Editing Birefringence (section)

{{short description|Refractive property of materials}}
[[File:Crystal on graph paper.jpg|right|thumb|A [[calcite]] crystal laid upon a graph paper with blue lines showing the double refraction]]
[[File:Positively birefringent material.svg|right|thumb|In this example, optic axis along the surface is shown perpendicular to plane of incidence. Incoming light in the {{mvar|s}} polarization (which means perpendicular to plane of incidence – and so in this example becomes "parallel polarisation" to optic axis, thus is called extraordinary ray) sees a greater [[refractive index]] than light in the {{mvar|p}} polarization (which becomes ordinary ray because "perpendicular polarisation" to optic axis) and so {{mvar|s}} polarization ray is undergoing greater [[Snell's law|refraction]] on entering and exiting the crystal.]]

'''Birefringence''', also called '''double refraction''', is the [[optical properties|optical property]] of a material having a [[refractive index]] that depends on the [[polarization (waves)|polarization]] and propagation direction of [[light]].<ref>{{cite web |url=https://olympus-lifescience.com/en/microscope-resource/primer/lightandcolor/birefringence |title=Olympus Microscopy Resource Center |publisher=Olympus Life Science Inc. |last1=Abramowitz |first1=Mortimer |last2=Davidson |first2=Michael W. |access-date=2021-07-21 }}</ref> These optically [[anisotropic]] materials are described as '''birefringent''' or '''birefractive'''. The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. [[Crystal]]s with non-cubic [[crystal structure]]s are often birefringent, as are [[plastic]]s under [[mechanical stress]].  

Birefringence is responsible for the [[optical phenomenon|phenomenon]] of '''double refraction''' whereby a [[ray (optics)|ray]] of light, when incident upon a birefringent material, is split by polarization into two rays taking slightly different paths. This effect was first described by Danish scientist [[Rasmus Bartholin]] in 1669, who observed it<ref>See:
* Erasmus Bartholin, [https://books.google.com/books?id=F7RAAAAAcAAJ&pg=PP11 ''Experimenta crystalli islandici disdiaclastici quibus mira & infolita refractio detegitur''] [Experiments on birefringent Icelandic crystal through which is detected a remarkable and unique refraction] (Copenhagen, Denmark: Daniel Paulli, 1669). 
* Erasmus Bartholin (January 16, 1671) [https://books.google.com/books?id=Zl5FAAAAcAAJ&pg=PA2141 "An account of sundry experiments made and communicated by that learn'd mathematician, Dr. Erasmus Bartholin, upon a chrystal-like body, sent to him out of Island,"] ''Philosophical Transactions of the Royal Society of London'', '''5''' : 2041–2048 (pdf pp 282–289).</ref> in [[Iceland spar]] ([[calcite]]) crystals which have one of the strongest birefringences. In the 19th century [[Augustin-Jean Fresnel]] described the phenomenon in terms of polarization, understanding light as a wave with field components in transverse polarization (perpendicular to the direction of the wave vector).<ref name=fresnel-1821a>A. Fresnel, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et&nbsp;seq., ''Annales de Chimie et de Physique'', Ser.&nbsp;2, vol.&nbsp;17, pp.&nbsp;102–111 (May&nbsp;1821), 167–96 (June&nbsp;1821), 312–15 ("Postscript", July&nbsp;1821); reprinted (with added section nos.) in Fresnel, 1866–70, vol.&nbsp;1, pp.&nbsp;609–648; translated as "On the calculation of the tints that polarization develops in crystalline plates, &amp;&nbsp;postscript", {{Zenodo|4058004}} (Creative Commons), 2021; §14.</ref><ref name=fresnel-1822-25>A. Fresnel, "Extrait d'un Mémoire sur la double réfraction", ''Annales de Chimie et de Physique'', Ser.&nbsp;2, vol.&nbsp;28, pp.&nbsp;263–279 (March&nbsp;1825); reprinted as "Extrait du second Mémoire sur la double réfraction" in Fresnel, 1866–70, vol.&nbsp;2, pp.&nbsp;465–478; translated as "Extract of a [second] memoir on double refraction", {{Zenodo|5442206}}, 2021 (open&nbsp;access).</ref>