page_title: Refractive index
section_title: Negative refractive index
hierarchical_section_title: Refractive index / Typical values / Negative refractive index
caption_attribution_description: English: Figure 2 Part of the left-handed metamaterial array configuration, which was constructed of copper split-ring resonators and wires mounted on interlocking sheets of fiberglass circuit board. The total array consists of 3 by 20 by 20 unit cells with overall dimensions of 10 by 100 by 100 mm. Split-ring resonator consisting of an inner square with a split on one side embedded in an outer square with a split on the other side. Split-ring resonators are on the front and right surfaces of the square grid, and single vertical wires are on the back and left surfaces. References: Chevalier, Christine T.; and Wilson, Jeffrey D.: Frequency Bandwidth Optimization of Left-Handed Metamaterial. NASA/TM--2004-213403, 2004. Wilson, Jeffrey D.; and Schwartz, Zachary D.: Multifocal Flat Lens With Left-Handed Metamaterial. Appl. Phys. Lett., vol. 86, no. 2, 2005. Smith, D.R., et al.: Composite Medium With Simultaneously Negative Permeability and Permittivity. Phys. Rev. Lett., vol. 84, no. 18, 2000. Shelby, R.A., et al.: Microwave Transmission Through a Two-Dimensional, Isotropic, Left-Handed Metamaterial. Appl. Phys. Lett., vol. 78, no. 4, 2001.
context_page_description: In optics, the refractive index of a material is a dimensionless number that describes how fast light travels through the material. It is defined as
  where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. Increasing refractive index corresponds to decreasing speed of light in the material.
  The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n₁ sinθ₁ = n₂ sinθ₂,
  where θ₁ and θ₂ are the angles of incidence and refraction, respectively, of a ray crossing the interface between two media with refractive indices n₁ and n₂. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity and Brewster's angle.
context_section_description: Recent research has also demonstrated the existence of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values. This can be achieved with periodically constructed metamaterials. The resulting negative refraction (i.e., a reversal of Snell's law) offers the possibility of the superlens and other new phenomena to be actively developed by means of metamaterials.
  Three conceptions- Veselago's negative-index medium, Pendry's superlense and Efimov's non-reflecting crystal are foundations of the theory of metamaterials with interesting properties of reflection.
caption: A split-ring resonator array arranged to produce a negative index of refraction for microwaves
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