Editing Birefringence (section)

== Common birefringent materials ==
[[File:Food Polarization-Dierking.jpg|right|thumb|Sandwiched in between crossed polarizers, clear polystyrene cutlery exhibits wavelength-dependent birefringence]]

The best characterized birefringent materials are [[crystals]]. Due to their specific [[crystal structures]] their refractive indices are well defined. Depending on the symmetry of a crystal structure (as determined by one of the 32 possible [[crystallographic point group]]s), crystals in that group may be forced to be isotropic (not birefringent), to have uniaxial symmetry, or neither in which case it is a biaxial crystal. The crystal structures permitting uniaxial and biaxial birefringence are noted in the two tables, below, listing the two or three principal refractive indices (at wavelength 590&nbsp;nm) of some better-known crystals.<ref name=hypertextbook/>

In addition to induced birefringence while under stress, many [[plastic]]s obtain permanent birefringence during manufacture due to stresses which are "frozen in" due to mechanical forces present when the plastic is molded or extruded.<ref>{{cite journal|doi=10.1002/pen.10347 | volume=38 | issue=10 | title=The use of birefringence for predicting the stiffness of injection molded polycarbonate discs | year=1998 | journal=Polymer Engineering & Science | pages=1770–1777 | last1 = Neves | first1 = N. M.| url=https://ris.utwente.nl/ws/files/6879171/Powell98use.pdf }}</ref> For example, ordinary [[cellophane]] is birefringent. [[Polarizer]]s are routinely used to detect stress,  either applied or frozen-in, in plastics such as [[polystyrene]] and [[polycarbonate]].

[[Cotton]] fiber is birefringent because of high levels of cellulosic material in the fibre's secondary cell wall which is directionally aligned with the cotton fibers.

Polarized light microscopy is commonly used in biological tissue, as many biological materials are linearly or circularly birefringent. Collagen, found in cartilage, tendon, bone, corneas, and several other areas in the body, is birefringent and commonly studied with polarized light microscopy.<ref>{{cite journal | last1 = Wolman | first1 = M. | last2 = Kasten | first2 = F. H. | year = 1986 | title = Polarized light microscopy in the study of the molecular structure of collagen and reticulin | journal = Histochemistry | volume = 85 | issue = 1| pages = 41–49 | doi=10.1007/bf00508652| pmid = 3733471 | s2cid = 25214054 }}</ref> Some proteins are also birefringent, exhibiting form birefringence.<ref>{{cite journal | last1 = Sano | first1 = Y | year = 1988 | title = Optical anistropy of bovine serum albumin | journal = J. Colloid Interface Sci. | volume = 124 | issue = 2| pages = 403–407 | doi=10.1016/0021-9797(88)90178-6|bibcode = 1988JCIS..124..403S }}</ref>

Inevitable manufacturing imperfections in [[optical fiber]] leads to birefringence, which is one cause of [[polarization mode dispersion|pulse broadening]] in [[fiber-optic communication]]s. Such imperfections can be geometrical (lack of circular symmetry), or due to unequal lateral stress applied to the optical fibre. Birefringence is ''intentionally'' introduced (for instance, by making the cross-section elliptical) in order to produce [[polarization-maintaining optical fiber]]s. Birefringence can be induced (or corrected) in optical fibers through bending them which causes anisotropy in form and stress given the axis around which it is bent and radius of curvature.

In addition to anisotropy in the electric polarizability that we have been discussing, anisotropy in the [[Permeability (electromagnetism)|magnetic permeability]] could be a source of birefringence. At optical frequencies, there is no measurable magnetic polarizability ({{nowrap|''μ'' {{=}} [[vacuum permeability|''μ''<sub>0</sub>]]}}) of natural materials, so this is not an actual source of birefringence.{{cn|date=September 2024}}
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{| class="wikitable sortable" style="margin: 0em 0em 1em 1em;"
|+ Uniaxial crystals, at 590&nbsp;nm<ref name=hypertextbook>{{cite journal|last=Elert|first=Glenn|title=Refraction|journal=The Physics Hypertextbook|year=2021|url=http://physics.info/refraction/}}</ref>
|-
! Material
! [[Crystal system]]
! {{math|''n''<sub>o</sub>}}
! {{math|''n''<sub>e</sub>}}
! {{math|Δ''n''}}
|-
| [[barium borate]] BaB<sub>2</sub>O<sub>4</sub> || [[Trigonal]] ||1.6776 ||1.5534 || −0.1242
|-
| [[beryl]] Be<sub>3</sub>Al<sub>2</sub>(SiO<sub>3</sub>)<sub>6</sub> || [[Hexagonal lattice system|Hexagonal]] || 1.602 || 1.557 || −0.045
|-
| [[calcite]] CaCO<sub>3</sub> || [[Trigonal]] || 1.658 || 1.486 || −0.172
|-
| [[ice]] H<sub>2</sub>O || [[Hexagonal lattice system|Hexagonal]] || 1.3090 || 1.3104 || +0.0014<ref name="HobbsIcePhysics">{{cite book |last1=Hobbs |first1=Peter Victor |title=Ice physics |date=2010 |publisher=Oxford University Press |location=New York |isbn=978-0-19-958771-1 |page=202}}</ref>
|-
| [[lithium niobate]] LiNbO<sub>3</sub> || [[Trigonal]] || 2.272 || 2.187 || −0.085
|-
| [[magnesium fluoride]] MgF<sub>2</sub> || [[Tetragonal]] || 1.380 || 1.385 || +0.006
|-
| [[quartz]] SiO<sub>2</sub> || [[Trigonal]] || 1.544 || 1.553 || +0.009
|-
| [[ruby]] Al<sub>2</sub>O<sub>3</sub> || [[Trigonal]] || 1.770 || 1.762|| −0.008
|-
| [[rutile]] TiO<sub>2</sub> || [[Tetragonal]] || 2.616 || 2.903 || +0.287
|-
| [[sapphire]] Al<sub>2</sub>O<sub>3</sub> || [[Trigonal]] || 1.768 || 1.760|| −0.008
|-
| [[silicon carbide]] SiC|| [[Hexagonal lattice system|Hexagonal]] || 2.647|| 2.693 || +0.046
|-
| [[tourmaline]] (complex silicate)|| [[Trigonal]] || 1.669 || 1.638 || −0.031
|-
| [[zircon]], high ZrSiO<sub>4</sub>|| [[Tetragonal]] || 1.960 || 2.015 || +0.055
|-
| zircon, low ZrSiO<sub>4</sub>|| [[Tetragonal]] || 1.920 || 1.967 || +0.047
|}
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{| class="wikitable sortable" style="margin: 0em 0em 1em 1em;"
|+ Biaxial crystals, at 590&nbsp;nm<ref name=hypertextbook/>
|-
! Material
! Crystal system
! {{math|''n''<sub>α</sub>}}
! {{math|''n''<sub>β</sub>}}
! {{math|''n''<sub>γ</sub>}}
|-
| [[borax]] Na<sub>2</sub>(B<sub>4</sub>O<sub>5</sub>)(OH)<sub>4</sub>·8H<sub>2</sub>O || [[Monoclinic]] || 1.447 || 1.469 || 1.472
|-
| [[Magnesium sulfate|epsom salt]] MgSO<sub>4</sub>·7H<sub>2</sub>O || [[Monoclinic]] || 1.433 || 1.455 || 1.461
|-
| [[mica]], [[biotite]] K(Mg,Fe)<sub>3</sub>(AlSi<sub>3</sub>O<sub>10</sub>)(F,OH)<sub>2</sub> || [[Monoclinic]] || 1.595 || 1.640 || 1.640
|-
| mica, [[muscovite]] KAl<sub>2</sub>(AlSi<sub>3</sub>O<sub>10</sub>)(F,OH)<sub>2</sub> || [[Monoclinic]] || 1.563 || 1.596 || 1.601
|-
| [[olivine]] (Mg,Fe)<sub>2</sub>SiO<sub>4</sub> || [[Orthorhombic]] || 1.640 || 1.660 || 1.680
|-
| [[perovskite]] [[Calcium titanate|CaTiO<sub>3</sub>]] || [[Orthorhombic]] || 2.300 || 2.340 || 2.380
|-
| [[topaz]] Al<sub>2</sub>SiO<sub>4</sub>(F,OH)<sub>2</sub> || [[Orthorhombic]] || 1.618 || 1.620 || 1.627
|-
| [[ulexite]] NaCaB<sub>5</sub>O<sub>6</sub>(OH)<sub>6</sub>·5H<sub>2</sub>O || [[Triclinic]] || 1.490 || 1.510 || 1.520
|}
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