Metamaterial

Building a metamaterial for microwave applications
The scale is inches; the smallest subdivision is 1.5875 mm.

A metamaterial is an artificially produced structure, the permeability of which for electric and magnetic fields ( permittivity  and permeability ) differs from that which is usual in nature. This is achieved through specially made, mostly periodic, microscopically fine structures ( cells, individual elements ) made of electrically or magnetically effective materials inside. ${\displaystyle \varepsilon _{\mathrm {r} }}$  ${\displaystyle \mu _{\mathrm {r} }}$

Metamaterials can have a negative real part of the complex index of refraction . When moving from the vacuum into such a material, waves are broken beyond the perpendicular in the negative direction. The waves propagate inside and outside the material on the same side of the solder. Common materials have a positive index of refraction. With them, waves are deflected towards the perpendicular when they transition into the respective material, but not beyond.

With metamaterials whose real part of the refractive index is <0, applications are conceivable that are in principle not possible with ordinary materials. They can make objects invisible by directing incoming waves around the objects.

The structure of metamaterials, with the help of which the refractive index is designed, must be significantly smaller than the wavelength of the radiation. This makes the construction for visible light considerably more difficult. Most of the metamaterials implemented so far are therefore designed for microwave radiation .

definition

The definition of metamaterials is still in flux:

• The more common definition limits the cell size to (significantly) smaller than a quarter of the wavelength in a vacuum. The arrangement behaves like a homogeneous medium. This means that the cell content primarily determines the function.
• Some authors also include photonic crystals , where the cell size is in the order of half a wavelength . Here, the cell size primarily determines the function.

The term metamaterial was coined by John Pendry in the late 1990s .

Physical basics

The specialty of metamaterials is that their material constants and negative values ​​can take on. From the point of view of field theory , this means that ${\displaystyle \varepsilon _{\mathrm {r} }}$ ${\displaystyle \mu _{\mathrm {r} }}$

• the field of the electric flux density (D-field) and that of the electric field strength (E-field) as well
• the field of the magnetic flux density (B field) and that of the magnetic field strength (H field)

are each directed opposite to each other.

There are no fundamental physical reasons opposing the different signs , since the D and E as well as the B and H fields are based on independent "mechanisms of formation" according to Maxwell's equations in their material-independent form:

Coulomb's law	${\displaystyle \operatorname {div} {\boldsymbol {D}}=\rho }$	D-fields are created by charges
Faraday's law	${\displaystyle \operatorname {rot} {\boldsymbol {E}}+{\frac {\partial {\boldsymbol {B}}}{\partial t}}=0}$	E-fields arise from changes in the magnetic flux, i.e. H. by changing the B-field or the geometry
Gaussian law for magnetic fields	${\displaystyle \operatorname {div} {\boldsymbol {B}}=0}$	B-fields are source-free; there are no magnetic monopoles .
Ampère's law	${\displaystyle \operatorname {rot} {\boldsymbol {H}}={\boldsymbol {j}}_{l}+{\frac {\partial {\boldsymbol {D}}}{\partial t}}}$	H-fields arise from changes in the D-field (conductor and displacement currents)

The different signs of D- and E-fields in metamaterials come about through clever arrangements and processes, which are characterized by the fact that the changes in the magnetic flux generate an E-field that points in the opposite direction to the D-field.

Similarly, the different signs of B and H fields come about because the changes in the electric field in metamaterials generate a magnetic flux (and thus a B field) that points in the opposite direction to the H field.

The wave vector , the electric and the magnetic field strength form a left - handed tripod in metamaterials - hence the name left-handed material .

properties

In 1968, the Soviet physicist Wiktor Wesselago theoretically investigated the propagation of waves in a medium with a negative refractive index. Henry Cabourn Pocklington had known since 1905 that the phase velocity and group velocity in such a material run counter to the flow of energy given by the Poynting vector . Wesselago now showed that the left-handedness of metamaterials leads to inverse Cherenkov radiation , inverse Doppler effect and inverse law of refraction . The inverse law of refraction leads to an exchange of convergence and divergence in the case of curved surfaces . In contrast to normal media, a concave lens made of metamaterial focuses incident radiation.

In addition, Ilya V. Shadrivov showed that the beam shift in the Goos-Hänchen effect with metamaterials also changes its sign.

Metamaterials can cause a repulsive (repulsive) Casimir effect .

Manufacturing

There are approaches to manufacturing that use resonance ( resonant approaches ) and those that do not ( non- resonant approaches ).

Resonant approaches

Split-Ring / Wire-Grid

With the split-ring / wire-grid approach (see figure above), the wire grid leads to negative permittivity, since in metals below the plasmon resonance, electrons behave like a plasma ( Drude model ). A resonator , usually designed as a (double) ring with a gap ( split ring ), leads to a magnetic dipole moment and a negative effective permeability, but only in a very narrow frequency range . The properties of the resonator can be selected in such a way that a negative refractive index results in the desired frequency range.

This arrangement has the property that low losses can only be achieved with a low bandwidth of the resonance. In addition, the losses due to the ohmic resistance of the metal increase with frequency. For visible light the absorption would be so dominant that it masks the effects of an unusual real part of the refractive index.

Dielectric spheres

The approach using dielectric spheres of different diameters in an NaCl grid has the advantage that the optical frequency range could also be opened up as a non-metallic structure. The theoretical work on this approach shows, however, that only very small bandwidths are to be expected and correspondingly extreme requirements would be placed on the tolerances of the manufacturing technology .

Non-resonant approaches

A possible way out of the bandwidth / attenuation problem, at least in the microwave range, are non-resonant concepts based on inverse line structures. These bandpass- like structures offer high bandwidth and low losses at the same time - as long as structures can be designed that behave like discrete series and parallel resonators. Due to the derivation from the line theory , the first metamaterials of this kind were one-dimensional and aroused the controversy as to whether it makes sense to speak of metamaterials or of applied filter theory . Generalizations on ( isotropic ) 2D / 3D arrangements have been presented theoretically, some have also been proven experimentally.

Possible applications

The planar lenses analyzed by Wesselago are potentially advantageous due to the lack of an optical axis ; the improvement in resolution demonstrated by John Pendry led to particularly great attention in physics and electrical engineering. It is characterized in that a point light source has a point image, i. In other words , in contrast to the usual lens, the evanescent wave vector spectrum of the source is resonantly amplified by the plane metamaterial lens and then 'reconstructed' in the image. This is not to be confused with finite resolution in conventional lenses due to the finite entrance pupil, diffraction limitation cannot be used as a comparison criterion, because Pendry's lens is infinitely large.

Another possible application of metamaterial is seen in the field of stealth technology or stealth technology. The underlying metamaterial is currently being researched at the University of Pennsylvania. The idea behind stealth technology is to make the material interact with light, much like atoms do. This happens on such a small level that the artificial structures are smaller than the light waves themselves. As a result, the optical properties should no longer be as limited as is the case with constitutive materials. Digitizing these meta-materials could be used to reproduce the light exactly on the other side. One advantage of such a meta-material is that light can not only be directed and reflected by magnifying glasses and mirrors, but can also be stretched, stretched, distorted and manipulated in other ways. This effect has been used for several years by the US company HyperStealth Biotechnology Corp. researched and tested as part of their Quantum Stealth Technology.

literature

Review article:

• S. Anantha Ramakrishna: Physics of negative refractive index materials . In: Reports on Progress in Physics . tape 68 , no. 2 , 2005, p. 449-521 , doi : 10.1088 / 0034-4885 / 68/2 / R06 .
• Vladimir M. Shalaev : Optical negative-index metamaterials . In: Nat Photon . tape 1 , no. 1 , 2007, p. 41-48 , doi : 10.1038 / nphoton.2006.49 .
• Victor Veselago, Leonid Braginsky, Valery Shklover, Christian Hafner: Negative Refractive Index Materials . In: Journal of Computational and Theoretical Nanoscience . tape 3 , no. 2 , 2006, p. 1–30 , doi : 10.1166 / jctn.2006.002 .

Monographs:

• Christophe Caloz, Tatsuo Itoh: Electromagnetic Metamaterials. Transmission Line Theory and Microwave Applications . Wiley & Sons, Hoboken NJ 2005, ISBN 0-471-66985-7 .
• GV Eleftheriades, KG Balmain: Negative Refraction Metamaterials. Fundamental Principles and Applications . Wiley & Sons, Hoboken NJ 2005, ISBN 0-471-60146-2 .
• Nader Engheta, Richard W. Ziolkowski: Electromagnetic Metamaterials. Physics and Engineering Aspects, Physics and Engineering Explorations . Wiley & Sons, Hoboken, NJ 2006, ISBN 0-471-76102-8 .
• Stefan A. Maier: Plasmonics - fundamentals and applications . Springer, New York 2007, ISBN 0-387-33150-6 .
• Andrey K. Sarychev, Vladimir M. Shalaev: Electrodynamics of metamaterials . World Scientific, Singapore 2007, ISBN 978-981-02-4245-9 .
• Sergei Tretyakov: Analytical Modeling in Applied Electromagnetics . Artech House, Boston 2003, ISBN 1-58053-367-1 .
• Ralf B. Wehrspohn : Nanophotonic materials - photonic crystals, plasmonics and metamaterials . Wiley-VCH, Weinheim 2008, ISBN 978-3-527-40858-0 .

Web links

Commons : Metamaterial  - collection of images, videos and audio files

• Collection of articles on the topic of "metamaterials". Spektrum.de 
• Niels Boeing: Magic in the material. In: technology Review 10/2009. Heise Verlag, December 28, 2009 . 
• Matthias Gräbner: Mutual fertilization. Metamaterials as a lens and aperture. In: Telepolis . December 1, 2006, accessed February 9, 2008 . 

Individual evidence

1. ^ Richard V. Craster, et al .: Acoustic metamaterials - negative refraction, imaging, lensing and cloaking. Springer Dordrecht 2013, ISBN 978-94-007-4812-5 , p. 3 ( limited preview in the Google book search).
2. ^ Victor G. Veselago : The electrodynamics of substances with simultaneously negative values ​​of e and µ . In: Soviet physics. Uspekhi (Sov. Phys. Usp) . tape  10 , no. 4 , 1968, p. 509-514 , doi : 10.1070 / PU1968v010n04ABEH003699 .
3. ^ Metamaterials could reduce friction in nanomachines . physorg.com, December 7, 2009, accessed October 5, 2010.
4. ^ R. Zhao, J. Zhou, Th. Koschny, EN Economou, CM Soukoulis: Repulsive Casimir Force in Chiral Metamaterials . In: Physical Review Letters . tape 103 , no. 10 , 2009, p. 103602 , doi : 10.1103 / PhysRevLett.103.103602 .
5. ↑ JB Pendry : Negative Refraction Makes a Perfect Lens . In: Physical Review Letters . tape  85 , no. 18 , September 30, 2000, pp. 3966 , doi : 10.1103 / PhysRevLett.85.3966 .
6. ↑ JB Pendry, D. Schurig, DR Smith : Controlling Electromagnetic Fields . In: Science . tape 312 , no. 5781 , May 23, 2006, p. 1780–1782 , doi : 10.1126 / science.1125907 .
7. ↑ Cristian Della Giovampaola, Nader Engheta: Digital metamaterials. In: Nature Materials. advance online publication, 2014, doi: 10.1038 / nmat4082 .
8. ↑ Development of a stealth camouflage suit