficiency of this patch antenna.
Novel flat lens horn antenna
This configuration uses flat aperture constructed of zero-index metamaterial. The zero-index metamaterial is a fully flat structure. This has advantages over ordinary (conventional) curved lenses, which results in a much improved directivity for this horn antenna configuration. In addition, references are made to the following devices: perfect lens, backward leaky-wave antenna, miniaturization of patch antenna, resonant cavity and coupler. These investigations have provided capabilities for the miniaturization of microwave source and non-source devices, circuits, antennas and the improvement of electromagnetic performances.Improvements in design
Research and applications of metamaterial based antennas. Related components are also researched.Subwavelength cavities and waveguides
When the interface between a pair of materials, which function as optical transmission media, have interactions as a result of opposing permittivity and / or permeability values that are either ordinary (positive) or extraordinary (negative), notable anomalous behaviors may occur. The pair of materials would be a DNG metamaterial (layer), paired with a DPS, ENG, or MNG layer. In these instances wave propagation behavior and properties may occur that would otherwise not happen if only DNG layers are paired together.At the interface between two media, the concept of the continuity of the tangential electric and magnetic field components can be applied. If either the permeability or permittivity of two media has opposite signs then the normal components of the tangential field, on both sides of the interface, will be discontinuous (at the boundary). This implies a concentrated resonant phenomenon at the interface. This appears to be similar to the current and voltage distributions at the junction between an inductor and capacitor, at the resonance of an L-C circuit. This can be cause for notable characteristics of wave interaction in metamaterial-based devices and components. This "interface resonance" is essentially independent of the total thickness of the paired layers. This is because it occurs along the discontinuity between two such conjugate materials.
Parallel-plate waveguiding structures
The geometry consists of two parallel plates as perfect conductors (PEC), an idealized structure, filled by two stacked planar slabs of homogeneous and isotropic materials with their respective constitutive parameters ε1, ε2, u1, u2. Each slab has thickness = d, slab 1 = d1, and slab 2 = d2. Choosing which combination of parameters to employ involves pairing of DPS and DNG or ENG and MNG materials. As mentioned previously, this is one pair of oppositely signed constitutive parameters, combined.Thin subwavelength cavity resonators
Phase compensation:The real component values for negative permittivity and permeability results in a real component values for negative refraction n. In a loss less medium, all that would exist is real values. This concept can then be used to map out phase compensation when a conventional lossless material, DPS, is matched with a lossless NIM (DNG).
In phase compensation, the DPS of thickness d1 has ε > 0 and µ > 0. Conversely, the NIM of thickness d2 has ε < 0 and µ < 0. Assume that the intrinsic impedance of the DPS dielectric material (d1) is the same as that of the outside region, and responding to a normally incident plane wave. The wave travels through the medium without any reflection because the DPS impedance and the outside impedance are equal. However, the plane wave at the end of DPS slab it is out of phase with the plane wave at the beginning of the material.
The plane wave then enters the lossless NIM (d2). At certain frequencies ε < 0 and µ < 0 and n < 0. Like the DPS, the NIM has intrinsic impedance which is equal to the outside, and, therefore, is lossless as well. The direction of power flow (i.e., the Poynting vector) in the first slab should be the same as that in the second one, because the power of the incident wave enters the first slab (without any reflection at the first interface), traverses the first slab, exits the second interface, enters the second slab and traverses it, and finally leaves the second slab. However, as stated earlier, the direction of power is anti-parallel to the direction of phase velocity. Therefore, the wave vector k2 is in the opposite direction of k1. Furthermore, whatever phase difference is developed by traversing the first slab, it can be decreased and even cancelled by traversing the second slab. If the ratio of the two thicknesses is d1 / d 2 = n2 / n1, then total phase difference between the front face, and the back face, of the matched DPS - NIM slabs, is zero. This demonstrates how the NIM slab at chosen frequencies acts as a phase compensator. It is important to note that this phase compensation process is not dependent on the thickness of d1 + d1 but only on the ratio of d1 / d 2. Therefore, d1 + d1 can be any value, as long as this ratio satisfies the above condition. Finally, even though this two-layer structure is present, the wave traversing this structure would not experience the phase difference.
Following this, the next step is the subwavelength cavity resonator.
Compact subwavelength 1-D cavity resonators using metamaterials:
The phase compensator described above can be used to conceptualize the possibility of designing a compact 1-D cavity resonator. The above two-layer structure is applied as two perfect
reflectors, or in other words, two perfect conducting plates.
Conceptually, what is constrained in the resonator is d1 / d2, not d1 + d2. Therefore, in principle, one can have a thin subwavelength cavity resonator for a given frequency, if at this frequency the second layer acts a metamaterial with negative permittivity and permeability and the ratio correlates to the correct values.
The cavity can conceptually be thin and can still be resonant, as long as the ratio of thicknesses is satisfied in the special dispersion relation. This can, in principle, provide possibility for having subwavelength thin compact cavity resonators.
Miniature cavity resonator utilizing FSS
Frequency selective surface (FSS) based metamaterials utilize equivalent LC circuitry configurations. Using FSS in a cavity allows for miniaturization, decrease of theresonant frequency, and also lowers the cut-off frequency along with other benefits, and smooth transition from a fast-wave to a slow-wave in a waveguide configuration.
Composite metamaterial based cavities
As an application for left-handed materials (LHM), four different cavities, operating in the microwave regime were fabricated and experimentally observed and described.Leaky mode propagation with metamaterial ground plane
A magnetic dipole was placed on metamaterial (slab) ground plane. The metamaterials have either constituent parameters that are both negative, or negative permittivity, or negative permeability. The dispersion and radiation properties of leaky waves supported by these metamaterial slabs, respectively, were investigated.Patented metamaterial antenna systems
There are a number of metamaterial antenna systems that have patentPatent
A patent is a form of intellectual property. It consists of a set of exclusive rights granted by a sovereign state to an inventor or their assignee for a limited period of time in exchange for the public disclosure of an invention....
s. On some of these patents the researcher
Researcher
A researcher is somebody who performs research, the search for knowledge or in general any systematic investigation to establish facts. Researchers can work in academic, industrial, government, or private institutions.-Examples of research institutions:...
s of metamaterials and metamaterial antenna system components in the lab now have patents.
Phased array systems and antennas for use in such systems are well known in areas such as telecommunications and other radar applications. In general phased array systems work by coherently reassembling signals over the entire array by using circuit elements to compensate for relative phase differences and time delays.
Phased array metamaterial antenna system
Patented in 2004, this particular phased array antenna system is useful in automotive radar applications. By using negative index metamaterialsNegative 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) as a biconcave lens to focus the microwaves transmitted by the antenna the sidelobes of the antenna are reduced. This equates to a reduction in radiated energy loss, and a relatively wider, useful bandwidth. Overall, because of the strategies implemented, this is an efficient (low-loss, reduced sidelobes), dynamically ranged phased array radar antenna system.
In addition, the signal amplitude is increased across the microstrip
Microstrip
Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components...
transmission lines (TL) by suspending the microstrip TLs above the ground plane at a predetermined distance. In other words, they are not in contact with a solid substrate. By suspending the microstrip transmission lines in this manner, dielectric signal loss is reduced significantly, thus resulting in a less-attenuated signal at its destination.
In addition, this phased array
Phased array
In wave theory, a phased array is an array of antennas in which the relative phases of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern of the array is reinforced in a desired direction and suppressed in undesired directions.An antenna array...
antenna system was designed to boost the performance of the Monolithic microwave integrated circuit
Monolithic Microwave Integrated Circuit
A Monolithic Microwave Integrated Circuit, or MMIC , is a type of integrated circuit device that operates at microwave frequencies . These devices typically perform functions such as microwave mixing, power amplification, low noise amplification, and high frequency switching...
(MMIC), among other benefits. A transmission line (microstrip) is created with photolithography. A metamaterial lens, consisting of a thin wire array (see section above), focuses the transmitted or received signals between the microstrip TL and the emitter / receiver elements.
The metamaterial lens also functions as an input device and consists of a number of periodic unit-cells disposed along the microstrip line. Furthermore, the metamaterial lens consists of multiple microstrip lines of the same make up; a plurality of periodic unit-cells. The periodic unit-cells are constructed of a plurality of electrical components; capacitors and inductors as components of multiple distributed circuits
Distributed element model
In electrical engineering, the distributed element model or transmission line model of electrical circuits assumes that the attributes of the circuit are distributed continuously throughout the material of the circuit...
.
The metamaterial of the phased array antenna system incorporates a conducting transmission element, a substrate comprising at least a first ground plane for grounding the transmission element, a plurality of unit-cell circuits composed periodically along the transmission element, at least one via
Via (electronics)
A via is a vertical electrical connection between different layers of conductors in a physical electronic circuit.- In IC :In integrated circuit design, a via is a small opening in an insulating oxide layer that allows a conductive connection between different layers. A via on an integrated circuit...
for electrically connecting the transmission element
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
to at least the first ground plane. It also includes a means for suspending this conducting transmission element predetermined distance away from the substrate in a way such that the transmission element is located at a second predetermined distance away from the ground plane.
ENG and MNG waveguides and scattering devices
US Patent issued on May 15, 2007. A structure for use in waveguiding or scattering of waves, the structure comprising first and second adjacent layers, the first layer comprising an epsilon-negative (ENG) material or a mu-negative (MNG) material, and the second layer comprising either a double-positive (DPS) material, a double-negative (DNG) material, an ENG material when the first layer is an MNG material, or a MNG material when the first layer is an ENG material.In the news
Pertaining to wireless infrastructure
December 2010 - Currently the variety of wireless devices is significantly expanding. For example, radio frequency identificationRadio Frequency Identification
Radio-frequency identification is a technology that uses radio waves to transfer data from an electronic tag, called RFID tag or label, attached to an object, through a reader for the purpose of identifying and tracking the object. Some RFID tags can be read from several meters away and beyond the...
(RFID) tags have broad applications. The possible uses now range from electronic key fobs that remotely turn over engines, work-related swipe cards, and are placed inside shoes so manufactureres may match separate components. Other wireless technologies are light switches, printers and microwave ovens. Such broad expansion leads to interference from competing signals. Metamaterials, fucnctional at miniature sizes can allow signals in, but keep them from getting out. Rather than the conventional absorbers at three inches thick, metamterials can be the size of thin films, two millimetres thick (78/1000 or .078 inches).
See also
- Acoustic metamaterialsAcoustic metamaterialsAcoustic metamaterials are artificially fabricated materials designed to control, direct, and manipulate sound in the form of sonic, infrasonic, or ultrasonic waves, as these might occur in gases, liquids, and solids. The hereditary line into acoustic metamaterials follows from theory and research...
- Chirality (electromagnetism)Chirality (electromagnetism)The term chiral describes an object, especially a molecule, which has or produces a non-superimposeable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism...
- MetamaterialMetamaterialMetamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
- Metamaterial cloakingMetamaterial cloakingMetamaterial cloaking is the scientific application of metamaterials in order to achieve invisibility-cloaking. This is accomplished by manipulating the paths traversed by light through a novel optical material....
- Negative index metamaterialsNegative index metamaterialsNegative index metamaterials or negative index materials are artificial structures where the refractive index has a negative value over some frequency range. This does not occur in any known natural materials, and thus is only achievable with engineered structures known as metamaterials...
- Nonlinear metamaterialsNonlinear metamaterialsA nonlinear metamaterial is an artificially constructed material that can exhibit properties not found in nature. Its response to electromagnetic radiation can be characterized by its permittivity and material permeability. The product of the permittivity and permeability results in the refractive...
- Photonic metamaterialsPhotonic metamaterialsPhotonic metamaterials, also known as Optical metamaterials, are a type of electromagnetic metamaterial, which are designed to interact with optical frequencies which are terahertz , infrared , and eventually, visible wavelengths. As a type of metamaterial, the periodic structures are made up of...
- Photonic crystalPhotonic crystalPhotonic crystals are periodic optical nanostructures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons...
- Seismic metamaterialsSeismic metamaterialsSeismic metamaterials, are metamaterials which are designed to counteract the adverse effects of seismic waves on artificial structures, which exist on or near the surface of the earth...
- Split-ring resonator
- SuperlensSuperlensA superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
- Tunable metamaterialsTunable metamaterialsA tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave interacts with a metamaterial. This means the capablitity to determine whether the EM wave is transmitted, reflected, or...
- 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...
- Acoustic dispersionAcoustic dispersionAcoustic dispersion is the phenomenon of a sound wave separating into its component frequencies as it passes through a material. The phase velocity of the sound wave is viewed as a function of frequency...
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- Books
- Metamaterials HandbookMetamaterials HandbookMetamaterials Handbook is a two-volume handbook on metamaterials edited by Filippo Capolino .The series is designed to cover all theory and application topics related to electromagnetic metamaterials. Disciplines have combined to study, and develop electromagnetic metamaterials...
- Metamaterials: Physics and Engineering ExplorationsMetamaterials: Physics and Engineering ExplorationsMetamaterials: Physics and Engineering Explorations is a book length introduction to the fundamental research and advancements in electromagnetic composite substances known as electromagnetic metamaterials. The discussion encompasses examination of the physics of metamaterial interactions, the...
- Metamaterials Handbook
- Books
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General references
External links
- U.S. Air Force Research Lab Demonstrated metamaterials technology transforms antenna radiation pattern
- The electrodynamics of substances with simultaneously negative values of ε and μ Victor G. Veselago.
- Microwave transmission-line networks for backward-wave media and reduction of scattering
- Radiating power through air
- NTIA Manual of Regulations and Procedures for Federal Radio Frequency Management. 2011.