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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 ...
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 ...
The net force on each ion is generally calculated explicitly at each numerical step. From this, the stress tensor of the system can be calculated and usually is calculated by the numerical package. By varying the convergence criteria, one can either seek a lowest energy structure or a structure that produces a desired stress tensor.
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
Optical properties of common minerals Name Crystal system Indicatrix Optical sign Birefringence Color in plain polars Anorthite: Triclinic: Biaxial (-) 0.013
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.
The directional dependence of a crystal's physical property is described by a 3D tensor and depends on the orientation of the crystal. Tensor shapes are more palpable by adding lighting effects (reflection and shadow). 2D sections of interest are selected for display by rotating the tensor interactively around one or more axes.