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The tensor and pseudovector forms of the Berry curvature are related to each other through the Levi-Civita antisymmetric tensor as , =,. In contrast to the Berry connection, which is physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions ...
Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media (such as crystals) in which light behaves differently depending on which direction the light is propagating. The index of refraction depends on both composition and crystal structure and can be calculated using the Gladstone–Dale ...
Note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution ("spheroid") but is described by three unequal principle refractive indices n α, n β and n γ. Thus there is no axis around which a rotation leaves the optical properties invariant (as there is with uniaxial crystals whose index ellipsoid is a spheroid).
Electro-optic modulators are usually built with electro-optic crystals exhibiting the Pockels effect. The transmitted beam is phase modulated with the electric signal applied to the crystal. Amplitude modulators can be built by putting the electro-optic crystal between two linear polarizers or in one path of a Mach–Zehnder interferometer.
Pockels cells are divided into two configurations depending on the crystals' electro-optic properties: longitudinal and transverse. Longitudinal Pockels cells operate with electric field applied along the crystal optic axis or along incident beam propagation. Such crystals include KDP, KD*P, and ADP.
In physics, tensor is an orientational order parameter that describes uniaxial and biaxial nematic liquid crystals and vanishes in the isotropic liquid phase. [1] The Q {\displaystyle \mathbf {Q} } tensor is a second-order, traceless, symmetric tensor and is defined by [ 2 ] [ 3 ] [ 4 ]
The tensor is zero in the isotropic liquid phase since the scalar order parameter is zero, but becomes non-zero in the nematic phase. Near the NI transition, the ( Helmholtz or Gibbs ) free energy density F {\displaystyle {\mathcal {F}}} is expanded about as
The Tensorial Anisotropy Index A T [5] extends the Zener ratio for fully anisotropic materials and overcomes the limitation of the AU that is designed for materials exhibiting internal symmetries of elastic crystals, which is not always observed in multi-component composites. It takes into consideration all the 21 coefficients of the fully ...