Difference between revisions of "Birefringence" - New World Encyclopedia

Revision as of 22:23, 3 February 2022

The letters on a paper covered by a calcite crystal show up as doubled. This is an example of the phenomenon of birefringence (double refraction).

Birefringence, or double refraction, is the splitting of a ray of light into two rays when it passes through certain types of material, such as calcite crystals. The two rays, called the ordinary ray and the extraordinary ray, travel at different speeds. Thus the material has two distinct indices of refraction, as measured from different directions. This effect can occur only if the structure of the material is anisotropic, so that the material's optical properties are not the same in all directions.

Birefringent materials are used in many optical devices, such as wave plates, liquid crystal displays, polarizing prisms, light modulators, and color filters.

Examples of birefringent materials

Birefringence was first described in calcite crystals by the Danish scientist Rasmus Bartholin in 1669. Since then, many birefringent crystals have been discovered.

Silicon carbide, also known as Moissanite, is strongly birefringent.

Many plastics are birefringent because their molecules are 'frozen' in a stretched conformation when the plastic is molded or extruded. For example, cellophane is a cheap birefringent material.

Cotton (Gossypium hirsutum) fiber is birefringent because of high levels of cellulosic material in the fiber's secondary cell wall.

Slight imperfections in optical fibers can cause birefringence, which can lead to distortion in fiber-optic communication.

Birefringence can also arise in magnetic (not dielectric) materials, but substantial variations in magnetic permeability of materials are rare at optical frequencies.

Birefringence can be observed in amyloid plaque deposits, such as are found in the brains of Alzheimer's victims. Modified proteins such as immunoglobulin light chains abnormally accumulate between cells, forming fibrils. Multiple folds of these fibers line up and take on a beta-pleated sheet conformation. Congo red dye intercalates between the folds and, when observed under polarized light, causes birefringence.

Calculation of birefringence

If the material has a single axis of anisotropy, (that is, it is uniaxial), birefringence can be formalized by assigning two different refractive indices to the material for different polarizations. The birefringence magnitude is then defined by:

$\Delta n=n_{e}-n_{o}\,$

where n_o and n_e are the refractive indices for polarizations perpendicular (ordinary) and parallel (extraordinary) to the axis of anisotropy, respectively.

Refractive indices of birefringent materials

The refractive indices of several (uniaxial) birefringent materials are listed below (at a wavelength of about 590 nm).^[1]

Material	n_o	n_e	Δn
beryl Be3Al2(SiO3)6	1.602	1.557	-0.045
calcite CaCO₃	1.658	1.486	-0.172
calomel Hg₂Cl₂	1.973	2.656	+0.683
ice H₂O	1.309	1.313	+0.014
lithium niobate LiNbO₃	2.272	2.187	-0.085
magnesium fluoride MgF₂	1.380	1.385	+0.006
quartz SiO₂	1.544	1.553	+0.009
ruby Al₂O₃	1.770	1.762	-0.008
rutile TiO₂	2.616	2.903	+0.287
peridot (Mg, Fe)2SiO4	1.690	1.654	-0.036
sapphire Al₂O₃	1.768	1.760	-0.008
sodium nitrate NaNO₃	1.587	1.336	-0.251
tourmaline (complex silicate )	1.669	1.638	-0.031
zircon, high ZrSiO₄	1.960	2.015	+0.055
zircon, low ZrSiO₄	1.920	1.967	+0.047

Creating birefringence

While birefringence is often found naturally (especially in crystals), there are several ways to create it in optically isotropic materials.

Birefringence results when isotropic materials are deformed such that the isotropy is lost in one direction (ie, stretched or bent).^[2]
Applying an electric field can induce molecules to line up or behave asymmetrically, introducing anisotropy and resulting in birefringence. (see Pockels effect)
Applying a magnetic field can cause a material to be circularly birefringent, with different indices of refraction for oppositely-handed circular polarizations (see Faraday effect).

Measuring birefringence by polarimetry

Birefringence and related optical effects (such as optical rotation and linear or circular dichroism) can be measured by measuring changes in the polarization of light passing through the material. These measurements are known as polarimetry.

A common feature of optical microscopes is a pair of crossed polarizing filters. Between the crossed polarizers, a birefringent sample will appear bright against a dark (isotropic) background.

Biaxial birefringence

Biaxial birefringence, also known as trirefringence, describes an anisotropic material that has more than one axis of anisotropy. For such a material, the refractive index tensor n, will in general have three distinct eigenvalues that can be labeled n_α, n_β and n_γ.

The refractive indices of some trirefringent materials are listed below (at wavelength ~ 590 nm).^[3]

Material	n_α	n_β	n_γ
borax	1.447	1.469	1.472
epsom salt MgSO₄•7(H₂O)	1.433	1.455	1.461
mica, biotite	1.595	1.640	1.640
mica, muscovite	1.563	1.596	1.601
olivine (Mg, Fe)₂SiO₄	1.640	1.660	1.680
perovskite CaTiO₃	2.300	2.340	2.380
topaz	1.618	1.620	1.627
ulexite	1.490	1.510	1.520

Elastic birefringence

Another form of birefringence is observed in anisotropic elastic materials. In these materials, shear waves split according to similar principles as the light waves discussed above. The study of birefringent shear waves in the earth is a part of seismology. Birefringence is also used in optical mineralogy to determine the chemical composition, and history of minerals and rocks.

Applications of birefringence

Birefringence is widely used in optical devices, such as liquid crystal displays, light modulators, color filters, wave plates, and optical axis gratings. It plays an important role in second harmonic generation and many other nonlinear processes. It is also utilized in medical diagnostics. Needle biopsy of suspected gouty joints will be negatively birefringent if urate crystals are present.

Notes

↑ Refraction Retrieved October 1, 2007.
↑ Example Retrieved October 1, 2007.
↑ Refraction Retrieved October 1, 2007.

References
ISBN links support NWE through referral fees

Born, Max, and Emil Wolf. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 7th ed. Cambridge, UK: Cambridge University Press, 1999. ISBN 0521642221
Elert, Glenn. The Physics Hypertextbook: Refraction hypertextbook.com, 2007. Retrieved September 3, 2019.
Halliday, David, Robert Resnick, and Kenneth S. Krane. Physics. Vol. 2, 5th ed. New York: John Wiley, 2001. ISBN 0471401943
Sharma, Kailash K. Optics: Principles and Applications. Burlington, MA: Academic Press, 2006. ISBN 0123706114

External links

All links retrieved February 3, 2022.

Birefrigent Materials Department of Physics and Astronomy, Georgia State University.
Birefringence Eric Weisstein's World of Physics.

Credits

New World Encyclopedia writers and editors rewrote and completed the Wikipedia article in accordance with New World Encyclopedia standards. This article abides by terms of the Creative Commons CC-by-sa 3.0 License (CC-by-sa), which may be used and disseminated with proper attribution. Credit is due under the terms of this license that can reference both the New World Encyclopedia contributors and the selfless volunteer contributors of the Wikimedia Foundation. To cite this article click here for a list of acceptable citing formats.The history of earlier contributions by wikipedians is accessible to researchers here:

Birefringence ^history

The history of this article since it was imported to New World Encyclopedia:

History of "Birefringence"

Note: Some restrictions may apply to use of individual images which are separately licensed.

[1] Refraction Retrieved October 1, 2007.

[2] Example Retrieved October 1, 2007.

[3] Refraction Retrieved October 1, 2007.

[1]

[2]

[3]

@@ Line 1: / Line 1: @@
-[[Image:Calcite.jpg|right|thumb|400px|A calcite crystal laid upon a paper with some letters showing the double refraction]]
+{{Copyedited}}{{Images OK}}{{Submitted}}{{Approved}}{{Paid}}
+[[Image:Calcite.jpg|right|thumb|400px|The letters on a paper covered by a calcite crystal show up as doubled. This is an example of the phenomenon of birefringence (double refraction).]]
-'''Birefringence''', or '''double refraction''', is the decomposition of a [[Ray (optics)|ray]] of [[light]] into two rays (the '''ordinary ray''' and the '''extraordinary ray''') when it passes through certain types of material, such as [[calcite]] [[crystal]]s, depending on the [[polarization]] of the light.  This effect can occur only if the structure of the material is [[anisotropic]]. If the material has a single [[anisotropy#Materials science and engineering|axis of anisotropy]], (i.e. it is [[Index ellipsoid#Uniaxial indicatrix|uniaxial]]) birefringence can be formalised by assigning two different [[refractive index|refractive indices]] to the material for different polarizations.  The birefringence magnitude is then defined by:
+'''Birefringence''', or '''double refraction''', is the splitting of a [[Ray (optics)|ray]] of [[light]] into two rays when it passes through certain types of material, such as [[calcite]] [[crystal]]s. The two rays, called the ''ordinary ray'' and the ''extraordinary ray'', travel at different speeds. Thus the material has two distinct indices of [[refraction]], as measured from different directions. This effect can occur only if the structure of the material is [[anisotropy|anisotropic]], so that the material's optical properties are not the same in all directions.
+{{toc}}
+Birefringent materials are used in many optical devices, such as [[wave plate]]s, [[liquid crystal display]]s, [[polarizer|polarizing]] [[prism (optics)|prisms]], [[electro-optic modulator|light modulators]], and [[Lyot filter|color filters]].
-<math>\Delta n=n_e-n_o\,</math>
+== Examples of birefringent materials ==
-where ''n''<sub>o</sub> and ''n''<sub>e</sub> are the refractive indices for polarizations perpendicular ('''ordinary''') and parallel ('''extraordinary''') to the axis of anisotropy respectively.
+Birefringence was first described in calcite crystals by the [[Denmark|Danish]] scientist [[Rasmus Bartholin]] in 1669. Since then, many birefringent crystals have been discovered.
-Birefringence can also arise in [[Magnetism|magnetic]], not [[dielectric]], materials, but substantial variations in magnetic [[Permeability (electromagnetism)|permeability]] of materials are rare at optical frequencies.
+[[Silicon carbide]], also known as Moissanite, is strongly birefringent.
+Many [[plastic]]s are birefringent because their [[molecule]]s are 'frozen' in a stretched conformation when the plastic is molded or extruded. For example, [[cellophane]] is a cheap birefringent material.
-== Electromagnetic waves in an anisotropic material ==
+Cotton (''Gossypium hirsutum'') fiber is birefringent because of high levels of cellulosic material in the fiber's secondary cell wall.
-More generally, birefringence can be defined by considering a dielectric [[permittivity]] and a refractive index that are [[tensor]]s. Consider a [[plane wave]] propagating in an anisotropic medium, with a relative permittivity tensor '''ε''', where the refractive index '''n''', is defined by '''n.n = ε'''. If the wave has an electric [[vector (spatial)|vector]] of the form:
-{{Equation|<math>\mathbf{E=E_0}\exp i(\mathbf{k \cdot r}-\omega t) \,</math>|2}}
+Slight imperfections in [[optical fiber]]s can cause birefringence, which can lead to distortion in [[fiber-optic communication]].
-where '''r''' is the position vector and ''t'' is time, then the [[wave vector]] '''k''' and the angular frequency ω must satisfy [[Maxwell's equations]] in the medium, leading to the equations:
+Birefringence can also arise in [[Magnetism|magnetic]] (not [[dielectric]]) materials, but substantial variations in magnetic [[Permeability (electromagnetism)|permeability]] of materials are rare at optical frequencies.
-{{Equation|<math>-\nabla \times \nabla \times \mathbf{E}=\frac{1}{c^2}\mathbf{\epsilon} \cdot \frac{\part^2 \mathbf{E}}{\partial t^2}</math>|3a}}
+Birefringence can be observed in [[amyloid]] plaque deposits, such as are found in the brains of [[Alzheimer's disease|Alzheimer's]] victims. Modified proteins such as [[immunoglobulin]] light chains abnormally accumulate between cells, forming fibrils. Multiple folds of these fibers line up and take on a beta-pleated sheet [[conformation]]. [[Congo red]] dye [[Intercalation (chemistry)|intercalates]] between the folds and, when observed under polarized light, causes birefringence.
-{{Equation|<math> \nabla \cdot \mathbf{\epsilon} \cdot \mathbf{E} =0 </math>|3b}}
+== Calculation of birefringence ==
-where ''c'' is the [[speed of light]] in a vacuum. Substituting eqn. 2 in eqns. 3a-b leads to the conditions:
+If the material has a single [[anisotropy#Materials science and engineering|axis of anisotropy]], (that is, it is [[Index ellipsoid#Uniaxial indicatrix|uniaxial]]), birefringence can be formalized by assigning two different [[refractive index|refractive indices]] to the material for different polarizations. The birefringence magnitude is then defined by:
-{{Equation|<math>|\mathbf{k}|^2\mathbf{E_0}-\mathbf{(k \cdot E_0) k}=    \frac{\omega^2}{c^2} \mathbf{\epsilon} \cdot \mathbf{E_0} </math>|4a}}
+<math>\Delta n=n_e-n_o\,</math>
-{{Equation|<math>\mathbf{k} \cdot \mathbf{\epsilon} \cdot \mathbf{E_0} =0 </math>|4b}}
-To find the allowed values of '''k''', '''E'''<sub>0</sub> can be eliminated from eq 4a. One way to do this is to write eqn 4a in [[Cartesian coordinates]], where the ''x'', ''y'' and ''z'' axes are chosen in the directions of the [[eigenvector]]s of '''ε''', so that
-{{Equation|<math>\mathbf{\epsilon}=\begin{bmatrix} n_x^2 & 0 & 0 \\ 0& n_y^2 & 0  \\ 0& 0& n_z^2 \end{bmatrix} \,</math>|4c}}
-Hence eqn 4a becomes
-{{Equation|<math>(-k_y^2-k_z^2+\frac{\omega^2n_x^2}{c^2})E_x + k_xk_yE_y + k_xk_zE_z =0</math>|5a}}
-{{Equation|<math>k_xk_yE_x + (-k_x^2-k_z^2+\frac{\omega^2n_y^2}{c^2})E_y +  k_yk_zE_z =0</math>|5b}}
-{{Equation|<math>k_xk_zE_x + k_yk_zE_y + (-k_x^2-k_y^2+\frac{\omega^2n_z^2}{c^2})E_z =0</math>|5c}}
-where ''E''<sub>x</sub>,  ''E''<sub>y</sub>,  ''E''<sub>z</sub>, ''k''<sub>x</sub>,  ''k''<sub>y</sub> and  ''k''<sub>z</sub> are the components of '''E'''<sub>0</sub> and  '''k'''. This is a set of linear equations in ''E''<sub>x</sub>,  ''E''<sub>y</sub>,  ''E''<sub>z</sub>, and they have a non-trivial solution if their [[determinant]] is zero:
-{{Equation|<math>\det\begin{bmatrix}
-(-k_y^2-k_z^2+\frac{\omega^2n_x^2}{c^2}) & k_xk_y & k_xk_z \\
-k_xk_y & (-k_x^2-k_z^2+\frac{\omega^2n_y^2}{c^2}) &  k_yk_z \\
-k_xk_z & k_yk_z & (-k_x^2-k_y^2+\frac{\omega^2n_z^2}{c^2}) \end{bmatrix}  =0\,</math>|6}}
-Multiplying out eqn (6), and rearranging the terms, we obtain
-{{Equation|<math>\frac{\omega^4}{c^4} - \frac{\omega^2}{c^2}\left(\frac{k_x^2+k_y^2}{n_z^2}+\frac{k_x^2+k_z^2}{n_y^2}+\frac{k_y^2+k_z^2}{n_x^2}\right) + \left(\frac{k_x^2}{n_y^2n_z^2}+\frac{k_y^2}{n_x^2n_z^2}+\frac{k_z^2}{n_x^2n_y^2}\right)(k_x^2+k_y^2+k_z^2)=0\, </math>|7}}
-In the case of a uniaxial material, where ''n''<sub>x</sub>=''n''<sub>y</sub>=''n<sub>o</sub>'' and ''n<sub>z</sub>''=''n<sub>e</sub>'' say, eqn 7 can be factorised into
-{{Equation|<math>\left(\frac{k_x^2}{n_o^2}+\frac{k_y^2}{n_o^2}+\frac{k_z^2}{n_o^2} -\frac{\omega^2}{c^2}\right)\left(\frac{k_x^2}{n_e^2}+\frac{k_y^2}{n_e^2}+\frac{k_z^2}{n_o^2} -\frac{\omega^2}{c^2}\right)=0\,.</math>|8}}
-Each of the factors in eqn 8 defines a surface in the space of vectors '''k''' — the '''surface of wave normals'''. The first factor defines a [[sphere]] and the second defines an [[ellipsoid]]. Therefore, for each direction of the wave normal, two wavevectors '''k''' are allowed. Values of '''k''' on the sphere correspond to the '''ordinary rays''' while values on the ellipsoid correspond to the '''extraordinary rays'''.
-For a biaxial material, eqn (7) cannot be factorised in the same way, and describes a more complicated pair of wave-normal surfaces.<ref name="bornwolf">Born M, and Wolf E, ''Principles of Optics'', 7th Ed. 1999 (Cambridge University Press), §15.3.3</ref>
-Birefringence is often measured for rays propagating along one of the optical axes (or measured in a two-dimensional material). In this case, '''n''' has two eigenvalues which can be labeled ''n''<sub>1</sub> and ''n''<sub>2</sub>. '''n''' can be diagonalised by:
-{{Equation|<math>\mathbf{n} = \mathbf{R(\chi)} \cdot \begin{bmatrix} n_1 & 0 \\ 0 & n_2 \end{bmatrix} \cdot \mathbf{R(\chi)}^\textrm{T} </math>|9}}
-where '''R'''(χ) is the rotation matrix through an angle χ. Rather than specifying the complete tensor '''n''', we may now simply specify the ''magnitude'' of the birefringence Δ''n'', and ''extinction angle'' χ, where Δ''n'' = ''n''<sub>1</sub>&nbsp;−&nbsp;''n''<sub>2</sub>.
-== Creating birefringence ==
-While birefringence is often found naturally (especially in crystals), there are several ways to create it in [[optical isotropy|optically isotropic]] materials.
-*Birefringence results when isotropic materials are deformed such that the isotropy is lost in one direction (ie, stretched or bent). [http://www.oberlin.edu/physics/catalog/demonstrations/optics/birefringence.html Example]
-*Applying an electric field can induce molecules to line up or behave asymmetrically, introducing anisotropy and resulting in birefringence. (''see'' [[Pockels effect]])
-*Applying a magnetic field can cause a material to be '''circularly birefringent''', with different indices of refraction for [[polarization#Theory|oppositely-handed circular polarizations]] (''see'' [[Faraday effect]]).
-== Examples of birefringent materials ==
-Many [[plastic]]s are birefringent, because their molecules are 'frozen' in a stretched conformation when the plastic is moulded or extruded. For example, [[cellophane]] is a cheap birefringent material. Birefringent materials are used in many devices which manipulate the polarization of light, such as [[wave plate]]s, [[polarizer|polarizing]] [[prism (optics)|prisms]], and [[Lyot filter]]s.
-There are many birefringent crystals: birefringence was first described in calcite crystals by the [[Denmark|Danish]] scientist [[Rasmus Bartholin]] in [[1669]].
-Birefringence can be observed in [[amyloid]] plaque deposits such as are found in the brains of [[Alzheimer's disease|Alzheimer's]] victims.  Modified proteins such as [[immunoglobulin]] light chains abnormally accumulate between cells, forming fibrils.  Multiple folds of these fibers line up and take on a beta-pleated sheet [[conformation]].  [[Congo red]] dye [[Intercalation (chemistry)|intercalates]] between the folds and, when observed under polarized light, causes birefringence.
-Cotton (Gossypium hirsutum) fiber is birefringent because of high levels of cellulosic material in the fiber's secondary cell wall.
-Slight imperfections in [[optical fiber]] can cause birefringence, which can cause distortion in [[fiber-optic communication]]; see [[polarization mode dispersion]].
+where ''n''<sub>o</sub> and ''n''<sub>e</sub> are the refractive indices for polarizations perpendicular (''ordinary'') and parallel (''extraordinary'') to the axis of anisotropy, respectively.
-[[Silicon carbide]], also known as Moissanite, is strongly birefringent.
+== Refractive indices of birefringent materials ==
-The refractive indices of several (uniaxial) birefringent materials are listed below (at wavelength ~ 590 nm), from [http://hypertextbook.com/physics/waves/refraction/].
+The refractive indices of several (uniaxial) birefringent materials are listed below (at a wavelength of about 590 nm).<ref>[http://hypertextbook.com/physics/waves/refraction/ Refraction] Retrieved October 1, 2007.</ref>
 <center>
@@ Line 118: / Line 69: @@
 |}
 </center>
+== Creating birefringence ==
+While birefringence is often found naturally (especially in crystals), there are several ways to create it in [[optical isotropy|optically isotropic]] materials.
+*Birefringence results when isotropic materials are deformed such that the isotropy is lost in one direction (ie, stretched or bent).<ref>[http://www.oberlin.edu/physics/catalog/demonstrations/optics/birefringence.html Example] Retrieved October 1, 2007.</ref>
+*Applying an electric field can induce molecules to line up or behave asymmetrically, introducing anisotropy and resulting in birefringence. (''see'' [[Pockels effect]])
+*Applying a magnetic field can cause a material to be ''circularly birefringent'', with different indices of refraction for [[polarization#Theory|oppositely-handed circular polarizations]] (''see'' [[Faraday effect]]).
+== Measuring birefringence by polarimetry ==
+Birefringence and related optical effects (such as [[optical rotation]] and linear or [[circular dichroism]]) can be measured by measuring changes in the polarization of light passing through the material. These measurements are known as [[polarimetry]].
+A common feature of optical microscopes is a pair of crossed [[polarizer|polarizing]] filters. Between the crossed polarizers, a birefringent sample will appear bright against a dark (isotropic) background.
 == Biaxial birefringence ==
-'''Biaxial birefringence''', also known as '''trirefringence''', describes an anisotropic material that has more than one axis of anisotropy. For such a material, the refractive index tensor '''n''', will in general have three distinct [[eigenvalues]] that can be labelled ''n''<sub>α</sub>, ''n''<sub>β</sub> and ''n''<sub>γ</sub>.
-The refractive indices of some trirefringent materials are listed below (at wavelength ~ 590 nm), from [http://hypertextbook.com/physics/waves/refraction/].
+''Biaxial birefringence'', also known as ''trirefringence'', describes an anisotropic material that has more than one axis of anisotropy. For such a material, the refractive index tensor '''n''', will in general have three distinct [[eigenvalues]] that can be labeled ''n''<sub>α</sub>, ''n''<sub>β</sub> and ''n''<sub>γ</sub>.
+The refractive indices of some trirefringent materials are listed below (at wavelength ~ 590 nm).<ref>[http://hypertextbook.com/physics/waves/refraction/ Refraction] Retrieved October 1, 2007.</ref>
 <center>
@@ Line 130: / Line 95: @@
 |[[borax]] ||1.447 ||1.469 ||1.472
 |-
-|[[Magnesium sulfate|epsom salt]] MgSO<sub>4</sub>·7(H<sub>2</sub>O) ||1.433 ||1.455 ||1.461
+|[[Magnesium sulfate|epsom salt]] MgSO<sub>4</sub>•7(H<sub>2</sub>O) ||1.433 ||1.455 ||1.461
 |-
 |[[mica]], [[biotite]] ||1.595 ||1.640 ||1.640
@@ Line 146: / Line 111: @@
 </center>
-== Measuring birefringence ==
+==Elastic birefringence==
-Birefringence and related optical effects (such as [[optical rotation]] and linear or [[circular dichroism]]) can be measured by measuring the changes in the polarization of light passing through the material. These measurements are known as [[polarimetry]].
-A common feature of optical microscopes is a pair of crossed [[polarizer|polarizing]] filters. Between the crossed polarizers, a birefringent sample will appear bright against a dark (isotropic) background.
+Another form of birefringence is observed in anisotropic [[elastic deformation|elastic]] materials. In these materials, [[S-wave|shear wave]]s split according to similar principles as the light waves discussed above. The study of birefringent shear waves in the earth is a part of [[seismology]]. Birefringence is also used in optical mineralogy to determine the chemical composition, and [[history]] of [[mineral]]s and [[rock]]s.
 == Applications of birefringence ==
-Birefringence is widely used in optical devices, such as [[liquid crystal display]]s, [[electro-optic modulator|light modulators]], [[Lyot filter|color filters]], [[wave plate]]s, [[optical axis gratings]], etc. It also plays important role in [[second harmonic generation]] and many other [[Nonlinear optics|nonlinear processes]].  It is also utilized in medical diagnostics.  Needle [[biopsies|biopsy]] of suspected [[gout]]y joints will be negatively birefringent if [[urate]] crystals are present.
-==Elastic birefringence==
+Birefringence is widely used in optical devices, such as [[liquid crystal display]]s, [[electro-optic modulator|light modulators]], [[Lyot filter|color filters]], [[wave plate]]s, and [[optical axis gratings]]. It plays an important role in [[second harmonic generation]] and many other [[Nonlinear optics|nonlinear processes]]. It is also utilized in medical diagnostics. Needle [[biopsies|biopsy]] of suspected [[gout]]y joints will be negatively birefringent if [[urate]] crystals are present.
-Another form of birefringence is observed in anisotropic [[elastic deformation|elastic]] materials.  In these materials, [[S-wave|shear wave]]s split according to similar principles as the light waves discussed above.  The study of birefringent shear waves in the earth is a part of [[seismology]]. Birefringence is also used in optical mineralogy to determine the chemical composition, and history of minerals and rocks.
+==See also==
+* [[Crystal]]
+* [[Light]]
+* [[Optics]]
+* [[Refraction]]
-== See also ==
+==Notes==
-{{Commons|Birefringence}}
+<references/>
-* [[Crystal optics]]
-* [[John Kerr (physicist)|John Kerr]]
-* [[Periodic poling]]
 ==References==
-<references />
-The Use of Birefringence for Predicting the Stiffness of Injection Moulded Polycarbonate Discs
+* Born, Max, and Emil Wolf. ''Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light''. 7th ed. Cambridge, UK: Cambridge University Press, 1999. ISBN 0521642221
-http://www.dep.uminho.pt/home/rec_humanos/mostra_curriculum.php3?pessoa=12&&menu=5&&idcategoria=1
+* Elert, Glenn. [http://hypertextbook.com/physics/waves/refraction/ The Physics Hypertextbook: Refraction] ''hypertextbook.com'', 2007. Retrieved September 3, 2019.
+* Halliday, David, Robert Resnick, and Kenneth S. Krane. ''Physics''. Vol. 2, 5th ed. New York: John Wiley, 2001. ISBN 0471401943
+* Sharma, Kailash K. ''Optics: Principles and Applications''. Burlington, MA: Academic Press, 2006. ISBN 0123706114
 ==External links==
-* [http://hypertextbook.com/physics/waves/refraction/ Refraction] in The Physics Hypertextbook by Glenn Elert, lists several birefringent/trirefringent materials.
+All links retrieved February 3, 2022.
+* [http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/biref.html Birefrigent Materials] ''Department of Physics and Astronomy, Georgia State University''.
+* [http://scienceworld.wolfram.com/physics/Birefringence.html Birefringence] ''Eric Weisstein's World of Physics''.
 [[Category:Physical sciences]]