Refraction |

**In General** > s.a. dispersion; electricity; light.

* __Idea__: The bending of light
when propagating in a medium in which the speed of light*v*_{p}
varies with position; When it occurs at the boundary between two homogeneous
media with different values of *n*, it is described by Snell's Law.

* __Index of refraction__:
Defined by *n*(*ω*):= *c*/*v*_{p}
= *k*/*k*_{vacuum};
For light, *k* = *ω*/*c* and *n* = *c*/*v*.

* __Complex index of refraction__: The imaginary part
of the index of refraction gives the absorption length in a material.

@ __References__: Champenois et al PRA(08)-a0711 [matter
waves in gases].

> __Related topics__: see Fermat's Principle;
Snell's Law.

> __Online resources__: see Wikipedia page.

**Negative Index of Refraction** > s.a.
[meta-materials]; electromagnetism
in curved spacetime; Kramers-Kronig Relations.

* __History__:
1968, Existence of materials which bend
light in the opposite direction to conventional materials (also known as left-handed
materials) first proposed; 2000, Demonstrated for the first time in experiments;
2003, Several experiments and simulations demonstrated that negative refraction
is real and that causality is not violated; 2005, New material discovered made
from layers of superconducting and ferromagnetic thin films (until now, negative refraction
had only been achieved in metamaterials and photonic crystals); Associated phenomena
are a reverse Doppler shift and backward Cerenkov radiation and pressure.

@ __General references__:
Veselago SPU(68); Smith et al PRL(00);
Smith
&
Kroll PRL(00);
Smith pw(03)may;
Zhang et al PRL(03)
+ pw(03)oct;
Pendry CP(04)
[rev]; Pendry & Smith PT(04)jun;
Lakhtakia & Mackay JPA(04)
[vacuum, gravitationally assisted]; Lakhtakia & McCall NJP(05)
[focus issue];
Ward et al NJP(05)
[physical origin]; news pw(05)dec, SFN(06)may;
McCall PRL(07)
[not with gravity]; Ramm PLA(08)-a0710 [in
acoustics], PLA(08)
[no perfect lenses]; Plum et al PRB(09),
Zhang et al PRL(09)
+ Wegener & Linden Phy(09);
Guney & Meyer PRA(09)-a0907 [and Klein paradox];
Mackay & Lakhtakia PLA(09) [not a covariant notion];
Forcella et al a1611 [and spatial non-locality];
Nguyen a1803 [mathematical results and applications].

@ __Experiments, realizations__:
Shelby et al Sci(01)apr
[experiment]; news pw(07)may
[natural material]; Velázquez-Ahumada et al AJP(11)apr [for microwaves]; Amariti et al JHEP(13)-a1107 [in hydrodynamics, and applications to quark-gluon plasma], JHEP(11)-a1107 [and superconductivity].

**Other Special Situations** > s.a. Rainbow.

@ __General references__: Kovadlo & Kochetkova a1101-conf [in Earth's atmosphere, fluctuations]; Gekelman et al AJP(11)sep [complex index of refraction, and plasma experiments]; Nazari & Nouri-Zonoz PRD(12)-a1110 [spacetime index of refraction].

@ __Other variations__: Jääskeläinen et al AJP(11)jun-a1012 [refraction in spacetime].

> __Gravity and curved-spacetime-related topics__: see modified versions of QED [spacetime index of refraction]; photon phenomenology [curved spacetime].

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send feedback and suggestions to bombelli at olemiss.edu – modified 14 mar 2018