Math 2.0

Optics, electromagnetic theory Definition

Metamaterial

Builds on PermittivityPermeabilityConstitutive relations of electromagnetism

Definition

A metamaterial for waves of wavelength λ\lambda is an artificial medium with these properties.

  1. It is built from a periodic or random arrangement of structured elements, its unit cells, whose size and spacing are much smaller than λ\lambda.
  2. For waves of wavelength λ\lambda it behaves as a homogeneous medium with effective constitutive relations. They have an effective permittivity εeff\varepsilon_{\mathrm{eff}} and an effective permeability μeff\mu_{\mathrm{eff}}.
  3. These effective parameters are determined mainly by the geometry of the unit cells, and they take values not found in the constituent materials.

Remarks

Example: take a lattice of small split metal rings, with spacing much less than the wavelength. Near the resonance of the rings, its effective permeability is negative over a band of frequencies. A lattice of thin metal wires has a negative effective permittivity below an effective plasma frequency. Combining the two gives a medium with εeff<0\varepsilon_{\mathrm{eff}} < 0 and μeff<0\mu_{\mathrm{eff}} < 0, and thus a negative refractive index.

Non-example: a photonic crystal with period comparable to λ\lambda fails clause 1 and clause 2. Waves resolve its structure, and its behaviour comes from Bragg scattering rather than from effective parameters.

The effective parameters are frequency dependent, and passive metamaterials with negative parameters are necessarily dispersive; in practice they are also lossy.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

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Constitutive relations of electromagnetism, concept, no evidence levelConstitutive relation…conceptPermeability, concept, no evidence levelPermeabilityconceptPermittivity, concept, no evidence levelPermittivityconceptMetamaterial, definition, no evidence levelMetamaterialdefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Constitutive relations of electromagnetism concept
  2. Permeability concept
  3. Permittivity concept
  4. Metamaterial definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Metamaterial
About this page
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MSC78A48, 78A10
DefinesMetamaterial
UsesPermittivity, Permeability, Constitutive relations of electromagnetism
Changed3 November 2026

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