i δ E Q Re and for ) for a material with an in-plane magnetization, (Ga,Mn)As exhibits a biaxial anisotropy with the magnetization aligned along (or close to) <100> directions. {\displaystyle {\vec {E}}} and H 2 Gemstones belonging to the cubic crystal system and amorphous gems have only one RI and therefore do not show birefringence; all other gemstones do. Q = In the approximation of no absorption, one obtains for the Voigt rotation in transmission geometry: As an illustration of the application of the Voigt effect, we give an example in the magnetic semiconductor (Ga,Mn)As where a large Voigt effect was observed. Q 0 A typical hysteresis cycle containing the Voigt effect is shown in figure 1. → In contrast to the common longitudinal/polar Kerr effect, the hysteresis cycle is even with respect to the magnetization, which is a signature of the Voigt effect. ⊥ sin is proportional to A way to simplify the problem consists to use the electric field displacement vector cos {\displaystyle {\vec {\nabla }}\times {\vec {H}}={\frac {1}{c}}{\frac {\partial {\vec {D}}}{\partial t}}} {\displaystyle {\vec {H}}} m {\displaystyle \Delta n} E {\displaystyle B_{1}} Some gemstones have more than one refractive index (RI) because these stones belong to crystal systems (anisotropic) that have atomic structures that cause an incident ray of light to be resolved into two rays traveling at different velocities. 0 If the light enters at an oblique angle, each vibration changes direction and travels along paths that differ from the original path AND differ from each other. are defined from the ratio H {\displaystyle B_{1}} {\displaystyle {\vec {m}}={\vec {M}}/M_{s}} − . The numerical difference between one RI value and the other RI value measured in any one case is called the "birefringence" for that test, and the difference between the highest possible RI and the lowest possible RI considering all possible directions is called the birefringence of the gemstone. {\displaystyle H_{0}} and Both vibrations were incident at perpendicular to the wave front so the velocity change does not cause a direction change. t = β with the two following formulae: where 1 m {\displaystyle {\vec {m}}={\begin{pmatrix}\cos \phi \\\sin \phi \\0\end{pmatrix}}} Biaxial gemstones (orthorhombic, monoclinic and triclinic systems) have two directions in which the incident light will react as if it were isotropic and therefore will have two optic axes. t sin ) and perpendicular This last denomination is closer in the physical sense, where the Voigt effect is a magnetic birefringence of the material with an index of refraction parallel ( {\displaystyle \psi } m ϵ sin Let us notice that we have , Let us notice that → − {\displaystyle n_{\parallel }} r L r In order to extract the Voigt rotation, we consider χ ) n m / + 1 E n We use the continuity equations for ∥ ω δ i . ( the angle of refraction will vary according to the angle of vibration). → D E This ray is named the ordinary ray (usually indicated with ω). cos {\displaystyle \operatorname {Re} (\chi )} μ ϕ This difference related to velocities is named "birefringence". → ) Detailed calculation and an illustration are given in sections below. ( / M → {\displaystyle m_{i}=M_{i}/M_{s}} i . is the material dielectric constant, 1 or 2 {\displaystyle \delta \beta } However, the use of transmission geometry is more common for paramagnetic liquid or cristal where the light can travel easily inside the material. r Refringence is when light changes velocity as it passes through a surface. ( n z β 0 ( {\displaystyle {\vec {E_{i}}}={\begin{pmatrix}\cos \beta \\\sin \beta \\0\end{pmatrix}}e^{-i\omega (t-n_{1}z/c)}} P is counted from the [100] crystallographic direction. = H 0 For instance: In uniaxial gemstones, one ray will vibrate in the direction perpendicular to the optic axis and will obey Snell's Law (one can calculate its angle of refraction). i β Q ( → s Many times this doubling may be difficult to identify depending on the stone size, so don’t rely on that alone for identification. {\displaystyle B_{2}} ( ( = E Refraction is when light changes direction as it passes through a surface.