What is negative permittivity

A Metamaterial is an artificially produced structure, the electromagnetic properties of which are similar to that of a conventional material due to permittivityr and permeability μr can be described, but these two parameters have values ​​that do not occur in nature.

Real, negative refractive indices

are of particular interest, but increasingly also positive real values ​​less than 1. Negative refractive indices cause antiparallel phase and group velocities. Waves with this property have been known as backward waves since 1905 (Pocklington) and have long been used in oscillators and amplifiers. In 1960 Veselago theoretically predicted that a hypothetical material with a negative refractive index would cause backward waves and what effects this would have [1].

Since no natural materials with these properties exist or have been found so far, they are synthesized, mostly through a periodic arrangement of cells.

The definition of metamaterials is still in flux; the more common one restricts the cell size to (significantly) smaller than a quarter of the free space wavelength. Some authors include photonic crystals, where the cell size is on the order of half a wavelength. The former, more common definition means that the arrangement behaves like an effective medium, i.e. H. not primarily the cell size (as with photonic crystals and frequency selective surfaces), but the cell content determines the function.

Electromagnetic properties of materials with a negative refractive index

In 1968, the Soviet physicist Victor Veselago theoretically investigated the propagation of electromagnetic waves in materials with a negative refractive index and their edges. The phase velocity and the direction of energy flow (pointing vector) in the material with a negative refractive index are antiparallel, as is the case with the backward waves that have been known for some time. In this case, the wave vector, the electric field strength and the magnetic field strength form a left-handed tripod - hence the name "left-handed material".

He showed that this leads to inverse Cherenkov radiation, inverse Doppler effect and inverse Snell's law of refraction. The latter describes that in the transition from the optically thinner to the optically denser medium, the wave is broken to the perpendicular. The refractive index, a normally positive number, describes how light or other electromagnetic radiation is deflected when it passes through the material. In the case of substances with a negative refractive index, an incident light beam is not refracted towards the perpendicular as is the case with conventional substances, but rather beyond the perpendicular in the negative direction. The light beam is therefore both inside and outside the material on the same side of the incidence perpendicular. In the case of curved surfaces, the inverse Snell's law leads to an interchange of convergent and divergent beam guidance, i.e. i.e., bundle concave lenses, scatter convex lenses.

In addition, Scharidow showed that the beam shift in the Goos-Hänchen effect also changes sign.


In nature, materials with negative permittivity and at the same time negative permeability do not occur, i. H. such materials must be synthesized. The synthesis does not necessarily have to take place periodically, but it makes the calculation easier and is therefore used by all groups. There are resonant and non-resonant approaches:

The first group includes the split-ring / wire-grid approach and the approach using dielectric spheres of different diameters in an NaCl grid.

With the split-ring / wire-grid approach, the wire grid leads to negative permittivity, since in metals below the plasmon resonance, electrons behave like a plasma (Drude model). A resonator, which is usually designed as a (double) ring with a gap, leads to a magnetic dipole moment and in a narrow frequency range to a negative effective permeability. The resonator design should be selected so that a negative refractive index results in the desired frequency range.

This arrangement shows the problem that low losses go hand in hand with (very) low bandwidth, on the other hand, structures designed for high losses allow tolerable bandwidths, but then the transmission coefficient drops. Since metallic losses increase with frequency, it is difficult to distinguish such metamaterial structures from absorbers in the optical frequency range.

The approach using dielectric spheres 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.

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. Based on the derivation from the line theory, the first such metamaterials 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, and some have also been proven experimentally.

In 2007, the split-ring approach is predominantly found among members of the physics community. The non-resonant, line-based approach is more likely to be found in electrical engineering, but is also beginning to gain a foothold in physics.

Possible applications

The planar lenses analyzed by Veselago are potentially advantageous due to the lack of an optical axis; the resolution improvement demonstrated by Pendry has attracted particular attention in physics and electrical engineering [2]. It is characterized in that a point light source has a point image, i. H. In contrast to the usual lens, the evanescent wave vector spectrum of the source is resonantly amplified by the planar 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.

In 2006, in [3][4] theoretically and experimentally presented a concept of how a stealth effect can be achieved with the help of a metamaterial envelope. This concept is not based on negative refractive indices, but on a continuous, anisotropic variation of the refractive index between 0 and 1. This concept is not entirely dissimilar to Luneberg lenses.

Any previously existing imaging system could be named as a potential application, and Pendry's cloak of invisibility could also be classified as a special metamaterial-based imaging system. In all scenarios, however, it should be noted that finite cell size, losses, finite dimensions of the lens and dispersion limit the resolution and lead to aberrations.

Systems working in the optical are a long way off, 3D metamaterials are necessary for this, and not even one-dimensional, not excessively attenuating metamaterials have been published in the optical. Therefore, the microwave range is still of particular interest; the focus may later shift to higher frequencies, similar to the development from MASER to LASER.

Published microwave applications are e.g. B. (controllable) directional antennas, couplers, radomes, reflectors, phase shifters / compensators, imaging systems and (when using active components) also soliton concepts.

Some metamaterial-based application concepts should be treated with caution: It is simply not possible to assume a hypothetical material with a negative refractive index and then wildly speculate what would be possible with it. The above-mentioned parameters such as the finite size of a metamaterial cell, losses, dispersion etc. are not negligible secondary effects, but crucial. One example is a proposal to increase the radiation resistance of Hertzian dipoles by using metamaterial sheathing and thereby making small antennas possible. The amusing slice of this concept is in [5] to find.


  1. V.G. Veselago, The electrodynamics of substances with simultaneously negative values ​​of ε and µ, So V. Phys. Usp. 10, 509 (1968)
  2. JB Pendry, Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett. 85, 3966 (2000)
  3. J.B. Pendry and D. Schurig and D.R. Smith, 'Controlling Electromagnetic Fields, Science 312, 1780 (2006)
  4. D. Schurig and J.J. Mock and B.J. Justice and S.A. Cummer and J.B. Pendry and A.F. Starr and D.R. Smith, 'Metamaterial Electromagnetic Cloak at Microwave Frequencies, Science 314, 977 (2006)
  5. R.C. Hansen, Electrically Small, Superdirective and Superconducting Antennas, Wiley, 2006


  • V.G. Veselago, Sov. Phys. Usp. 10, 509 (1968)
  • J. B. Pendry, Nature 423, 22 (2003)
  • Sergei Tretyakov, "Analytical Modeling in Applied Electrodynamics", Artech House, 2003
  • C. Caloz and T. Itoh, "Electromagnetic Metamaterials", Wiley, 2005
  • G.V. Eleftheriades and K.G. Balmain, "Negative-Refraction Metamaterials," Wiley, 2005
  • N. Engheta and R.W. Ziolkowski, "Electromagnetic Metamaterials", Wiley, 2006

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