An optic axis of a crystal is a direction in which a ray of transmitted light suffers no

birefringence Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...

(double refraction). An optic axis is a direction rather than a single line: all rays that are parallel to that direction exhibit the same lack of birefringence. Crystals may have a single optic axis, in which case they are ''uniaxial'', or two different optic axes, in which case they are ''biaxial''. Non-crystalline materials generally have no birefringence and thus, no optic axis. A uniaxial crystal (e.g.

calcite Calcite is a Carbonate minerals, carbonate mineral and the most stable Polymorphism (materials science), polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on ...

quartz Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical form ...

) is

isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...

within the plane

orthogonal In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...

to the optic axis of the crystal.

Explanation

The internal structure of crystals (the specific structure of the

crystal lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...

, and the specific atoms or molecules of which it is composed) causes the speed of light in the material, and therefore the material's

refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...

, to depend on both the light's direction of propagation and its polarization. The dependence on polarization causes birefringence, in which two perpendicular polarizations propagate at different speeds and refract at different angles in the crystal. This causes a ray of light to split into an

ordinary ray Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefring ...

and an

extraordinary ray Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefrin ...

, with orthogonal polarizations. For light propagating along an optic axis, though, the speed does not depend on the polarization, so there is no birefringence although there can be

optical activity Optical rotation, also known as polarization rotation or circular birefringence, is the rotation of the orientation of the plane of polarization about the optical axis of linearly polarized light as it travels through certain materials. Circul ...

(a rotation of the plane of polarization). The refractive index of the ordinary ray is constant for any direction in the crystal. The refractive index of the extraordinary ray varies depending on its direction.

Liquid crystal directors

The mobile axis of a

liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. T ...

is called a

director Director may refer to: Literature * ''Director'' (magazine), a British magazine * ''The Director'' (novel), a 1971 novel by Henry Denker * ''The Director'' (play), a 2000 play by Nancy Hasty Music * Director (band), an Irish rock band * ''D ...

. It is the space and time average of the orientation of the long molecular axis within a small volume element of material demonstrating a

mesophase In chemistry and chemical physics, a mesophase is a state of matter intermediate between liquid and solid. Gelatin is a common example of a partially ordered structure in a mesophase. Further, biological structures such as the lipid bilayers of cel ...

. Electrical manipulation of the director enables

liquid-crystal display A liquid-crystal display (LCD) is a flat-panel display A flat-panel display (FPD) is an electronic display used to display visual content such as text or images. It is present in consumer, medical, transportation, and industrial equipmen ...

Notes and references

Polarization (waves) Optical mineralogy {{optics-stub

Explanation

Liquid crystal directors

See also

Notes and references