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 PRL(17)-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 7 jan 2019