2009:. Polarization-sensitive optical coherence tomography measurements obtained from healthy human subjects have demonstrated a change in birefringence of the retinal nerve fiber layer as a function of location around the optic nerve head. The same technology was recently applied in the living human retina to quantify the polarization properties of vessel walls near the optic nerve. While retinal vessel walls become thicker and less birefringent in patients who suffer from hypertension, hinting at a decrease in vessel wall condition, the vessel walls of diabetic patients do not experience a change in thickness, but do see an increase in birefringence, presumably due to fibrosis or inflammation.
1896:
553:
1887:
754:
32:
5416:
2051:
4822:
5807:
871:
20:
2093:
4936:
4378:
5487:
565:, and this has affected some terminology in use. Isotropic materials have symmetry in all directions and the refractive index is the same for any polarization direction. An anisotropic material is called "birefringent" because it will generally refract a single incoming ray in two directions, which we now understand correspond to the two different polarizations. This is true of either a uniaxial or biaxial material.
1776:
5411:{\displaystyle {\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}^{2}n_{z}^{2}}}+{\frac {k_{y}^{2}}{n_{x}^{2}n_{z}^{2}}}+{\frac {k_{z}^{2}}{n_{x}^{2}n_{y}^{2}}}\right)\left(k_{x}^{2}+k_{y}^{2}+k_{z}^{2}\right)=0}
890:), 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 nm) of some better-known crystals.
4817:{\displaystyle {\begin{vmatrix}\left(-k_{y}^{2}-k_{z}^{2}+{\frac {\omega ^{2}n_{x}^{2}}{c^{2}}}\right)&k_{x}k_{y}&k_{x}k_{z}\\k_{x}k_{y}&\left(-k_{x}^{2}-k_{z}^{2}+{\frac {\omega ^{2}n_{y}^{2}}{c^{2}}}\right)&k_{y}k_{z}\\k_{x}k_{z}&k_{y}k_{z}&\left(-k_{x}^{2}-k_{y}^{2}+{\frac {\omega ^{2}n_{z}^{2}}{c^{2}}}\right)\end{vmatrix}}=0}
5802:{\displaystyle \left({\frac {k_{x}^{2}}{n_{\mathrm {o} }^{2}}}+{\frac {k_{y}^{2}}{n_{\mathrm {o} }^{2}}}+{\frac {k_{z}^{2}}{n_{\mathrm {o} }^{2}}}-{\frac {\omega ^{2}}{c^{2}}}\right)\left({\frac {k_{x}^{2}}{n_{\mathrm {e} }^{2}}}+{\frac {k_{y}^{2}}{n_{\mathrm {e} }^{2}}}+{\frac {k_{z}^{2}}{n_{\mathrm {o} }^{2}}}-{\frac {\omega ^{2}}{c^{2}}}\right)=0}
1787:) is horizontally polarized (5) and passes through the liquid-crystal modulator (3) sandwiched in between transparent layers (2, 4) containing electrodes. Horizontally polarized light is blocked by the vertically oriented polarizer (1), except where its polarization has been rotated by the liquid crystal (3), appearing bright to the viewer.
6261:, Ser. 2, vol. 17, pp. 102–111 (May 1821), 167–96 (June 1821), 312–15 ("Postscript", July 1821); reprinted (with added section nos.) in Fresnel, 1866–70, vol. 1, pp. 609–648; translated as "On the calculation of the tints that polarization develops in crystalline plates, & postscript",
146:
2972:
922:
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. Some
744:
is less than zero. In other words, the polarization of the fast (or slow) wave is perpendicular to the optic axis when the birefringence of the crystal is positive (or negative, respectively). In the case of biaxial crystals, all three of the principal axes have different refractive indices, so this
664:
exhibit birefringence, with all polarizations in such a beam experiencing the same index of refraction. It is very different when the three principal refractive indices are all different; then an incoming ray in any of those principal directions will still encounter two different refractive indices.
506:
polarization (the "extraordinary ray" in this case, whose electric field polarization includes a component in the direction of the optic axis). In addition, a distinct form of double refraction occurs, even with normal incidence, in cases where the optic axis is not along the refracting surface (nor
470:
When an arbitrary beam of light strikes the surface of a birefringent material at non-normal incidence, the polarization component normal to the optic axis (ordinary ray) and the other linear polarization (extraordinary ray) will be refracted toward somewhat different paths. Natural light, so-called
1942:
The birefringence of tissue inside a living human thigh was measured using polarization-sensitive optical coherence tomography at 1310 nm and a single mode fiber in a needle. Skeletal muscle birefringence was Δn = 1.79 × 10 ± 0.18×10, adipose Δn = 0.07 × 10 ± 0.50 × 10, superficial aponeurosis
1741:
been affected by birefringence remains in a polarization that is totally rejected by the second polarizer ("analyzer"). The addition of quarter-wave plates permits examination using circularly polarized light. Determination of the change in polarization state using such an apparatus is the basis of
685:
is the one with a lower effective refractive index. When a beam is incident on such a material from air (or any material with a lower refractive index), the slow ray is thus refracted more towards the normal than the fast ray. In the example figure at top of this page, it can be seen that refracted
527:
resulting in an additional separation between these beams. So even in the case of normal incidence, where one would compute the angle of refraction as zero (according to Snell's law, regardless of the effective index of refraction), the energy of the extraordinary ray is propagated at an angle. If
349:
When the light propagates either along or orthogonal to the optic axis, such a lateral shift does not occur. In the first case, both polarizations are perpendicular to the optic axis and see the same effective refractive index, so there is no extraordinary ray. In the second case the extraordinary
3606:
697:. In this case, there is essentially no spatial separation between the polarizations, the phase of the wave in the parallel polarization (the slow ray) will be retarded with respect to the perpendicular polarization. These directions are thus known as the slow axis and fast axis of the waveplate.
6101:
a spatial shift for the ordinary ray (hence its name) which will refract as if the material were non-birefringent with an index the same as the two axes which are not the optic axis. For a biaxial crystal neither ray is deemed "ordinary" nor would generally be refracted according to a refractive
6068:
a difference not only in the magnitude but the direction of the two rays. For instance, the photograph through a calcite crystal (top of page) shows a shifted image in the two polarizations; this is due to the optic axis being neither parallel nor normal to the crystal surface. And even when the
568:
In a uniaxial material, one ray behaves according to the normal law of refraction (corresponding to the ordinary refractive index), so an incoming ray at normal incidence remains normal to the refracting surface. As explained above, the other polarization can deviate from normal incidence, which
556:
Comparison of positive and negative birefringence : In positive birefringence (figure 1), the ordinary ray (p-polarisation in this case w.r.t. magenta-coloured plane of incidence), perpendicular to optic axis A is the fast ray (F) while the extraordinary ray (s-polarisation in this case and
6033:
according to the above convention). Historically that accounts for the use of the term "biaxial" for such crystals, as the existence of exactly two such special directions (considered "axes") was discovered well before polarization and birefringence were understood physically. These two special
3268:
169:, meaning that there is a single direction governing the optical anisotropy whereas all directions perpendicular to it (or at a given angle to it) are optically equivalent. Thus rotating the material around this axis does not change its optical behaviour. This special direction is known as the
207:
refractive index. Because the index of refraction depends on the polarization when unpolarized light enters a uniaxial birefringent material, it is split into two beams travelling in different directions, one having the polarization of the ordinary ray and the other the polarization of the
2807:
1938:
crystals, in contrast, show weak positive birefringence. Urate crystals appear yellow, and calcium pyrophosphate crystals appear blue when their long axes are aligned parallel to that of a red compensator filter, or a crystal of known birefringence is added to the sample for comparison.
2037:
Dermatologists use dermatoscopes to view skin lesions. Dermoscopes use polarized light, allowing the user to view crystalline structures corresponding to dermal collagen in the skin. These structures may appear as shiny white lines or rosette shapes and are only visible under polarized
2076:. When such a sample is placed between two crossed polarizers, colour patterns can be observed, because polarization of a light ray is rotated after passing through a birefringent material and the amount of rotation is dependent on wavelength. The experimental method called
580:
when it has a single direction of symmetry in its optical behavior, which we term the optic axis. It also happens to be the axis of symmetry of the index ellipsoid (a spheroid in this case). The index ellipsoid could still be described according to the refractive indices,
5982:
When those two propagation constants are equal then the effective refractive index is independent of polarization, and there is consequently no birefringence encountered by a wave traveling in that particular direction. For a uniaxial crystal, this is the optic axis, the
315:
as if there were no birefringence involved. The extraordinary ray, as its name suggests, propagates unlike any wave in an isotropic optical material. Its refraction (and reflection) at a surface can be understood using the effective refractive index (a value in between
4314:
4107:
3900:
2596:
449:
which are defined as directions along which light may propagate without birefringence, i.e., directions along which the wavelength is independent of polarization. For this reason, birefringent materials with three distinct refractive indices are called
781:
Form birefringence, whereby structure elements such as rods, having one refractive index, are suspended in a medium with a different refractive index. When the lattice spacing is much smaller than a wavelength, such a structure is described as a
6284:, Ser. 2, vol. 28, pp. 263–279 (March 1825); reprinted as "Extrait du second Mémoire sur la double réfraction" in Fresnel, 1866–70, vol. 2, pp. 465–478; translated as "Extract of a memoir on double refraction",
2864:
2399:
391:
polarizations would be classified as extraordinary rays but with different effective refractive indices. Being extraordinary waves, the direction of power flow is not identical to the direction of the wave vector in either case.
3369:
186:(for "ordinary") regardless of its specific polarization. For rays with any other propagation direction, there is one linear polarization that is perpendicular to the optic axis, and a ray with that polarization is called an
3139:
6014:
are distinct, it can be shown that there are exactly two such directions, where the two sheets of the wave-vector surface touch; these directions are not at all obvious and do not lie along any of the three principal axes
2721:
573:. The terms "ordinary" and "extraordinary" are still applied to the polarization components perpendicular to and not perpendicular to the optic axis respectively, even in cases where no double refraction is involved.
475:, consists of equal amounts of energy in any two orthogonal polarizations. Even linearly polarized light has some energy in both polarizations, unless aligned along one of the two axes of birefringence. According to
665:
But it turns out that there are two special directions (at an angle to all of the 3 axes) where the refractive indices for different polarizations are again equal. For this reason, these crystals were designated as
199:. For a ray propagating in the same direction but with a polarization perpendicular to that of the ordinary ray, the polarization direction will be partly in the direction of (parallel to) the optic axis, and this
2272:
1804:, cause their pixels to become lighter or darker through rotation of the polarization (circular birefringence) of linearly polarized light as viewed through a sheet polarizer at the screen's surface. Similarly,
297:
778:
results when a normally isotropic solid is stressed and deformed (i.e., stretched or bent) causing a loss of physical isotropy and consequently a loss of isotropy in the material's permittivity tensor;
1842:. The crystals used for these purposes are almost always birefringent. By adjusting the angle of incidence, the effective refractive index of the extraordinary ray can be tuned in order to achieve
4130:
3923:
3716:
1870:
direction. Therefore, no light from the source will be accepted by the analyzer, and the field will appear dark. Areas of the sample possessing birefringence will generally couple some of the
946:. 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.
6037:
A general state of polarization launched into the medium can always be decomposed into two waves, one in each of those two polarizations, which will then propagate with different wavenumbers
3035:
346:
as photographed above. Rotating the calcite crystal will cause one of the two images, that of the extraordinary ray, to rotate slightly around that of the ordinary ray, which remains fixed.
2135:
656:
and the origin of this term is more complicated and frequently misunderstood. In a uniaxial crystal, different polarization components of a beam will travel at different phase velocities,
6061:
vectors are still in the same direction. That is true when each of the two polarizations is either normal to the optic axis (the ordinary ray) or parallel to it (the extraordinary ray).
4926:
4885:
2517:
532:
between the two beams. This is commonly observed using a piece of calcite cut along its natural cleavage, placed above a paper with writing, as in the above photographs. On the contrary,
2657:
494:
The different angles of refraction for the two polarization components are shown in the figure at the top of this page, with the optic axis along the surface (and perpendicular to the
897:
obtain permanent birefringence during manufacture due to stresses which are "frozen in" due to mechanical forces present when the plastic is molded or extruded. For example, ordinary
137:
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).
39:
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
6953:
Afsharan, Hadi; Hackmann, Michael J.; Wang, Qiang; Navaeipour, Farzaneh; Jayasree, Stephy Vijaya Kumar; Zawadzki, Robert J.; Silva, Dilusha; Joo, Chulmin; Cense, Barry (2021-07-01).
2080:
used for analyzing stress distribution in solids is based on the same principle. There has been recent research on using stress-induced birefringence in a glass plate to generate an
1878:
polarization; these areas will then appear bright against the dark background. Modifications to this basic principle can differentiate between positive and negative birefringence.
1737:. Polarized light microscopes, which contain two polarizers that are at 90° to each other on either side of the sample, are used to visualize birefringence, since light that has
121:
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
1943:Δn = 5.08 × 10 ± 0.73 × 10 and interstitial tissue Δn = 0.65 × 10 ±0.39 × 10. These measurements may be important for the development of a less invasive method to diagnose
6822:
Reed M. Jost; Joost Felius; Eileen E. Birch (August 2014). "High sensitivity of binocular retinal birefringence screening for anisometropic amblyopia without strabismus".
6034:
directions are generally not of particular interest; biaxial crystals are rather specified by their three refractive indices corresponding to the three axes of symmetry.
1904:
Gout and pseudogout crystals viewed under a microscope with a red compensator, which slows red light in one orientation (labeled "polarized light axis"). Urate crystals (
2967:{\displaystyle (-\mathbf {k} \cdot \mathbf {k} )\mathbf {E} +(\mathbf {k} \cdot \mathbf {E} )\mathbf {k} =-\mu _{0}\omega ^{2}({\boldsymbol {\varepsilon }}\mathbf {E} )}
1912:
appear yellow when their long axis is parallel to the slow transmission axis of the red compensator and appear blue when perpendicular. The opposite colors are seen in
1913:
6237:"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,"
149:
Doubly refracted image as seen through a calcite crystal, seen through a rotating polarizing filter illustrating the opposite polarization states of the two images.
2329:
677:
In a birefringent material, a wave consists of two polarization components which generally are governed by different effective refractive indices. The so-called
540:
the surface of the plate, so that with (approximately) normal incidence there will be no shift in the image from light of either polarization, simply a relative
919:
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.
6642:
Gilbert, Larry; Weber, M.F.; Strharsky, R.J.; Stover, C.A.; Nevitt, T.J.; Ouderkirk, A.J. (2001). "Giant birefringent optics in multilayer polymer filters".
1757:. This provides a measure of the degree of order within these fluid layers and how this order is disrupted when the layer interacts with other biomolecules.
7063:"Non-Invasive Retinal Blood Vessel Wall Measurements with Polarization-Sensitive Optical Coherence Tomography for Diabetes Assessment: A Quantitative Study"
6348:
Born & Wolf, 2002, pp. 807–808. (In 19th-century terminology, the ordinary ray is said to be polarized in the plane of the optic axis; but this "
3601:{\displaystyle \left(-k_{x}^{2}-k_{y}^{2}-k_{z}^{2}\right)E_{x}+k_{x}^{2}E_{x}+k_{x}k_{y}E_{y}+k_{x}k_{z}E_{z}=-{\frac {\omega ^{2}n_{x}^{2}}{c^{2}}}E_{x}}
2072:, birefringence results. The stress can be applied externally or is "frozen in" after a birefringent plastic ware is cooled after it is manufactured using
6097:
vector of the incident wave, as projected onto the surface of the interface, must all be identical. For a uniaxial crystal it will be found that there is
3263:{\displaystyle \mathbf {\varepsilon } =\varepsilon _{0}{\begin{bmatrix}n_{x}^{2}&0&0\\0&n_{y}^{2}&0\\0&0&n_{z}^{2}\end{bmatrix}}}
520:
690:
polarization (with its electric vibration along the direction of the optic axis, thus called the extraordinary ray) is the slow ray in given scenario.
5847:. The first factor being zero defines a sphere; this is the solution for so-called ordinary rays, in which the effective refractive index is exactly
938:. Such imperfections can be geometrical (lack of circular symmetry), or due to unequal lateral stress applied to the optical fibre. Birefringence is
6372:
6073:
parallel to the surface, this will occur for waves launched at non-normal incidence (as depicted in the explanatory figure). In these cases the two
2802:{\displaystyle -\nabla \times \nabla \times \mathbf {E} =(\mathbf {k} \cdot \mathbf {E} )\mathbf {k} -(\mathbf {k} \cdot \mathbf {k} )\mathbf {E} }
434:. Thus there is no axis around which a rotation leaves the optical properties invariant (as there is with uniaxial crystals whose index ellipsoid
367:, in which there is no distortion of the image but an intentional modification of the state of polarization of the incident wave. For instance, a
7386:
7270:
M.V. Berry and M.R. Jeffrey, "Conical diffraction: Hamilton's diabolical point at the heart of crystal optics", in E. Wolf (ed.),
2112:
materials. In these materials, the two polarizations split according to their effective refractive indices, which are also sensitive to stress.
1749:
Birefringence measurements have been made with phase-modulated systems for examining the transient flow behaviour of fluids. Birefringence of
6908:"Thickness and Birefringence of Healthy Retinal Nerve Fiber Layer Tissue Measured with Polarization-Sensitive Optical Coherence Tomography"
2242:
1962:
light chains abnormally accumulate between cells, forming fibrils. Multiple folds of these fibers line up and take on a beta-pleated sheet
7014:"Hypertension-associated changes in retinal blood vessel walls measured in vivo with polarization-sensitive optical coherence tomography"
1997:. In healthy subjects, the maximum retardation induced by the Henle fiber layer is approximately 22 degrees at 840 nm. Furthermore,
660:
for rays in the direction of what we call the optic axis. Thus the optic axis has the particular property that rays in that direction do
1820:
are thin birefringent sheets widely used in certain optical equipment for modifying the polarization state of light passing through it.
2030:
to select the ones with highest chances of successful pregnancy. Birefringence of particles biopsied from pulmonary nodules indicates
1733:) can be observed by measuring any change in the polarization of light passing through the material. These measurements are known as
886:
their refractive indices are well defined. Depending on the symmetry of a crystal structure (as determined by one of the 32 possible
472:
342:. This causes an additional shift in that beam, even when launched at normal incidence, as is popularly observed using a crystal of
6849:
Cense, Barry; Wang, Qiang; Lee, Sangyeol; Zhao, Liang; Elsner, Ann E.; Hitzenberger, Christoph K.; Miller, Donald T. (2013-11-01).
245:
7122:"Birefringence characteristics in sperm heads allow for the selection of reacted spermatozoa for intracytoplasmic sperm injection"
6447:
Wolman, M.; Kasten, F. H. (1986). "Polarized light microscopy in the study of the molecular structure of collagen and reticulin".
6047:. Applying the different phase of propagation to those two waves over a specified propagation distance will result in a generally
5896:. Therefore, for any arbitrary direction of propagation (other than in the direction of the optic axis), two distinct wavevectors
745:
designation does not apply. But for any defined ray direction one can just as well designate the fast and slow ray polarizations.
7163:"Automatic user-independent zona pellucida imaging at the oocyte stage allows for the prediction of preimplantation development"
6157:
943:
4309:{\displaystyle k_{x}k_{z}E_{x}+k_{y}k_{z}E_{y}+\left(-k_{x}^{2}-k_{y}^{2}+{\frac {\omega ^{2}n_{z}^{2}}{c^{2}}}\right)E_{z}=0}
4102:{\displaystyle k_{x}k_{y}E_{x}+\left(-k_{x}^{2}-k_{z}^{2}+{\frac {\omega ^{2}n_{y}^{2}}{c^{2}}}\right)E_{y}+k_{y}k_{z}E_{z}=0}
3895:{\displaystyle \left(-k_{y}^{2}-k_{z}^{2}+{\frac {\omega ^{2}n_{x}^{2}}{c^{2}}}\right)E_{x}+k_{x}k_{y}E_{y}+k_{x}k_{z}E_{z}=0}
765:
While the best known source of birefringence is the entrance of light into an anisotropic crystal, it can result in otherwise
6659:
6534:
528:
exiting the crystal through a face parallel to the incoming face, the direction of both rays will be restored, but leaving a
6203:
1854:
Birefringence is utilized in medical diagnostics. One powerful accessory used with optical microscopes is a pair of crossed
5872:
axis. This solution corresponds to the so-called extraordinary rays in which the effective refractive index is in between
6955:"Polarization properties of retinal blood vessel walls measured with polarization sensitive optical coherence tomography"
6550:
Frattini, P. L.; Fuller, G. G. (1984). "A note on phase-modulated flow birefringence: a promising rheo-optical method".
5979:(and thus effective refractive indices) corresponding to the propagation of two linear polarizations in that direction.
5905:
For a biaxial material a similar but more complicated condition on the two waves can be described; the locus of allowed
2677:
90:. The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material.
669:, with the two "axes" in this case referring to ray directions in which propagation does not experience birefringence.
6257:
A. Fresnel, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et seq.,
3125:
in the direction of the optic axis of a uniaxial crystal), resulting in a diagonal matrix for the permittivity tensor
3004:
487:
which separates incoming light into two linear polarizations using prisms composed of a birefringent material such as
6313:
2591:{\displaystyle -\nabla \times \nabla \times \mathbf {E} =\mu _{0}{\frac {\partial ^{2}}{\partial t^{2}}}\mathbf {D} }
681:
is the component for which the material has the higher effective refractive index (slower phase velocity), while the
7012:
Afsharan, Hadi; Anilkumar, Vidyalakshmi; Silva, Dilusha; Dwivedi, Girish; Joo, Chulmin; Cense, Barry (2024-01-01).
2017:
1754:
502:
polarization (the "ordinary ray" in this case, having its electric vector perpendicular to the optic axis) and the
4890:
4849:
35:
In this example, optic axis along the surface is shown perpendicular to plane of incidence. Incoming light in the
3286:
where the diagonal values are squares of the refractive indices for polarizations along the three principal axes
2628:
1982:
950:
874:
Sandwiched in between crossed polarizers, clear polystyrene cutlery exhibits wavelength-dependent birefringence
761:
with coloured fringes due to stress birefringence of partially polarised skylight through a circular polariser
363:. A crystal with its optic axis in this orientation, parallel to the optical surface, may be used to create a
7436:
2084:
and full
Poincare beams (optical beams that have every possible polarization state across a cross-section).
953:
could be a source of birefringence. At optical frequencies, there is no measurable magnetic polarizability (
2119:
traveling through the solid Earth (the Earth's liquid core does not support shear waves) is widely used in
1971:
931:
887:
5987:
direction according to the above construction. But when all three refractive indices (or permittivities),
7441:
6369:
1944:
1823:
To manufacture polarizers with high transmittance, birefringent crystals are used in devices such as the
949:
In addition to anisotropy in the electric polarizability that we have been discussing, anisotropy in the
1862:
direction after passing through the first polarizer, but above the specimen is a polarizer (a so-called
7348:(London: Taylor & Francis, 1852), pp. 238–333. (Cited page numbers are from the translation.)
6851:"Henle fiber layer phase retardation measured with polarization-sensitive optical coherence tomography"
6085:
constrained by the boundary condition which requires that the components of the two transmitted waves'
2306:
2199:
1998:
1835:
557:
parallel to optic axis A) is the slow ray (S). In negative birefringence (figure 2), it is the reverse.
6379:
First published in StoneChat, the
Journal of the UK Facet Cutter's Guild. January–March. edition 2005.
5915:) is a 4th-degree two-sheeted surface, so that in a given direction there are generally two permitted
2005:
fiber layer to indirectly quantify its thickness, which is of use in the assessment and monitoring of
6959:
6777:
1931:
935:
1895:
552:
47:
polarization (which becomes ordinary ray because "perpendicular polarisation" to optic axis) and so
7414:
6954:
6850:
6112:
1301:
1121:
1070:
6906:
Cense, Barry; Chen, Teresa C.; Park, B. Hyle; Pierce, Mark C.; Boer, Johannes F. de (2004-08-01).
1843:
1816:
is a specialized narrowband spectral filter employing the wavelength dependence of birefringence.
399:
for given directions of the polarization. Note that for biaxial crystals the index ellipsoid will
387:
refractive indices corresponding to three principal axes of the crystal. For most ray directions,
1824:
1805:
508:
383:
The case of so-called biaxial crystals is substantially more complex. These are characterized by
170:
7203:
6907:
6415:"The use of birefringence for predicting the stiffness of injection molded polycarbonate discs"
6236:
6055:
for instance. With a waveplate, there is no spatial displacement between the two rays as their
2462:
1989:(photoreceptor axons that go radially outward from the fovea) provides a reliable detection of
1955:
1797:
1780:
753:
7337:
7333:
1886:
6349:
6229:
Experimenta crystalli islandici disdiaclastici quibus mira & infolita refractio detegitur
6227:
6137:
3098:
2297:
2153:
1935:
1828:
854:
372:
134:
6758:
705:
Uniaxial birefringence is classified as positive when the extraordinary index of refraction
561:
Much of the work involving polarization preceded the understanding of light as a transverse
173:
of the material. Light propagating parallel to the optic axis (whose polarization is always
7329:
7313:
7215:
7025:
6559:
6499:
2394:{\displaystyle \mathbf {E} =\mathbf {E} _{0}e^{i(\mathbf {k} \cdot \mathbf {r} -\omega t)}}
1831:
and other variants. Layered birefringent polymer sheets can also be used for this purpose.
562:
71:
6414:
8:
6675:
Frances Lixey, Mary (1983-06-01). "Inexpensive
Compensator for a Polarizing Microscope".
2215:
2109:
1746:, by which the optical properties of specular surfaces can be gauged through reflection.
959:
833:
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7219:
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368:
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6799:
6736:
6711:
6472:
5902:
are allowed corresponding to the polarizations of the ordinary and extraordinary rays.
2126:
Birefringence is widely used in mineralogy to identify rocks, minerals, and gemstones.
1963:
1801:
1730:
1162:
905:
are routinely used to detect stress, either applied or frozen-in, in plastics such as
883:
828:
takes place generally not in materials which are anisotropic but rather ones which are
495:
110:
63:
7396:
Artist
Austine Wood Comarow employs birefringence to create kinetic figurative images.
7287:
6603:
6586:
3119:
axes chosen in the directions of the symmetry axes of the crystal (or simply choosing
942:
introduced (for instance, by making the cross-section elliptical) in order to produce
7241:
7233:
7184:
7179:
7162:
7143:
7138:
7121:
7102:
7084:
7043:
6994:
6976:
6935:
6927:
6888:
6870:
6804:
6741:
6692:
6655:
6530:
6511:
6464:
6309:
2073:
2069:
2055:
1475:
303:
153:
A mathematical description of wave propagation in a birefringent medium is presented
103:
95:
7317:, 7th Ed., Cambridge University Press, 1999 (reprinted with corrections, 2002).
7038:
7013:
6476:
7283:
7223:
7174:
7133:
7092:
7074:
7033:
6984:
6968:
6919:
6878:
6862:
6831:
6794:
6786:
6731:
6723:
6684:
6647:
6598:
6567:
6507:
6456:
6429:
6142:
2191:
1839:
1726:
1616:
858:
849:
824:
798:
766:
758:
480:
122:
67:
40:
31:
6771:
McBride, Jeffrey M.; Hackmann, Michael J.; Nimphius, Sophia; Cense, Barry (2022).
1974:
between the folds and, when observed under polarized light, causes birefringence.
7364:
7360:
6835:
6376:
6178:
6147:
6132:
2218:). In an anisotropic material exhibiting birefringence, the relationship between
2077:
1295:
1137:
837:
817:
516:
484:
396:
335:
236:
208:
extraordinary ray. The ordinary ray will always experience a refractive index of
1994:
145:
6117:
2081:
2050:
1959:
1809:
1750:
985:
844:
790:
569:
cannot be described using the law of refraction. This thus became known as the
512:
483:
of each of these two polarizations. This is clearly seen, for instance, in the
476:
133:) crystals which have one of the strongest birefringences. In the 19th century
52:
7390:
6761:
Author: Alan N. Baer; Chief Editor: Herbert S. Diamond. Updated: Nov 22, 2010.
6688:
1958:
patients when stained with a dye such as Congo Red. Modified proteins such as
693:
Using a thin slab of that material at normal incidence, one would implement a
7430:
7237:
7088:
7047:
6980:
6931:
6874:
6696:
6585:
Doyle, P. S.; Shaqfeh, E. S. G.; McKinley, G. H.; Spiegelberg, S. H. (1998).
1978:
1765:
1020:
927:
910:
870:
27:
crystal laid upon a graph paper with blue lines showing the double refraction
7391:
853:(having slightly different indices of refraction for left- and right-handed
462:
along which the group velocity of the light is independent of polarization.
7245:
7188:
7147:
7106:
6998:
6939:
6892:
6808:
6127:
2182:
2022:
1743:
1657:
1624:
1597:
783:
511:
of the birefringent material is not exactly in the direction of the wave's
217:, whereas the refractive index of the extraordinary ray will be in between
126:
118:
7120:
Gianaroli L.; Magli M. C.; Ferraretti A. P.; et al. (December 2008).
7061:
Afsharan, Hadi; Silva, Dilusha; Joo, Chulmin; Cense, Barry (August 2023).
6824:
Journal of
American Association for Pediatric Ophthalmology and Strabismus
6745:
6635:
6468:
2134:
968:) of natural materials, so this is not an actual source of birefringence.
479:
of refraction, the two angles of refraction are governed by the effective
7410:
7228:
7079:
6923:
6866:
6651:
6356:
to the vibration; cf. Fresnel, 1827, tr. Hobson, p. 318.)
6308:. Vol. 1. Palo Alto: Blackwell Scientific Publications. p. 28.
6152:
5966:
5434:
In the case of a uniaxial material, choosing the optic axis to be in the
4367:
2453:
2296:
is now a 3 × 3 permittivity tensor. We assume linearity and no
2002:
1813:
1734:
906:
813:
794:
652:
Materials in which all three refractive indices are different are termed
541:
524:
360:
339:
79:
19:
7119:
6972:
6821:
6790:
6727:
6460:
2120:
2116:
2092:
2039:
2013:
1990:
1613:
1568:
1530:
1489:
1459:
1370:
1348:
1317:
1250:
1171:
898:
805:
6433:
3082:
will not be needed for the further steps in the following derivation.
847:, where a longitudinal magnetic field causes some materials to become
7332:; reprinted as "Second mémoire..." in Fresnel, 1866–70, vol. 2,
7202:
Beckley, Amber M.; Brown, Thomas G.; Alonso, Miguel A. (2010-05-10).
6772:
6571:
6122:
6052:
5832:
2843:
and noting that differentiation in time results in multiplication by
2267:{\displaystyle \mathbf {D} ={\boldsymbol {\varepsilon }}\mathbf {E} }
2065:
2059:
2031:
1967:
1855:
1817:
1784:
1695:
1547:
902:
694:
533:
515:
for the extraordinary ray. The direction of power flow (given by the
364:
239:. The magnitude of the difference is quantified by the birefringence
6290:
6267:
1725:
Birefringence and other polarization-based optical effects (such as
6587:"Relaxation of dilute polymer solutions following extensional flow"
6051:
net polarization state at that point; this is the principle of the
5863:
2100:
observed in different polarizations using a rotating polarizer (or
2006:
1323:
1279:
1266:
1225:
1196:
1146:
1095:
1033:
879:
404:
7322:
Mémoires de l'Académie Royale des
Sciences de l'Institut de France
6395:
2698:, and use the spatial dependence in which each differentiation in
1846:, which is required for the efficient operation of these devices.
407:") but is described by three unequal principle refractive indices
4887:, the constant terms cancel. After eliminating the common factor
1951:
1673:
1584:
1509:
1086:
894:
797:, whereby an applied electric field induces birefringence due to
608:, along three coordinate axes; in this case two are equal. So if
488:
343:
130:
99:
91:
24:
7355:
H. de Sénarmont, E. Verdet, and L. Fresnel), 1866–70,
4359:, so it can have a nontrivial solution (that is, one other than
6584:
6285:
6262:
2614:
With no free charges, Maxwell's equation for the divergence of
2231:
2097:
2027:
1339:
1241:
1187:
923:
proteins are also birefringent, exhibiting form birefringence.
916:
829:
809:
350:
ray propagates at a different phase velocity (corresponding to
6952:
5921:
vectors (and their opposites). By inspection one can see that
893:
In addition to induced birefringence while under stress, many
7381:
7011:
6490:
Sano, Y (1988). "Optical anistropy of bovine serum albumin".
6280:
A. Fresnel, "Extrait d'un Mémoire sur la double réfraction",
1775:
1640:
1433:
1049:
292:{\displaystyle \Delta n=n_{\mathrm {e} }-n_{\mathrm {o} }\,.}
75:
7421:
6770:
2152:
In an isotropic medium (including free space) the so-called
157:. Following is a qualitative explanation of the phenomenon.
6773:"In vivo PS-OCT needle probe scan of human skeletal muscle"
6641:
1927:
1909:
1505:
1212:
7160:
2315:. The electric field of a plane wave of angular frequency
1914:
calcium pyrophosphate dihydrate crystal deposition disease
7395:
7382:
Stress
Analysis Apparatus (based on Birefringence theory)
6240:
2142:
vectors for a fixed frequency for a biaxial crystal (see
2068:
solids do not exhibit birefringence. When they are under
1920:
image): blue when parallel and yellow when perpendicular.
1111:
7422:
7161:
Ebner T.; Balaban B.; Moser M.; et al. (May 2009).
6177:
Although related, note that this is not the same as the
498:), so that the angle of refraction is different for the
4846:, and rearranging the terms according to the powers of
1783:. Light reflected by the surface (6) (or coming from a
395:
The two refractive indices can be determined using the
359:) but still has the power flow in the direction of the
7320:
A. Fresnel, 1827, "Mémoire sur la double réfraction",
6712:"Acute gout and the accident and emergency department"
4387:
3166:
7266:
7264:
7060:
5490:
4939:
4893:
4852:
4381:
4133:
3926:
3719:
3372:
3310:
in this form, and substituting in the speed of light
3142:
3007:
2867:
2724:
2631:
2520:
2332:
2245:
454:. Additionally, there are two distinct axes known as
248:
235:, depending on the ray direction as described by the
177:
to the optic axis) is governed by a refractive index
6370:
Birefringence for facetors I: what is birefringence?
6905:
3690:. Rearranging, we can write (and similarly for the
3070:, even though that is no longer generally true for
1858:filters. Light from the source is polarized in the
804:By the self or forced alignment into thin films of
748:
190:and is governed by the same refractive index value
165:The simplest type of birefringence is described as
7261:
7201:
6529:. New York: Oxford University Press. p. 202.
5927:is generally satisfied for two positive values of
5801:
5410:
4920:
4879:
4816:
4308:
4101:
3894:
3600:
3262:
3029:
2966:
2801:
2651:
2590:
2393:
2266:
878:The best characterized birefringent materials are
291:
3064:is orthogonal to the direction of the wavevector
774:
441:Although there is no axis of symmetry, there are
7428:
6912:Investigative Ophthalmology & Visual Science
6848:
6327:
6325:
3030:{\displaystyle \mathbf {k} \cdot \mathbf {D} =0}
2054:Color pattern of a plastic box with "frozen in"
1926:For instance, needle aspiration of fluid from a
1812:of polarized light followed by a polarizer. The
865:
7359:(3 volumes), Paris: Imprimerie Impériale;
6518:
6389:
6387:
6385:
2837:through application of the permittivity tensor
2087:
2045:
1796:Birefringence is used in many optical devices.
523:is at a finite angle from the direction of the
6549:
6274:
6201:
3657:(at any given position in space and time) and
2162:) is just proportional to the electric field (
1834:Birefringence also plays an important role in
1764:, a technique based on holographic tomography
930:leads to birefringence, which is one cause of
6674:
6322:
3076:as would be the case in an isotropic medium.
2438:is a vector describing the electric field at
832:. This can include liquids where there is an
306:) of the ordinary ray is simply described by
7274:, vol. 50, Amsterdam: Elsevier, 2007,
6446:
6382:
6251:
4921:{\displaystyle {\frac {\omega ^{2}}{c^{2}}}}
4880:{\displaystyle {\frac {\omega ^{2}}{c^{2}}}}
2704:(for instance) results in multiplication by
836:of a chiral molecule, that is, one that has
6709:
6668:
6232:(Copenhagen, Denmark: Daniel Paulli, 1669).
6202:Abramowitz, Mortimer; Davidson, Michael W.
2652:{\displaystyle \nabla \cdot \mathbf {D} =0}
1954:plaques such as are found in the brains of
6102:index equal to one of the principal axes.
1930:joint will reveal negatively birefringent
926:Inevitable manufacturing imperfections in
7227:
7178:
7137:
7096:
7078:
7037:
6988:
6882:
6798:
6735:
6683:(6). Oxford University Press (OUP): 382.
6611:
6602:
6289:
6266:
2108:Birefringence is observed in anisotropic
507:exactly normal to it); in this case, the
338:) is not exactly in the direction of the
285:
6759:The Approach to the Painful Joint Workup
6591:Journal of Non-Newtonian Fluid Mechanics
6306:Optical Mineralogy: Theory and Technique
5933:. Or, for a specified optical frequency
2133:
2091:
2049:
1808:modulate the intensity of light through
1774:
869:
752:
551:
144:
30:
18:
5939:and direction normal to the wavefronts
5479:, this expression can be factored into
2952:
2255:
2016:allow the selection of spermatozoa for
944:polarization-maintaining optical fibers
700:
51:polarization ray is undergoing greater
7429:
7400:
6303:
6158:Huygens principle of double refraction
632:axes, then the extraordinary index is
6524:
6412:
6393:
6235:Erasmus Bartholin (January 16, 1671)
4332:This is a set of linear equations in
2990:Applying the differentiation rule to
672:
160:
109:Birefringence is responsible for the
7357:Oeuvres complètes d'Augustin Fresnel
7336:; translated by A.W. Hobson as
6489:
6331:Landau, L. D., and Lifshitz, E. M.,
6204:"Olympus Microscopy Resource Center"
5835:surface in the space of wavevectors
5481:
4930:
4928:from the remaining terms, we obtain
4372:
4124:
3917:
3710:
3363:
3133:
2998:
2858:
2715:
2622:
2511:
2323:
2321:can be written in the general form:
2236:
971:
723:. Negative birefringence means that
465:
378:
55:on entering and exiting the crystal.
6333:Electrodynamics of Continuous Media
6246: : 2041–2048 (pdf pp 282–289).
714:is greater than the ordinary index
536:specifically have their optic axis
13:
5748:
5709:
5670:
5597:
5558:
5519:
2734:
2728:
2632:
2567:
2557:
2530:
2524:
2452:. Then we shall find the possible
1810:electrically induced birefringence
1791:
977:Uniaxial crystals, at 590 nm
375:from a linearly polarized source.
279:
264:
249:
14:
7458:
7375:
6422:Polymer Engineering & Science
5825:Setting either of the factors in
3355:component of the vector equation
2675:We can apply the vector identity
2012:Birefringence characteristics in
1950:Birefringence can be observed in
1390:Biaxial crystals, at 590 nm
203:will be governed by a different,
7180:10.1016/j.fertnstert.2009.03.106
7139:10.1016/j.fertnstert.2008.10.024
7018:Optics and Lasers in Engineering
6710:Hardy RH, Nation B (June 1984).
6282:Annales de Chimie et de Physique
6259:Annales de Chimie et de Physique
6079:vectors can be found by solving
6064:In the more general case, there
5890:, depending on the direction of
3017:
3009:
2957:
2918:
2910:
2902:
2891:
2883:
2875:
2795:
2787:
2779:
2768:
2760:
2752:
2741:
2639:
2584:
2537:
2373:
2365:
2343:
2334:
2260:
2247:
2018:intracytoplasmic sperm injection
1894:
1885:
1755:dual-polarization interferometry
749:Sources of optical birefringence
403:be an ellipsoid of revolution ("
334:). Its power flow (given by the
16:Refractive property of materials
7305:
7252:
7195:
7154:
7113:
7054:
7039:10.1016/j.optlaseng.2023.107838
7005:
6946:
6899:
6842:
6815:
6764:
6752:
6703:
6578:
6543:
6483:
6440:
6406:
6171:
5856:regardless of the direction of
1983:retinal birefringence screening
1770:
1762:3D measurement of birefringence
645:axis, which is also called the
98:are often birefringent, as are
7258:Born & Wolf, 2002, §15.3.3
6359:
6342:
6297:
6271:(Creative Commons), 2021; §14.
6217:
6195:
4840:Evaluating the determinant of
3085:Finding the allowed values of
2961:
2948:
2914:
2898:
2887:
2868:
2791:
2775:
2764:
2748:
2386:
2361:
2230:must now be described using a
2115:The study of birefringence in
2001:uses the birefringence of the
1720:
547:
140:
1:
7338:"Memoir on double refraction"
7288:10.1016/S0079-6638(07)50002-8
6644:Optical Interference Coatings
6604:10.1016/S0377-0257(97)00113-4
6337:Course of Theoretical Physics
6188:
5841:that are allowed for a given
2831:can be expressed in terms of
888:crystallographic point groups
866:Common birefringent materials
544:between the two light waves.
74:and propagation direction of
7340:, in R. Taylor (ed.),
6836:10.1016/j.jaapos.2014.07.017
6525:Hobbs, Peter Victor (2010).
6512:10.1016/0021-9797(88)90178-6
4322:
4115:
3908:
3704:
3614:
3357:
3276:
3078:
3054:
3043:
2992:
2980:
2852:
2827:
2815:
2694:
2665:
2604:
2088:Other cases of birefringence
2046:Stress-induced birefringence
302:The propagation (as well as
125:in 1669, who observed it in
7:
7311:M. Born and E. Wolf, 2002,
6105:
6081:
5969:(or propagation constants)
5923:
5827:
5815:
5424:
4842:
4830:
4366:) as long as the following
2407:
2280:
2144:
2058:placed between two crossed
1945:Duchenne muscular dystrophy
1849:
1840:nonlinear optical processes
1779:Reflective twisted-nematic
861:while the field is applied.
371:is commonly used to create
154:
82:materials are described as
10:
7463:
7328:(for 1824, printed 1827),
6619:"Birefringent_ Polarizers"
6375:December 14, 2013, at the
6339:1960 (Pergamon Press), §79
6304:Ehlers, Ernest G. (1987).
6294:, 2021 (open access).
6206:. Olympus Life Science Inc
5965:, it is satisfied for two
1999:scanning laser polarimetry
1874:-polarized light into the
1836:second-harmonic generation
1800:, the most common sort of
936:fiber-optic communications
6960:Biomedical Optics Express
6855:Biomedical Optics Express
6778:Biomedical Optics Express
6400:The Physics Hypertextbook
3097:is easiest done by using
2692:to the left hand side of
2129:
1932:monosodium urate crystals
769:materials in a few ways:
7415:University of Nottingham
6492:J. Colloid Interface Sci
6164:
2423:is the position vector,
882:. Due to their specific
7369:vol. 3 (1870)
7365:vol. 2 (1868)
7361:vol. 1 (1866)
6689:10.1093/labmed/14.6.382
5862:. The second defines a
5831:to zero will define an
2825:The right hand side of
2138:Surface of the allowed
1995:anisometropic amblyopia
1798:Liquid-crystal displays
850:circularly birefringent
509:dielectric polarization
66:of a material having a
5803:
5412:
4922:
4881:
4818:
4310:
4103:
3896:
3684:are the components of
3651:are the components of
3602:
3264:
3031:
2968:
2803:
2653:
2592:
2395:
2268:
2149:
2105:
2062:
2026:uses birefringence on
1788:
1781:liquid-crystal display
1753:can be measured using
875:
855:circular polarizations
825:Circular birefringence
762:
558:
304:reflection coefficient
293:
150:
56:
28:
7401:Merrifield, Michael.
7204:"Full Poincaré beams"
6413:Neves, N. M. (1998).
6394:Elert, Glenn (2021).
6350:plane of polarization
5804:
5413:
4923:
4882:
4819:
4311:
4104:
3897:
3603:
3265:
3099:Cartesian coordinates
3032:
2969:
2804:
2654:
2593:
2396:
2298:magnetic permeability
2269:
2181:where the material's
2154:electric displacement
2137:
2095:
2053:
1993:and possibly also of
1936:Calcium pyrophosphate
1778:
951:magnetic permeability
873:
756:
641:corresponding to the
624:corresponding to the
576:A material is termed
555:
373:circular polarization
294:
148:
135:Augustin-Jean Fresnel
34:
22:
7437:Polarization (waves)
7314:Principles of Optics
7229:10.1364/OE.18.010777
7080:10.3390/biom13081230
6924:10.1167/iovs.03-1160
6867:10.1364/BOE.4.002296
6652:10.1364/OIC.2001.FA2
6646:. OSA. p. FA2.
6113:Cotton–Mouton effect
5866:symmetric about the
5488:
4937:
4891:
4850:
4379:
4131:
3924:
3717:
3370:
3140:
3005:
2865:
2722:
2629:
2518:
2330:
2243:
775:Stress birefringence
757:View from under the
701:Positive or negative
563:electromagnetic wave
246:
70:that depends on the
7220:2010OExpr..1810777B
7214:(10): 10777–10785.
7030:2024OptLE.17207838A
6811:– via Optica.
6677:Laboratory Medicine
6564:1984JRheo..28...61F
6552:Journal of Rheology
6504:1988JCIS..124..403S
6226:Erasmus Bartholin,
5758:
5741:
5719:
5702:
5680:
5663:
5607:
5590:
5568:
5551:
5529:
5512:
5396:
5378:
5360:
5332:
5317:
5301:
5278:
5263:
5247:
5224:
5209:
5193:
5161:
5145:
5127:
5104:
5088:
5070:
5047:
5031:
5013:
4781:
4750:
4732:
4621:
4590:
4572:
4461:
4430:
4412:
4271:
4240:
4222:
4031:
4000:
3982:
3791:
3760:
3742:
3574:
3464:
3431:
3413:
3395:
3251:
3217:
3183:
2479:, we can eliminate
2463:Maxwell's equations
2216:index of refraction
1825:Glan–Thompson prism
1391:
978:
834:enantiomeric excess
767:optically isotropic
205:direction-dependent
7442:Optical mineralogy
7342:Scientific Memoirs
7272:Progress in Optics
6973:10.1364/BOE.426079
6791:10.1364/BOE.446169
6728:10.1136/emj.1.2.89
6461:10.1007/bf00508652
5913:wavevector surface
5799:
5742:
5727:
5703:
5688:
5664:
5649:
5591:
5576:
5552:
5537:
5513:
5498:
5440:direction so that
5408:
5382:
5364:
5346:
5318:
5303:
5287:
5264:
5249:
5233:
5210:
5195:
5179:
5147:
5131:
5113:
5090:
5074:
5056:
5033:
5017:
4999:
4918:
4877:
4814:
4802:
4767:
4736:
4718:
4607:
4576:
4558:
4447:
4416:
4398:
4306:
4257:
4226:
4208:
4099:
4017:
3986:
3968:
3892:
3777:
3746:
3728:
3598:
3560:
3450:
3417:
3399:
3381:
3260:
3254:
3237:
3203:
3169:
3027:
2964:
2799:
2649:
2588:
2391:
2264:
2150:
2106:
2063:
1866:) oriented in the
1802:flat-panel display
1789:
1731:circular dichroism
1389:
1320:(complex silicate)
1163:magnesium fluoride
976:
884:crystal structures
876:
808:molecules such as
763:
673:Fast and slow rays
559:
496:plane of incidence
369:quarter-wave plate
289:
161:Uniaxial materials
151:
96:crystal structures
78:. These optically
57:
43:than light in the
29:
7334:pp. 479–596
6861:(11): 2296–2306.
6661:978-1-55752-682-3
6536:978-0-19-958771-1
6434:10.1002/pen.10347
6428:(10): 1770–1777.
6091:vectors, and the
5823:
5822:
5786:
5759:
5720:
5681:
5635:
5608:
5569:
5530:
5432:
5431:
5334:
5280:
5226:
5162:
5105:
5048:
4989:
4962:
4916:
4875:
4838:
4837:
4793:
4633:
4473:
4330:
4329:
4283:
4123:
4122:
4043:
3916:
3915:
3803:
3622:
3621:
3586:
3284:
3283:
3051:
3050:
2988:
2987:
2823:
2822:
2673:
2672:
2612:
2611:
2581:
2415:
2414:
2288:
2287:
2074:injection molding
2070:mechanical stress
2056:mechanical stress
1829:Glan–Taylor prism
1717:
1716:
1710:
1709:
1385:
1384:
1364:zircon, low ZrSiO
901:is birefringent.
571:extraordinary ray
521:inhomogenous wave
473:unpolarized light
466:Double refraction
379:Biaxial materials
201:extraordinary ray
115:double refraction
104:mechanical stress
7454:
7418:
7354:
7347:
7330:pp. 45–176
7327:
7299:
7297:
7295:
7281:
7279:
7268:
7259:
7256:
7250:
7249:
7231:
7199:
7193:
7192:
7182:
7158:
7152:
7151:
7141:
7117:
7111:
7110:
7100:
7082:
7058:
7052:
7051:
7041:
7009:
7003:
7002:
6992:
6967:(7): 4340–4362.
6950:
6944:
6943:
6918:(8): 2606–2612.
6903:
6897:
6896:
6886:
6846:
6840:
6839:
6819:
6813:
6812:
6802:
6785:(3): 1386–1397.
6768:
6762:
6756:
6750:
6749:
6739:
6707:
6701:
6700:
6672:
6666:
6665:
6639:
6633:
6632:
6630:
6629:
6615:
6609:
6608:
6606:
6582:
6576:
6575:
6572:10.1122/1.549768
6547:
6541:
6540:
6522:
6516:
6515:
6487:
6481:
6480:
6444:
6438:
6437:
6419:
6410:
6404:
6403:
6391:
6380:
6363:
6357:
6346:
6340:
6335:, Vol. 8 of the
6329:
6320:
6319:
6301:
6295:
6293:
6278:
6272:
6270:
6255:
6249:
6221:
6215:
6214:
6212:
6211:
6199:
6182:
6175:
6143:Optical rotation
6096:
6090:
6078:
6060:
6046:
6044:
6032:
6026:
6020:
6013:
6004:
5995:
5978:
5976:
5964:
5963:
5961:
5960:
5958:
5951:
5948:
5938:
5932:
5920:
5910:
5901:
5895:
5889:
5880:
5871:
5861:
5855:
5846:
5840:
5817:
5808:
5806:
5805:
5800:
5792:
5788:
5787:
5785:
5784:
5775:
5774:
5765:
5760:
5757:
5752:
5751:
5740:
5735:
5726:
5721:
5718:
5713:
5712:
5701:
5696:
5687:
5682:
5679:
5674:
5673:
5662:
5657:
5648:
5641:
5637:
5636:
5634:
5633:
5624:
5623:
5614:
5609:
5606:
5601:
5600:
5589:
5584:
5575:
5570:
5567:
5562:
5561:
5550:
5545:
5536:
5531:
5528:
5523:
5522:
5511:
5506:
5497:
5482:
5478:
5462:
5439:
5426:
5417:
5415:
5414:
5409:
5401:
5397:
5395:
5390:
5377:
5372:
5359:
5354:
5340:
5336:
5335:
5333:
5331:
5326:
5316:
5311:
5300:
5295:
5286:
5281:
5279:
5277:
5272:
5262:
5257:
5246:
5241:
5232:
5227:
5225:
5223:
5218:
5208:
5203:
5192:
5187:
5178:
5168:
5164:
5163:
5160:
5155:
5146:
5144:
5139:
5126:
5121:
5111:
5106:
5103:
5098:
5089:
5087:
5082:
5069:
5064:
5054:
5049:
5046:
5041:
5032:
5030:
5025:
5012:
5007:
4997:
4990:
4988:
4987:
4978:
4977:
4968:
4963:
4961:
4960:
4951:
4950:
4941:
4931:
4927:
4925:
4924:
4919:
4917:
4915:
4914:
4905:
4904:
4895:
4886:
4884:
4883:
4878:
4876:
4874:
4873:
4864:
4863:
4854:
4832:
4823:
4821:
4820:
4815:
4807:
4806:
4799:
4795:
4794:
4792:
4791:
4782:
4780:
4775:
4766:
4765:
4755:
4749:
4744:
4731:
4726:
4707:
4706:
4697:
4696:
4685:
4684:
4675:
4674:
4661:
4660:
4651:
4650:
4639:
4635:
4634:
4632:
4631:
4622:
4620:
4615:
4606:
4605:
4595:
4589:
4584:
4571:
4566:
4547:
4546:
4537:
4536:
4523:
4522:
4513:
4512:
4501:
4500:
4491:
4490:
4479:
4475:
4474:
4472:
4471:
4462:
4460:
4455:
4446:
4445:
4435:
4429:
4424:
4411:
4406:
4373:
4365:
4358:
4349:
4340:
4324:
4315:
4313:
4312:
4307:
4299:
4298:
4289:
4285:
4284:
4282:
4281:
4272:
4270:
4265:
4256:
4255:
4245:
4239:
4234:
4221:
4216:
4196:
4195:
4186:
4185:
4176:
4175:
4163:
4162:
4153:
4152:
4143:
4142:
4125:
4117:
4108:
4106:
4105:
4100:
4092:
4091:
4082:
4081:
4072:
4071:
4059:
4058:
4049:
4045:
4044:
4042:
4041:
4032:
4030:
4025:
4016:
4015:
4005:
3999:
3994:
3981:
3976:
3956:
3955:
3946:
3945:
3936:
3935:
3918:
3910:
3901:
3899:
3898:
3893:
3885:
3884:
3875:
3874:
3865:
3864:
3852:
3851:
3842:
3841:
3832:
3831:
3819:
3818:
3809:
3805:
3804:
3802:
3801:
3792:
3790:
3785:
3776:
3775:
3765:
3759:
3754:
3741:
3736:
3711:
3701:
3695:
3689:
3683:
3674:
3665:
3656:
3650:
3641:
3632:
3616:
3607:
3605:
3604:
3599:
3597:
3596:
3587:
3585:
3584:
3575:
3573:
3568:
3559:
3558:
3548:
3540:
3539:
3530:
3529:
3520:
3519:
3507:
3506:
3497:
3496:
3487:
3486:
3474:
3473:
3463:
3458:
3446:
3445:
3436:
3432:
3430:
3425:
3412:
3407:
3394:
3389:
3364:
3354:
3348:
3347:
3345:
3344:
3330:
3327:
3315:
3309:
3303:
3297:
3291:
3278:
3269:
3267:
3266:
3261:
3259:
3258:
3250:
3245:
3216:
3211:
3182:
3177:
3160:
3159:
3147:
3134:
3130:
3124:
3118:
3112:
3106:
3096:
3090:
3075:
3069:
3063:
3045:
3036:
3034:
3033:
3028:
3020:
3012:
2999:
2982:
2973:
2971:
2970:
2965:
2960:
2955:
2947:
2946:
2937:
2936:
2921:
2913:
2905:
2894:
2886:
2878:
2859:
2849:
2842:
2836:
2817:
2808:
2806:
2805:
2800:
2798:
2790:
2782:
2771:
2763:
2755:
2744:
2716:
2712:
2703:
2691:
2667:
2658:
2656:
2655:
2650:
2642:
2623:
2619:
2606:
2597:
2595:
2594:
2589:
2587:
2582:
2580:
2579:
2578:
2565:
2564:
2555:
2553:
2552:
2540:
2512:
2508:
2504:
2502:
2501:
2493:
2490:
2478:
2471:
2460:
2451:
2444:
2437:
2428:
2422:
2409:
2400:
2398:
2397:
2392:
2390:
2389:
2376:
2368:
2352:
2351:
2346:
2337:
2324:
2320:
2314:
2295:
2282:
2273:
2271:
2270:
2265:
2263:
2258:
2250:
2237:
2229:
2223:
2213:
2207:
2189:
2180:
2167:
2161:
1898:
1889:
1877:
1873:
1869:
1861:
1806:light modulators
1727:optical rotation
1428:
1418:
1408:
1392:
1388:
1015:
1007:
997:
979:
975:
972:
967:
932:pulse broadening
859:optical activity
799:nonlinear optics
759:Sky Pool, London
743:
722:
713:
644:
640:
631:
627:
623:
607:
598:
589:
505:
501:
481:refractive index
456:optical ray axes
445:optical axes or
433:
424:
415:
397:index ellipsoids
358:
333:
324:
314:
298:
296:
295:
290:
284:
283:
282:
269:
268:
267:
234:
225:
216:
198:
185:
123:Rasmus Bartholin
68:refractive index
64:optical property
50:
46:
41:refractive index
38:
7462:
7461:
7457:
7456:
7455:
7453:
7452:
7451:
7427:
7426:
7403:"Birefringence"
7378:
7352:
7351:A. Fresnel (ed.
7345:
7325:
7308:
7303:
7302:
7293:
7291:
7277:
7275:
7269:
7262:
7257:
7253:
7200:
7196:
7159:
7155:
7118:
7114:
7059:
7055:
7010:
7006:
6951:
6947:
6904:
6900:
6847:
6843:
6820:
6816:
6769:
6765:
6757:
6753:
6708:
6704:
6673:
6669:
6662:
6640:
6636:
6627:
6625:
6617:
6616:
6612:
6597:(1–3): 79–110.
6583:
6579:
6548:
6544:
6537:
6523:
6519:
6488:
6484:
6445:
6441:
6417:
6411:
6407:
6392:
6383:
6377:Wayback Machine
6364:
6360:
6352:" is the plane
6347:
6343:
6330:
6323:
6316:
6302:
6298:
6279:
6275:
6256:
6252:
6222:
6218:
6209:
6207:
6200:
6196:
6191:
6186:
6185:
6179:index ellipsoid
6176:
6172:
6167:
6162:
6148:Periodic poling
6133:Index ellipsoid
6108:
6092:
6086:
6074:
6056:
6040:
6038:
6028:
6022:
6016:
6011:
6006:
6002:
5997:
5993:
5988:
5972:
5970:
5954:
5952:
5949:
5944:
5943:
5941:
5940:
5934:
5928:
5916:
5906:
5897:
5891:
5888:
5882:
5879:
5873:
5867:
5857:
5854:
5848:
5842:
5836:
5780:
5776:
5770:
5766:
5764:
5753:
5747:
5746:
5736:
5731:
5725:
5714:
5708:
5707:
5697:
5692:
5686:
5675:
5669:
5668:
5658:
5653:
5647:
5646:
5642:
5629:
5625:
5619:
5615:
5613:
5602:
5596:
5595:
5585:
5580:
5574:
5563:
5557:
5556:
5546:
5541:
5535:
5524:
5518:
5517:
5507:
5502:
5496:
5495:
5491:
5489:
5486:
5485:
5477:
5469:
5464:
5461:
5453:
5446:
5441:
5435:
5391:
5386:
5373:
5368:
5355:
5350:
5345:
5341:
5327:
5322:
5312:
5307:
5302:
5296:
5291:
5285:
5273:
5268:
5258:
5253:
5248:
5242:
5237:
5231:
5219:
5214:
5204:
5199:
5194:
5188:
5183:
5177:
5176:
5172:
5156:
5151:
5140:
5135:
5122:
5117:
5112:
5110:
5099:
5094:
5083:
5078:
5065:
5060:
5055:
5053:
5042:
5037:
5026:
5021:
5008:
5003:
4998:
4996:
4995:
4991:
4983:
4979:
4973:
4969:
4967:
4956:
4952:
4946:
4942:
4940:
4938:
4935:
4934:
4910:
4906:
4900:
4896:
4894:
4892:
4889:
4888:
4869:
4865:
4859:
4855:
4853:
4851:
4848:
4847:
4801:
4800:
4787:
4783:
4776:
4771:
4761:
4757:
4756:
4754:
4745:
4740:
4727:
4722:
4714:
4710:
4708:
4702:
4698:
4692:
4688:
4686:
4680:
4676:
4670:
4666:
4663:
4662:
4656:
4652:
4646:
4642:
4640:
4627:
4623:
4616:
4611:
4601:
4597:
4596:
4594:
4585:
4580:
4567:
4562:
4554:
4550:
4548:
4542:
4538:
4532:
4528:
4525:
4524:
4518:
4514:
4508:
4504:
4502:
4496:
4492:
4486:
4482:
4480:
4467:
4463:
4456:
4451:
4441:
4437:
4436:
4434:
4425:
4420:
4407:
4402:
4394:
4390:
4383:
4382:
4380:
4377:
4376:
4360:
4356:
4351:
4347:
4342:
4338:
4333:
4294:
4290:
4277:
4273:
4266:
4261:
4251:
4247:
4246:
4244:
4235:
4230:
4217:
4212:
4204:
4200:
4191:
4187:
4181:
4177:
4171:
4167:
4158:
4154:
4148:
4144:
4138:
4134:
4132:
4129:
4128:
4087:
4083:
4077:
4073:
4067:
4063:
4054:
4050:
4037:
4033:
4026:
4021:
4011:
4007:
4006:
4004:
3995:
3990:
3977:
3972:
3964:
3960:
3951:
3947:
3941:
3937:
3931:
3927:
3925:
3922:
3921:
3880:
3876:
3870:
3866:
3860:
3856:
3847:
3843:
3837:
3833:
3827:
3823:
3814:
3810:
3797:
3793:
3786:
3781:
3771:
3767:
3766:
3764:
3755:
3750:
3737:
3732:
3724:
3720:
3718:
3715:
3714:
3697:
3691:
3685:
3681:
3676:
3672:
3667:
3663:
3658:
3652:
3648:
3643:
3639:
3634:
3630:
3625:
3592:
3588:
3580:
3576:
3569:
3564:
3554:
3550:
3549:
3547:
3535:
3531:
3525:
3521:
3515:
3511:
3502:
3498:
3492:
3488:
3482:
3478:
3469:
3465:
3459:
3454:
3441:
3437:
3426:
3421:
3408:
3403:
3390:
3385:
3377:
3373:
3371:
3368:
3367:
3350:
3343:
3337:
3331:
3328:
3325:
3324:
3322:
3317:
3311:
3305:
3299:
3293:
3287:
3253:
3252:
3246:
3241:
3235:
3230:
3224:
3223:
3218:
3212:
3207:
3201:
3195:
3194:
3189:
3184:
3178:
3173:
3162:
3161:
3155:
3151:
3143:
3141:
3138:
3137:
3126:
3120:
3114:
3108:
3102:
3092:
3086:
3071:
3065:
3059:
3058:indicates that
3016:
3008:
3006:
3003:
3002:
2956:
2951:
2942:
2938:
2932:
2928:
2917:
2909:
2901:
2890:
2882:
2874:
2866:
2863:
2862:
2844:
2838:
2832:
2794:
2786:
2778:
2767:
2759:
2751:
2740:
2723:
2720:
2719:
2710:
2705:
2699:
2676:
2638:
2630:
2627:
2626:
2615:
2583:
2574:
2570:
2566:
2560:
2556:
2554:
2548:
2544:
2536:
2519:
2516:
2515:
2500:
2494:
2491:
2488:
2487:
2485:
2480:
2473:
2466:
2461:. By combining
2456:
2446:
2439:
2436:
2430:
2424:
2418:
2372:
2364:
2357:
2353:
2347:
2342:
2341:
2333:
2331:
2328:
2327:
2316:
2312:
2301:
2300:in the medium:
2291:
2259:
2254:
2246:
2244:
2241:
2240:
2225:
2219:
2209:
2205:
2195:
2185:
2169:
2168:) according to
2163:
2157:
2132:
2090:
2078:photoelasticity
2048:
1924:
1923:
1922:
1921:
1901:
1900:
1899:
1891:
1890:
1875:
1871:
1867:
1859:
1852:
1794:
1792:Optical devices
1773:
1723:
1718:
1691:
1687:
1683:
1679:
1654:
1650:
1646:
1620:
1594:
1590:
1565:
1561:
1557:
1553:
1527:
1523:
1519:
1515:
1485:
1481:
1455:
1451:
1447:
1443:
1439:
1427:
1421:
1417:
1411:
1407:
1401:
1398:Crystal system
1367:
1345:
1296:silicon carbide
1276:
1272:
1247:
1222:
1218:
1193:
1168:
1143:
1138:lithium niobate
1117:
1092:
1067:
1063:
1059:
1055:
1030:
1026:
1010:
1006:
1000:
996:
990:
965:
954:
868:
818:liquid crystals
751:
742:
735:
724:
721:
715:
712:
706:
703:
675:
642:
639:
633:
629:
625:
622:
615:
609:
606:
600:
597:
591:
588:
582:
550:
517:Poynting vector
503:
499:
485:Wollaston prism
468:
432:
426:
423:
417:
414:
408:
381:
357:
351:
336:Poynting vector
332:
326:
323:
317:
313:
307:
278:
277:
273:
263:
262:
258:
247:
244:
243:
237:index ellipsoid
233:
227:
224:
218:
215:
209:
197:
191:
184:
178:
163:
143:
94:with non-cubic
48:
44:
36:
17:
12:
11:
5:
7460:
7450:
7449:
7444:
7439:
7425:
7424:
7419:
7398:
7393:
7388:
7384:
7377:
7376:External links
7374:
7373:
7372:
7349:
7318:
7307:
7304:
7301:
7300:
7260:
7251:
7208:Optics Express
7194:
7173:(3): 913–920.
7167:Fertil. Steril
7153:
7132:(3): 807–813.
7126:Fertil. Steril
7112:
7053:
7004:
6945:
6898:
6841:
6814:
6763:
6751:
6716:Arch Emerg Med
6702:
6667:
6660:
6634:
6610:
6577:
6542:
6535:
6517:
6498:(2): 403–407.
6482:
6449:Histochemistry
6439:
6405:
6381:
6358:
6341:
6321:
6314:
6296:
6273:
6250:
6248:
6247:
6233:
6216:
6193:
6192:
6190:
6187:
6184:
6183:
6169:
6168:
6166:
6163:
6161:
6160:
6155:
6150:
6145:
6140:
6135:
6130:
6125:
6120:
6118:Crystal optics
6115:
6109:
6107:
6104:
6009:
6000:
5991:
5886:
5877:
5852:
5821:
5820:
5811:
5809:
5798:
5795:
5791:
5783:
5779:
5773:
5769:
5763:
5756:
5750:
5745:
5739:
5734:
5730:
5724:
5717:
5711:
5706:
5700:
5695:
5691:
5685:
5678:
5672:
5667:
5661:
5656:
5652:
5645:
5640:
5632:
5628:
5622:
5618:
5612:
5605:
5599:
5594:
5588:
5583:
5579:
5573:
5566:
5560:
5555:
5549:
5544:
5540:
5534:
5527:
5521:
5516:
5510:
5505:
5501:
5494:
5475:
5467:
5459:
5451:
5444:
5430:
5429:
5420:
5418:
5407:
5404:
5400:
5394:
5389:
5385:
5381:
5376:
5371:
5367:
5363:
5358:
5353:
5349:
5344:
5339:
5330:
5325:
5321:
5315:
5310:
5306:
5299:
5294:
5290:
5284:
5276:
5271:
5267:
5261:
5256:
5252:
5245:
5240:
5236:
5230:
5222:
5217:
5213:
5207:
5202:
5198:
5191:
5186:
5182:
5175:
5171:
5167:
5159:
5154:
5150:
5143:
5138:
5134:
5130:
5125:
5120:
5116:
5109:
5102:
5097:
5093:
5086:
5081:
5077:
5073:
5068:
5063:
5059:
5052:
5045:
5040:
5036:
5029:
5024:
5020:
5016:
5011:
5006:
5002:
4994:
4986:
4982:
4976:
4972:
4966:
4959:
4955:
4949:
4945:
4913:
4909:
4903:
4899:
4872:
4868:
4862:
4858:
4836:
4835:
4826:
4824:
4813:
4810:
4805:
4798:
4790:
4786:
4779:
4774:
4770:
4764:
4760:
4753:
4748:
4743:
4739:
4735:
4730:
4725:
4721:
4717:
4713:
4709:
4705:
4701:
4695:
4691:
4687:
4683:
4679:
4673:
4669:
4665:
4664:
4659:
4655:
4649:
4645:
4641:
4638:
4630:
4626:
4619:
4614:
4610:
4604:
4600:
4593:
4588:
4583:
4579:
4575:
4570:
4565:
4561:
4557:
4553:
4549:
4545:
4541:
4535:
4531:
4527:
4526:
4521:
4517:
4511:
4507:
4503:
4499:
4495:
4489:
4485:
4481:
4478:
4470:
4466:
4459:
4454:
4450:
4444:
4440:
4433:
4428:
4423:
4419:
4415:
4410:
4405:
4401:
4397:
4393:
4389:
4388:
4386:
4354:
4345:
4336:
4328:
4327:
4318:
4316:
4305:
4302:
4297:
4293:
4288:
4280:
4276:
4269:
4264:
4260:
4254:
4250:
4243:
4238:
4233:
4229:
4225:
4220:
4215:
4211:
4207:
4203:
4199:
4194:
4190:
4184:
4180:
4174:
4170:
4166:
4161:
4157:
4151:
4147:
4141:
4137:
4121:
4120:
4111:
4109:
4098:
4095:
4090:
4086:
4080:
4076:
4070:
4066:
4062:
4057:
4053:
4048:
4040:
4036:
4029:
4024:
4020:
4014:
4010:
4003:
3998:
3993:
3989:
3985:
3980:
3975:
3971:
3967:
3963:
3959:
3954:
3950:
3944:
3940:
3934:
3930:
3914:
3913:
3904:
3902:
3891:
3888:
3883:
3879:
3873:
3869:
3863:
3859:
3855:
3850:
3846:
3840:
3836:
3830:
3826:
3822:
3817:
3813:
3808:
3800:
3796:
3789:
3784:
3780:
3774:
3770:
3763:
3758:
3753:
3749:
3745:
3740:
3735:
3731:
3727:
3723:
3702:components of
3679:
3670:
3661:
3646:
3637:
3628:
3620:
3619:
3610:
3608:
3595:
3591:
3583:
3579:
3572:
3567:
3563:
3557:
3553:
3546:
3543:
3538:
3534:
3528:
3524:
3518:
3514:
3510:
3505:
3501:
3495:
3491:
3485:
3481:
3477:
3472:
3468:
3462:
3457:
3453:
3449:
3444:
3440:
3435:
3429:
3424:
3420:
3416:
3411:
3406:
3402:
3398:
3393:
3388:
3384:
3380:
3376:
3341:
3335:
3282:
3281:
3272:
3270:
3257:
3249:
3244:
3240:
3236:
3234:
3231:
3229:
3226:
3225:
3222:
3219:
3215:
3210:
3206:
3202:
3200:
3197:
3196:
3193:
3190:
3188:
3185:
3181:
3176:
3172:
3168:
3167:
3165:
3158:
3154:
3150:
3146:
3049:
3048:
3039:
3037:
3026:
3023:
3019:
3015:
3011:
2986:
2985:
2976:
2974:
2963:
2959:
2954:
2950:
2945:
2941:
2935:
2931:
2927:
2924:
2920:
2916:
2912:
2908:
2904:
2900:
2897:
2893:
2889:
2885:
2881:
2877:
2873:
2870:
2856:then becomes:
2821:
2820:
2811:
2809:
2797:
2793:
2789:
2785:
2781:
2777:
2774:
2770:
2766:
2762:
2758:
2754:
2750:
2747:
2743:
2739:
2736:
2733:
2730:
2727:
2708:
2671:
2670:
2661:
2659:
2648:
2645:
2641:
2637:
2634:
2610:
2609:
2600:
2598:
2586:
2577:
2573:
2569:
2563:
2559:
2551:
2547:
2543:
2539:
2535:
2532:
2529:
2526:
2523:
2498:
2434:
2413:
2412:
2403:
2401:
2388:
2385:
2382:
2379:
2375:
2371:
2367:
2363:
2360:
2356:
2350:
2345:
2340:
2336:
2310:
2286:
2285:
2276:
2274:
2262:
2257:
2253:
2249:
2203:
2194:(and equal to
2131:
2128:
2089:
2086:
2082:optical vortex
2047:
2044:
1960:immunoglobulin
1903:
1902:
1893:
1892:
1884:
1883:
1882:
1881:
1880:
1851:
1848:
1844:phase matching
1793:
1790:
1772:
1769:
1751:lipid bilayers
1729:and linear or
1722:
1719:
1715:
1714:
1708:
1707:
1704:
1701:
1698:
1693:
1689:
1685:
1681:
1677:
1670:
1669:
1666:
1663:
1660:
1655:
1652:
1648:
1644:
1637:
1636:
1633:
1630:
1627:
1622:
1618:
1610:
1609:
1606:
1603:
1600:
1595:
1592:
1588:
1581:
1580:
1577:
1574:
1571:
1566:
1563:
1559:
1555:
1551:
1543:
1542:
1539:
1536:
1533:
1528:
1525:
1521:
1517:
1513:
1502:
1501:
1498:
1495:
1492:
1487:
1483:
1479:
1472:
1471:
1468:
1465:
1462:
1457:
1453:
1449:
1445:
1441:
1437:
1430:
1429:
1425:
1419:
1415:
1409:
1405:
1399:
1396:
1386:
1383:
1382:
1379:
1376:
1373:
1368:
1365:
1361:
1360:
1357:
1354:
1351:
1346:
1343:
1336:
1335:
1332:
1329:
1326:
1321:
1314:
1313:
1310:
1307:
1304:
1299:
1292:
1291:
1288:
1285:
1282:
1277:
1274:
1270:
1263:
1262:
1259:
1256:
1253:
1248:
1245:
1238:
1237:
1234:
1231:
1228:
1223:
1220:
1216:
1209:
1208:
1205:
1202:
1199:
1194:
1191:
1184:
1183:
1180:
1177:
1174:
1169:
1166:
1159:
1158:
1155:
1152:
1149:
1144:
1141:
1134:
1133:
1130:
1127:
1124:
1119:
1115:
1108:
1107:
1104:
1101:
1098:
1093:
1090:
1083:
1082:
1079:
1076:
1073:
1068:
1065:
1061:
1057:
1053:
1046:
1045:
1042:
1039:
1036:
1031:
1028:
1024:
1017:
1016:
1008:
1004:
998:
994:
988:
986:Crystal system
983:
970:
963:
867:
864:
863:
862:
857:), similar to
845:Faraday effect
841:
838:stereo isomers
821:
802:
787:
779:
750:
747:
740:
733:
719:
710:
702:
699:
674:
671:
649:in this case.
637:
620:
613:
604:
595:
586:
549:
546:
513:electric field
467:
464:
430:
421:
412:
380:
377:
355:
330:
321:
311:
300:
299:
288:
281:
276:
272:
266:
261:
257:
254:
251:
231:
222:
213:
195:
182:
162:
159:
142:
139:
15:
9:
6:
4:
3:
2:
7459:
7448:
7445:
7443:
7440:
7438:
7435:
7434:
7432:
7423:
7420:
7416:
7412:
7408:
7407:Sixty Symbols
7404:
7399:
7397:
7394:
7392:
7389:
7387:
7385:
7383:
7380:
7379:
7370:
7366:
7362:
7358:
7350:
7344:, vol.
7343:
7339:
7335:
7331:
7324:, vol.
7323:
7319:
7316:
7315:
7310:
7309:
7289:
7285:
7273:
7267:
7265:
7255:
7247:
7243:
7239:
7235:
7230:
7225:
7221:
7217:
7213:
7209:
7205:
7198:
7190:
7186:
7181:
7176:
7172:
7168:
7164:
7157:
7149:
7145:
7140:
7135:
7131:
7127:
7123:
7116:
7108:
7104:
7099:
7094:
7090:
7086:
7081:
7076:
7072:
7068:
7064:
7057:
7049:
7045:
7040:
7035:
7031:
7027:
7023:
7019:
7015:
7008:
7000:
6996:
6991:
6986:
6982:
6978:
6974:
6970:
6966:
6962:
6961:
6956:
6949:
6941:
6937:
6933:
6929:
6925:
6921:
6917:
6913:
6909:
6902:
6894:
6890:
6885:
6880:
6876:
6872:
6868:
6864:
6860:
6856:
6852:
6845:
6837:
6833:
6829:
6825:
6818:
6810:
6806:
6801:
6796:
6792:
6788:
6784:
6780:
6779:
6774:
6767:
6760:
6755:
6747:
6743:
6738:
6733:
6729:
6725:
6721:
6717:
6713:
6706:
6698:
6694:
6690:
6686:
6682:
6678:
6671:
6663:
6657:
6653:
6649:
6645:
6638:
6624:
6620:
6614:
6605:
6600:
6596:
6592:
6588:
6581:
6573:
6569:
6565:
6561:
6557:
6553:
6546:
6538:
6532:
6528:
6521:
6513:
6509:
6505:
6501:
6497:
6493:
6486:
6478:
6474:
6470:
6466:
6462:
6458:
6454:
6450:
6443:
6435:
6431:
6427:
6423:
6416:
6409:
6401:
6397:
6390:
6388:
6386:
6378:
6374:
6371:
6367:
6362:
6355:
6354:perpendicular
6351:
6345:
6338:
6334:
6328:
6326:
6317:
6315:0-86542-323-7
6311:
6307:
6300:
6292:
6287:
6283:
6277:
6269:
6264:
6260:
6254:
6245:
6241:
6238:
6234:
6231:
6230:
6225:
6224:
6220:
6205:
6198:
6194:
6180:
6174:
6170:
6159:
6156:
6154:
6151:
6149:
6146:
6144:
6141:
6139:
6136:
6134:
6131:
6129:
6126:
6124:
6121:
6119:
6116:
6114:
6111:
6110:
6103:
6100:
6095:
6089:
6084:
6083:
6077:
6072:
6067:
6062:
6059:
6054:
6050:
6043:
6035:
6031:
6025:
6019:
6012:
6003:
5994:
5986:
5980:
5975:
5968:
5957:
5947:
5937:
5931:
5926:
5925:
5919:
5914:
5911:vectors (the
5909:
5903:
5900:
5894:
5885:
5876:
5870:
5865:
5860:
5851:
5845:
5839:
5834:
5830:
5829:
5819:
5812:
5810:
5796:
5793:
5789:
5781:
5777:
5771:
5767:
5761:
5754:
5743:
5737:
5732:
5728:
5722:
5715:
5704:
5698:
5693:
5689:
5683:
5676:
5665:
5659:
5654:
5650:
5643:
5638:
5630:
5626:
5620:
5616:
5610:
5603:
5592:
5586:
5581:
5577:
5571:
5564:
5553:
5547:
5542:
5538:
5532:
5525:
5514:
5508:
5503:
5499:
5492:
5484:
5483:
5480:
5474:
5470:
5458:
5454:
5447:
5438:
5428:
5421:
5419:
5405:
5402:
5398:
5392:
5387:
5383:
5379:
5374:
5369:
5365:
5361:
5356:
5351:
5347:
5342:
5337:
5328:
5323:
5319:
5313:
5308:
5304:
5297:
5292:
5288:
5282:
5274:
5269:
5265:
5259:
5254:
5250:
5243:
5238:
5234:
5228:
5220:
5215:
5211:
5205:
5200:
5196:
5189:
5184:
5180:
5173:
5169:
5165:
5157:
5152:
5148:
5141:
5136:
5132:
5128:
5123:
5118:
5114:
5107:
5100:
5095:
5091:
5084:
5079:
5075:
5071:
5066:
5061:
5057:
5050:
5043:
5038:
5034:
5027:
5022:
5018:
5014:
5009:
5004:
5000:
4992:
4984:
4980:
4974:
4970:
4964:
4957:
4953:
4947:
4943:
4933:
4932:
4929:
4911:
4907:
4901:
4897:
4870:
4866:
4860:
4856:
4845:
4844:
4834:
4827:
4825:
4811:
4808:
4803:
4796:
4788:
4784:
4777:
4772:
4768:
4762:
4758:
4751:
4746:
4741:
4737:
4733:
4728:
4723:
4719:
4715:
4711:
4703:
4699:
4693:
4689:
4681:
4677:
4671:
4667:
4657:
4653:
4647:
4643:
4636:
4628:
4624:
4617:
4612:
4608:
4602:
4598:
4591:
4586:
4581:
4577:
4573:
4568:
4563:
4559:
4555:
4551:
4543:
4539:
4533:
4529:
4519:
4515:
4509:
4505:
4497:
4493:
4487:
4483:
4476:
4468:
4464:
4457:
4452:
4448:
4442:
4438:
4431:
4426:
4421:
4417:
4413:
4408:
4403:
4399:
4395:
4391:
4384:
4375:
4374:
4371:
4369:
4363:
4357:
4348:
4339:
4326:
4319:
4317:
4303:
4300:
4295:
4291:
4286:
4278:
4274:
4267:
4262:
4258:
4252:
4248:
4241:
4236:
4231:
4227:
4223:
4218:
4213:
4209:
4205:
4201:
4197:
4192:
4188:
4182:
4178:
4172:
4168:
4164:
4159:
4155:
4149:
4145:
4139:
4135:
4127:
4126:
4119:
4112:
4110:
4096:
4093:
4088:
4084:
4078:
4074:
4068:
4064:
4060:
4055:
4051:
4046:
4038:
4034:
4027:
4022:
4018:
4012:
4008:
4001:
3996:
3991:
3987:
3983:
3978:
3973:
3969:
3965:
3961:
3957:
3952:
3948:
3942:
3938:
3932:
3928:
3920:
3919:
3912:
3905:
3903:
3889:
3886:
3881:
3877:
3871:
3867:
3861:
3857:
3853:
3848:
3844:
3838:
3834:
3828:
3824:
3820:
3815:
3811:
3806:
3798:
3794:
3787:
3782:
3778:
3772:
3768:
3761:
3756:
3751:
3747:
3743:
3738:
3733:
3729:
3725:
3721:
3713:
3712:
3709:
3707:
3706:
3700:
3694:
3688:
3682:
3673:
3664:
3655:
3649:
3640:
3631:
3618:
3611:
3609:
3593:
3589:
3581:
3577:
3570:
3565:
3561:
3555:
3551:
3544:
3541:
3536:
3532:
3526:
3522:
3516:
3512:
3508:
3503:
3499:
3493:
3489:
3483:
3479:
3475:
3470:
3466:
3460:
3455:
3451:
3447:
3442:
3438:
3433:
3427:
3422:
3418:
3414:
3409:
3404:
3400:
3396:
3391:
3386:
3382:
3378:
3374:
3366:
3365:
3362:
3360:
3359:
3353:
3340:
3334:
3320:
3314:
3308:
3302:
3296:
3290:
3280:
3273:
3271:
3255:
3247:
3242:
3238:
3232:
3227:
3220:
3213:
3208:
3204:
3198:
3191:
3186:
3179:
3174:
3170:
3163:
3156:
3152:
3148:
3144:
3136:
3135:
3132:
3129:
3123:
3117:
3111:
3105:
3100:
3095:
3089:
3083:
3081:
3080:
3074:
3068:
3062:
3057:
3056:
3047:
3040:
3038:
3024:
3021:
3013:
3001:
3000:
2997:
2995:
2994:
2984:
2977:
2975:
2943:
2939:
2933:
2929:
2925:
2922:
2906:
2895:
2879:
2871:
2861:
2860:
2857:
2855:
2854:
2848:
2841:
2835:
2830:
2829:
2819:
2812:
2810:
2783:
2772:
2756:
2745:
2737:
2731:
2725:
2718:
2717:
2714:
2711:
2702:
2697:
2696:
2690:
2689:
2685:
2681:
2669:
2662:
2660:
2646:
2643:
2635:
2625:
2624:
2621:
2618:
2608:
2601:
2599:
2575:
2571:
2561:
2549:
2545:
2541:
2533:
2527:
2521:
2514:
2513:
2510:
2507:
2497:
2483:
2477:
2470:
2464:
2459:
2455:
2449:
2442:
2433:
2429:is time, and
2427:
2421:
2411:
2404:
2402:
2383:
2380:
2377:
2369:
2358:
2354:
2348:
2338:
2326:
2325:
2322:
2319:
2313:
2309:
2304:
2299:
2294:
2284:
2277:
2275:
2251:
2239:
2238:
2235:
2233:
2228:
2222:
2217:
2212:
2206:
2202:
2198:
2193:
2188:
2184:
2179:
2176:
2172:
2166:
2160:
2155:
2147:
2146:
2141:
2136:
2127:
2124:
2122:
2118:
2113:
2111:
2103:
2099:
2096:Birefringent
2094:
2085:
2083:
2079:
2075:
2071:
2067:
2061:
2057:
2052:
2043:
2041:
2035:
2033:
2029:
2025:
2024:
2019:
2015:
2010:
2008:
2004:
2000:
1996:
1992:
1988:
1984:
1980:
1979:ophthalmology
1975:
1973:
1969:
1965:
1961:
1957:
1953:
1948:
1946:
1940:
1937:
1933:
1929:
1919:
1916:(pseudogout,
1915:
1911:
1907:
1897:
1888:
1879:
1865:
1857:
1847:
1845:
1841:
1837:
1832:
1830:
1826:
1821:
1819:
1815:
1811:
1807:
1803:
1799:
1786:
1782:
1777:
1768:
1767:can be used.
1766:
1763:
1758:
1756:
1752:
1747:
1745:
1740:
1736:
1732:
1728:
1713:
1705:
1702:
1699:
1697:
1694:
1675:
1672:
1671:
1667:
1664:
1661:
1659:
1656:
1642:
1639:
1638:
1634:
1631:
1628:
1626:
1623:
1621:
1615:
1612:
1611:
1607:
1604:
1601:
1599:
1596:
1586:
1583:
1582:
1578:
1575:
1572:
1570:
1567:
1549:
1545:
1544:
1540:
1537:
1534:
1532:
1529:
1511:
1507:
1504:
1503:
1499:
1496:
1493:
1491:
1488:
1477:
1474:
1473:
1469:
1466:
1463:
1461:
1458:
1435:
1432:
1431:
1424:
1420:
1414:
1410:
1404:
1400:
1397:
1394:
1393:
1387:
1380:
1377:
1374:
1372:
1369:
1363:
1362:
1358:
1355:
1352:
1350:
1347:
1341:
1338:
1337:
1333:
1330:
1327:
1325:
1322:
1319:
1316:
1315:
1311:
1308:
1305:
1303:
1300:
1297:
1294:
1293:
1289:
1286:
1283:
1281:
1278:
1268:
1265:
1264:
1260:
1257:
1254:
1252:
1249:
1243:
1240:
1239:
1235:
1232:
1229:
1227:
1224:
1214:
1211:
1210:
1206:
1203:
1200:
1198:
1195:
1189:
1186:
1185:
1181:
1178:
1175:
1173:
1170:
1164:
1161:
1160:
1156:
1153:
1150:
1148:
1145:
1139:
1136:
1135:
1131:
1128:
1125:
1123:
1120:
1113:
1110:
1109:
1105:
1102:
1099:
1097:
1094:
1088:
1085:
1084:
1080:
1077:
1074:
1072:
1069:
1051:
1048:
1047:
1043:
1040:
1037:
1035:
1032:
1022:
1021:barium borate
1019:
1018:
1014:
1009:
1003:
999:
993:
989:
987:
984:
981:
980:
974:
973:
969:
966:
962:
957:
952:
947:
945:
941:
940:intentionally
937:
933:
929:
928:optical fiber
924:
920:
918:
914:
912:
911:polycarbonate
908:
904:
900:
896:
891:
889:
885:
881:
872:
860:
856:
852:
851:
846:
842:
839:
835:
831:
827:
826:
822:
819:
815:
811:
807:
803:
800:
796:
792:
788:
785:
780:
777:
776:
772:
771:
770:
768:
760:
755:
746:
739:
732:
728:
718:
709:
698:
696:
691:
689:
684:
680:
670:
668:
663:
659:
655:
650:
648:
636:
619:
612:
603:
594:
585:
579:
574:
572:
566:
564:
554:
545:
543:
539:
535:
531:
526:
522:
518:
514:
510:
497:
492:
490:
486:
482:
478:
474:
463:
461:
457:
453:
448:
444:
439:
438:a spheroid).
437:
429:
420:
411:
406:
402:
398:
393:
390:
386:
376:
374:
370:
366:
362:
354:
347:
345:
341:
337:
329:
320:
310:
305:
286:
274:
270:
259:
255:
252:
242:
241:
240:
238:
230:
221:
212:
206:
202:
194:
189:
181:
176:
175:perpendicular
172:
168:
158:
156:
147:
138:
136:
132:
128:
124:
120:
116:
112:
107:
105:
101:
97:
93:
89:
85:
81:
77:
73:
69:
65:
61:
60:Birefringence
54:
42:
33:
26:
21:
7406:
7356:
7341:
7321:
7312:
7306:Bibliography
7271:
7254:
7211:
7207:
7197:
7170:
7166:
7156:
7129:
7125:
7115:
7070:
7067:Biomolecules
7066:
7056:
7021:
7017:
7007:
6964:
6958:
6948:
6915:
6911:
6901:
6858:
6854:
6844:
6830:(4): e5–e6.
6827:
6823:
6817:
6782:
6776:
6766:
6754:
6722:(2): 89–95.
6719:
6715:
6705:
6680:
6676:
6670:
6643:
6637:
6626:. Retrieved
6622:
6613:
6594:
6590:
6580:
6558:(1): 61–70.
6555:
6551:
6545:
6526:
6520:
6495:
6491:
6485:
6455:(1): 41–49.
6452:
6448:
6442:
6425:
6421:
6408:
6399:
6396:"Refraction"
6365:
6361:
6353:
6344:
6336:
6332:
6305:
6299:
6281:
6276:
6258:
6253:
6243:
6239:
6228:
6219:
6208:. Retrieved
6197:
6173:
6128:Iceland spar
6098:
6093:
6087:
6080:
6075:
6070:
6065:
6063:
6057:
6048:
6041:
6036:
6029:
6023:
6017:
6007:
5998:
5989:
5984:
5981:
5973:
5955:
5945:
5935:
5929:
5922:
5917:
5912:
5907:
5904:
5898:
5892:
5883:
5874:
5868:
5858:
5849:
5843:
5837:
5826:
5824:
5813:
5472:
5465:
5456:
5449:
5442:
5436:
5433:
5422:
4841:
4839:
4828:
4361:
4352:
4343:
4334:
4331:
4320:
4113:
3906:
3703:
3698:
3692:
3686:
3677:
3668:
3659:
3653:
3644:
3635:
3626:
3623:
3612:
3356:
3351:
3338:
3332:
3318:
3312:
3306:
3300:
3294:
3288:
3285:
3274:
3127:
3121:
3115:
3109:
3103:
3093:
3091:for a given
3087:
3084:
3077:
3072:
3066:
3060:
3053:
3052:
3041:
2991:
2989:
2978:
2851:
2846:
2839:
2833:
2826:
2824:
2813:
2706:
2700:
2693:
2687:
2683:
2679:
2674:
2663:
2616:
2613:
2602:
2505:
2495:
2481:
2475:
2468:
2457:
2454:wave vectors
2447:
2440:
2431:
2425:
2419:
2416:
2405:
2317:
2307:
2302:
2292:
2289:
2278:
2226:
2220:
2210:
2200:
2196:
2186:
2183:permittivity
2177:
2174:
2170:
2164:
2158:
2151:
2143:
2139:
2125:
2114:
2107:
2101:
2064:
2036:
2023:zona imaging
2021:
2020:. Likewise,
2011:
1987:Henle fibers
1986:
1981:, binocular
1976:
1972:intercalates
1964:conformation
1949:
1941:
1925:
1917:
1905:
1863:
1853:
1833:
1822:
1795:
1771:Applications
1761:
1759:
1748:
1744:ellipsometry
1738:
1724:
1711:
1658:Orthorhombic
1625:Orthorhombic
1598:Orthorhombic
1422:
1412:
1402:
1342:, high ZrSiO
1012:
1001:
991:
960:
955:
948:
939:
925:
921:
915:
892:
877:
848:
823:
784:metamaterial
773:
764:
737:
730:
726:
716:
707:
704:
692:
687:
682:
678:
676:
666:
661:
657:
653:
651:
646:
634:
617:
610:
601:
592:
583:
577:
575:
570:
567:
560:
537:
529:
493:
469:
459:
455:
451:
446:
442:
440:
435:
427:
418:
409:
400:
394:
388:
384:
382:
352:
348:
327:
318:
308:
301:
228:
219:
210:
204:
200:
192:
188:ordinary ray
187:
179:
174:
166:
164:
152:
127:Iceland spar
114:
108:
88:birefractive
87:
84:birefringent
83:
72:polarization
59:
58:
7411:Brady Haran
7073:(8): 1230.
6527:Ice physics
6153:Pleochroism
6069:optic axis
5967:wavenumbers
5833:ellipsoidal
4368:determinant
2509:to obtain:
2117:shear waves
2014:sperm heads
2003:optic nerve
1956:Alzheimer's
1814:Lyot filter
1735:polarimetry
1721:Measurement
907:polystyrene
814:surfactants
806:amphiphilic
795:Kerr effect
548:Terminology
542:phase shift
525:wave vector
519:) for this
477:Snell's law
361:wave vector
340:wave vector
141:Explanation
80:anisotropic
7431:Categories
7024:: 107838.
6628:2024-03-15
6210:2021-07-21
6189:References
2682:) = ∇(∇ ⋅
2620:vanishes:
2234:equation:
2190:is just a
2121:seismology
2060:polarizers
2040:dermoscopy
1991:strabismus
1908:image) in
1856:polarizing
1838:and other
1818:Waveplates
1614:perovskite
1569:Monoclinic
1531:Monoclinic
1490:Monoclinic
1476:epsom salt
1460:Monoclinic
1371:Tetragonal
1349:Tetragonal
1318:tourmaline
1251:Tetragonal
1172:Tetragonal
903:Polarizers
899:cellophane
647:optic axis
534:waveplates
171:optic axis
117:whereby a
111:phenomenon
53:refraction
7447:Asymmetry
7238:1094-4087
7089:2218-273X
7048:0143-8166
6981:2156-7085
6932:1552-5783
6875:2156-7085
6697:0007-5027
6366:Brad Amos
6138:John Kerr
6123:Dichroism
6053:waveplate
6049:different
5768:ω
5762:−
5617:ω
5611:−
4971:ω
4965:−
4944:ω
4898:ω
4857:ω
4759:ω
4734:−
4716:−
4599:ω
4574:−
4556:−
4439:ω
4414:−
4396:−
4370:is zero:
4249:ω
4224:−
4206:−
4009:ω
3984:−
3966:−
3769:ω
3744:−
3726:−
3552:ω
3545:−
3415:−
3397:−
3379:−
3153:ε
3145:ε
3101:with the
3014:⋅
2996:we find:
2953:ε
2940:ω
2930:μ
2926:−
2907:⋅
2880:⋅
2872:−
2784:⋅
2773:−
2757:⋅
2738:×
2735:∇
2732:×
2729:∇
2726:−
2713:to find:
2678:∇ × (∇ ×
2636:⋅
2633:∇
2568:∂
2558:∂
2546:μ
2534:×
2531:∇
2528:×
2525:∇
2522:−
2381:ω
2378:−
2370:⋅
2256:ε
2066:Isotropic
2032:silicosis
1968:Congo red
1785:backlight
1696:Triclinic
1548:muscovite
1395:Material
1302:Hexagonal
1122:Hexagonal
1071:Hexagonal
982:Material
695:waveplate
686:ray with
460:biradials
447:binormals
365:waveplate
271:−
250:Δ
7413:for the
7246:20588931
7189:19439291
7148:19064263
7107:37627295
7098:10452597
6999:34457418
6940:15277483
6893:24298395
6809:35414965
6477:25214054
6373:Archived
6106:See also
5864:spheroid
3361:becomes
2102:analyzer
2007:glaucoma
1864:analyzer
1850:Medicine
1760:For the
1512:K(Mg,Fe)
1324:Trigonal
1280:Trigonal
1267:sapphire
1226:Trigonal
1197:Trigonal
1147:Trigonal
1132:+0.0014
1096:Trigonal
1044:−0.1242
1034:Trigonal
895:plastics
880:crystals
683:fast ray
679:slow ray
578:uniaxial
405:spheroid
167:uniaxial
100:plastics
92:Crystals
7353:
7294:
7278:
7216:Bibcode
7026:Bibcode
6990:8367251
6884:3829392
6800:8973164
6746:6536274
6737:1285204
6560:Bibcode
6500:Bibcode
6469:3733471
6291:5442206
6288::
6268:4058004
6265::
5962:
5942:
3346:
3323:
3304:. With
2503:
2486:
2214:is the
2110:elastic
2028:oocytes
1985:of the
1952:amyloid
1674:ulexite
1587:(Mg,Fe)
1585:olivine
1562:)(F,OH)
1524:)(F,OH)
1510:biotite
1381:+0.047
1359:+0.055
1334:−0.031
1312:+0.046
1290:−0.008
1261:+0.287
1236:−0.008
1207:+0.009
1182:+0.006
1157:−0.085
1106:−0.172
1087:calcite
1081:−0.045
843:By the
812:, some
791:Pockels
789:By the
667:biaxial
654:biaxial
489:calcite
452:biaxial
344:calcite
131:calcite
62:is the
25:calcite
7244:
7236:
7187:
7146:
7105:
7095:
7087:
7046:
6997:
6987:
6979:
6938:
6930:
6891:
6881:
6873:
6807:
6797:
6744:
6734:
6695:
6658:
6533:
6475:
6467:
6312:
6286:Zenodo
6263:Zenodo
6045:|
6039:|
5977:|
5971:|
5959:|
5953:|
3705:eq. 4a
3624:where
3358:eq. 4a
3349:, the
3316:using
3079:Eq. 4b
3055:Eq. 4b
2993:eq. 3b
2853:eq. 3a
2828:eq. 3a
2695:eq. 3a
2417:where
2290:where
2232:tensor
2208:where
2192:scalar
2130:Theory
2098:rutile
1712:
1706:1.520
1668:1.627
1651:(F,OH)
1635:2.380
1608:1.680
1579:1.601
1546:mica,
1541:1.640
1500:1.461
1470:1.472
1340:zircon
1242:rutile
1188:quartz
1129:1.3104
1126:1.3090
1041:1.5534
1038:1.6776
917:Cotton
830:chiral
810:lipids
658:except
102:under
7296:20–21
7290:, at
7280:13–50
6473:S2CID
6418:(PDF)
6223:See:
6165:Notes
6082:eq. 6
5924:eq. 6
5828:eq. 8
4843:eq. 6
2686:) − ∇
2145:eq. 7
1928:gouty
1918:right
1703:1.510
1700:1.490
1676:NaCaB
1665:1.620
1662:1.618
1641:topaz
1632:2.340
1629:2.300
1617:CaTiO
1605:1.660
1602:1.640
1576:1.596
1573:1.563
1554:(AlSi
1538:1.640
1535:1.595
1516:(AlSi
1497:1.455
1494:1.433
1467:1.469
1464:1.447
1448:)(OH)
1434:borax
1378:1.967
1375:1.920
1356:2.015
1353:1.960
1331:1.638
1328:1.669
1309:2.693
1306:2.647
1287:1.760
1284:1.768
1258:2.903
1255:2.616
1233:1.762
1230:1.770
1204:1.553
1201:1.544
1179:1.385
1176:1.380
1154:2.187
1151:2.272
1140:LiNbO
1103:1.486
1100:1.658
1078:1.557
1075:1.602
1050:beryl
538:along
530:shift
385:three
155:below
76:light
7242:PMID
7234:ISSN
7185:PMID
7144:PMID
7103:PMID
7085:ISSN
7044:ISSN
6995:PMID
6977:ISSN
6936:PMID
6928:ISSN
6889:PMID
6871:ISSN
6805:PMID
6742:PMID
6693:ISSN
6656:ISBN
6623:Home
6531:ISBN
6465:PMID
6310:ISBN
6005:and
5881:and
5463:and
3696:and
3298:and
3113:and
2474:∇ ×
2472:and
2467:∇ ×
2465:for
2224:and
1970:dye
1910:gout
1906:left
1684:(OH)
1506:mica
1478:MgSO
1213:ruby
1089:CaCO
1060:(SiO
909:and
628:and
599:and
425:and
389:both
325:and
226:and
106:.
7326:VII
7292:pp.
7284:doi
7276:pp.
7224:doi
7175:doi
7134:doi
7093:PMC
7075:doi
7034:doi
7022:172
6985:PMC
6969:doi
6920:doi
6879:PMC
6863:doi
6832:doi
6795:PMC
6787:doi
6732:PMC
6724:doi
6685:doi
6648:doi
6599:doi
6568:doi
6508:doi
6496:124
6457:doi
6430:doi
6099:not
4364:= 0
2450:= 0
2443:= 0
2123:.
1977:In
1739:not
1688:·5H
1647:SiO
1591:SiO
1550:KAl
1482:·7H
1452:·8H
1298:SiC
1244:TiO
1190:SiO
1165:MgF
1112:ice
1023:BaB
934:in
816:or
793:or
662:not
458:or
443:two
401:not
119:ray
113:of
86:or
7433::
7409:.
7405:.
7367:,
7363:,
7282:,
7263:^
7240:.
7232:.
7222:.
7212:18
7210:.
7206:.
7183:.
7171:94
7169:.
7165:.
7142:.
7130:93
7128:.
7124:.
7101:.
7091:.
7083:.
7071:13
7069:.
7065:.
7042:.
7032:.
7020:.
7016:.
6993:.
6983:.
6975:.
6965:12
6963:.
6957:.
6934:.
6926:.
6916:45
6914:.
6910:.
6887:.
6877:.
6869:.
6857:.
6853:.
6828:18
6826:.
6803:.
6793:.
6783:13
6781:.
6775:.
6740:.
6730:.
6718:.
6714:.
6691:.
6681:14
6679:.
6654:.
6621:.
6595:76
6593:.
6589:.
6566:.
6556:28
6554:.
6506:.
6494:.
6471:.
6463:.
6453:85
6451:.
6426:38
6424:.
6420:.
6398:.
6384:^
6368:.
6324:^
6242:,
6071:is
6066:is
6027:,
6021:,
5996:,
5471:=
5455:=
5448:=
4350:,
4341:,
4323:5d
4116:5c
3909:5b
3708:)
3675:,
3666:,
3642:,
3633:,
3615:5a
3321:=
3292:,
3277:4c
3131::
3107:,
3044:4b
2981:4a
2850:,
2847:iω
2816:3c
2707:ik
2666:3b
2605:3a
2484:=
2445:,
2305:=
2173:=
2148:).
2042:.
2034:.
1966:.
1947:.
1934:.
1827:,
1643:Al
1560:10
1522:10
1508:,
1440:(B
1436:Na
1269:Al
1215:Al
1056:Al
1052:Be
958:=
913:.
736:−
729:=
616:=
590:,
491:.
436:is
416:,
23:A
7417:.
7371:.
7346:V
7298:.
7286::
7248:.
7226::
7218::
7191:.
7177::
7150:.
7136::
7109:.
7077::
7050:.
7036::
7028::
7001:.
6971::
6942:.
6922::
6895:.
6865::
6859:4
6838:.
6834::
6789::
6748:.
6726::
6720:1
6699:.
6687::
6664:.
6650::
6631:.
6607:.
6601::
6574:.
6570::
6562::
6539:.
6514:.
6510::
6502::
6479:.
6459::
6436:.
6432::
6402:.
6318:.
6244:5
6213:.
6181:.
6094:k
6088:k
6076:k
6058:k
6042:k
6030:z
6024:y
6018:x
6015:(
6010:z
6008:n
6001:y
5999:n
5992:x
5990:n
5985:z
5983:±
5974:k
5956:k
5950:/
5946:k
5936:ω
5930:ω
5918:k
5908:k
5899:k
5893:k
5887:e
5884:n
5878:o
5875:n
5869:z
5859:k
5853:o
5850:n
5844:ω
5838:k
5818:)
5816:8
5814:(
5797:0
5794:=
5790:)
5782:2
5778:c
5772:2
5755:2
5749:o
5744:n
5738:2
5733:z
5729:k
5723:+
5716:2
5710:e
5705:n
5699:2
5694:y
5690:k
5684:+
5677:2
5671:e
5666:n
5660:2
5655:x
5651:k
5644:(
5639:)
5631:2
5627:c
5621:2
5604:2
5598:o
5593:n
5587:2
5582:z
5578:k
5572:+
5565:2
5559:o
5554:n
5548:2
5543:y
5539:k
5533:+
5526:2
5520:o
5515:n
5509:2
5504:x
5500:k
5493:(
5476:e
5473:n
5468:z
5466:n
5460:o
5457:n
5452:y
5450:n
5445:x
5443:n
5437:z
5427:)
5425:7
5423:(
5406:0
5403:=
5399:)
5393:2
5388:z
5384:k
5380:+
5375:2
5370:y
5366:k
5362:+
5357:2
5352:x
5348:k
5343:(
5338:)
5329:2
5324:y
5320:n
5314:2
5309:x
5305:n
5298:2
5293:z
5289:k
5283:+
5275:2
5270:z
5266:n
5260:2
5255:x
5251:n
5244:2
5239:y
5235:k
5229:+
5221:2
5216:z
5212:n
5206:2
5201:y
5197:n
5190:2
5185:x
5181:k
5174:(
5170:+
5166:)
5158:2
5153:x
5149:n
5142:2
5137:z
5133:k
5129:+
5124:2
5119:y
5115:k
5108:+
5101:2
5096:y
5092:n
5085:2
5080:z
5076:k
5072:+
5067:2
5062:x
5058:k
5051:+
5044:2
5039:z
5035:n
5028:2
5023:y
5019:k
5015:+
5010:2
5005:x
5001:k
4993:(
4985:2
4981:c
4975:2
4958:4
4954:c
4948:4
4912:2
4908:c
4902:2
4871:2
4867:c
4861:2
4833:)
4831:6
4829:(
4812:0
4809:=
4804:|
4797:)
4789:2
4785:c
4778:2
4773:z
4769:n
4763:2
4752:+
4747:2
4742:y
4738:k
4729:2
4724:x
4720:k
4712:(
4704:z
4700:k
4694:y
4690:k
4682:z
4678:k
4672:x
4668:k
4658:z
4654:k
4648:y
4644:k
4637:)
4629:2
4625:c
4618:2
4613:y
4609:n
4603:2
4592:+
4587:2
4582:z
4578:k
4569:2
4564:x
4560:k
4552:(
4544:y
4540:k
4534:x
4530:k
4520:z
4516:k
4510:x
4506:k
4498:y
4494:k
4488:x
4484:k
4477:)
4469:2
4465:c
4458:2
4453:x
4449:n
4443:2
4432:+
4427:2
4422:z
4418:k
4409:2
4404:y
4400:k
4392:(
4385:|
4362:E
4355:z
4353:E
4346:y
4344:E
4337:x
4335:E
4325:)
4321:(
4304:0
4301:=
4296:z
4292:E
4287:)
4279:2
4275:c
4268:2
4263:z
4259:n
4253:2
4242:+
4237:2
4232:y
4228:k
4219:2
4214:x
4210:k
4202:(
4198:+
4193:y
4189:E
4183:z
4179:k
4173:y
4169:k
4165:+
4160:x
4156:E
4150:z
4146:k
4140:x
4136:k
4118:)
4114:(
4097:0
4094:=
4089:z
4085:E
4079:z
4075:k
4069:y
4065:k
4061:+
4056:y
4052:E
4047:)
4039:2
4035:c
4028:2
4023:y
4019:n
4013:2
4002:+
3997:2
3992:z
3988:k
3979:2
3974:x
3970:k
3962:(
3958:+
3953:x
3949:E
3943:y
3939:k
3933:x
3929:k
3911:)
3907:(
3890:0
3887:=
3882:z
3878:E
3872:z
3868:k
3862:x
3858:k
3854:+
3849:y
3845:E
3839:y
3835:k
3829:x
3825:k
3821:+
3816:x
3812:E
3807:)
3799:2
3795:c
3788:2
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3773:2
3762:+
3757:2
3752:z
3748:k
3739:2
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3730:k
3722:(
3699:z
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3687:k
3680:z
3678:k
3671:y
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3660:k
3654:E
3647:z
3645:E
3638:y
3636:E
3629:x
3627:E
3617:)
3613:(
3594:x
3590:E
3582:2
3578:c
3571:2
3566:x
3562:n
3556:2
3542:=
3537:z
3533:E
3527:z
3523:k
3517:x
3513:k
3509:+
3504:y
3500:E
3494:y
3490:k
3484:x
3480:k
3476:+
3471:x
3467:E
3461:2
3456:x
3452:k
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3428:2
3423:z
3419:k
3410:2
3405:y
3401:k
3392:2
3387:x
3383:k
3375:(
3352:x
3342:0
3339:ε
3336:0
3333:μ
3329:/
3326:1
3319:c
3313:c
3307:ε
3301:z
3295:y
3289:x
3279:)
3275:(
3256:]
3248:2
3243:z
3239:n
3233:0
3228:0
3221:0
3214:2
3209:y
3205:n
3199:0
3192:0
3187:0
3180:2
3175:x
3171:n
3164:[
3157:0
3149:=
3128:ε
3122:z
3116:z
3110:y
3104:x
3094:ω
3088:k
3073:E
3067:k
3061:D
3046:)
3042:(
3025:0
3022:=
3018:D
3010:k
2983:)
2979:(
2962:)
2958:E
2949:(
2944:2
2934:0
2923:=
2919:k
2915:)
2911:E
2903:k
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2892:E
2888:)
2884:k
2876:k
2869:(
2845:−
2840:ε
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2814:(
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2742:E
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2680:A
2668:)
2664:(
2647:0
2644:=
2640:D
2617:D
2607:)
2603:(
2585:D
2576:2
2572:t
2562:2
2550:0
2542:=
2538:E
2506:B
2499:0
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2492:/
2489:1
2482:H
2476:H
2469:E
2458:k
2448:t
2441:r
2435:0
2432:E
2426:t
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2387:)
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2366:k
2362:(
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2339:=
2335:E
2318:ω
2311:0
2308:μ
2303:μ
2293:ε
2283:)
2281:1
2279:(
2261:E
2252:=
2248:D
2227:E
2221:D
2211:n
2204:0
2201:ε
2197:n
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2178:E
2175:ɛ
2171:D
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2156:(
2140:k
2104:)
1876:y
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1868:y
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1653:2
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1426:γ
1423:n
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1413:n
1406:α
1403:n
1366:4
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1275:3
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1013:n
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1005:e
1002:n
995:o
992:n
964:0
961:μ
956:μ
840:;
820:;
801:;
786:;
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725:Δ
720:o
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643:z
638:γ
635:n
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37:s
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