Birefringence

Birefringence property of the optically anisotropic media is referred to, to separate a light beam into two orthogonally polarized sub-beams. The cause of this effect is the difference in the refractive index ( no and NAO) depending on the direction of propagation and polarization of the light. A prominent example of such a material is calcite ( calcite, and calcite ) at which the birefringence was discovered in 1669 by Erasmus Bartholin.

Isotropic materials can be caused by external influences such as mechanical stress ( deformation or stress birefringence ), electric fields ( electric birefringence, electro-optical Kerr effect) or magnetic fields (magnetic birefringence, Cotton -Mouton effect, in general, see magneto-optics ), are birefringent. Liquids with high toughness can act birefringent in flow due to internal friction. - Most liquid crystals are spontaneously birefringent.

Closely related to the birefringence of the dichroism.

Physical cause

Birefringence occurs in optically anisotropic crystals. They have different polarization to the incident light direction and a different refractive index. The corresponding index ellipsoid can be optically uniaxial (eg tetragonal crystals ) or three main axes have (eg orthorhombic symmetry). In this particular case, namely the case of optically biaxial crystals ( biaxial), are generally both extremely refracted rays ( electric field, dielectric and induction, not have the same direction, the propagation vector, is perpendicular to not as usual, to see literature).

The axes of a birefringent crystal are not to be confused with the optical axis of a system of lenses and mirrors.

Ordinary and extraordinary beam

The ordinary ray and the extraordinary ray can be defined by the orientation of its electric field on the plane which is spanned by the (optical axis) and the direction of propagation of the incident beam (main section). The ordinary ray is the fraction of the incident beam, the electric field is perpendicular to the main section. For the ordinary ray in uniaxial crystals applies Snell's law for isotropic media. For the second beam, the extraordinary ray, the Snell's law does not apply, however, it will also be broken at normal incidence on the birefringent crystal. Its electric field oscillates in the main section of the crystal. The elementary waves of the extraordinary beam forming spheroids that of the ordinary ray contrast spherical waves that satisfy Huygens' principle. The wave fronts of the extraordinary and the ordinary ray propagate at different speeds.

The corresponding refractive indices are calculated as follows:

And

Where c is the speed of light in vacuum.

The difference of the refractive indexes () is a measure of the birefringence. The sign is referred to as optical character or optical orientation. For calcite. Calcite is therefore an optically negative uniaxial crystal. In it, the extraordinary ray is moving faster than the ordinary ray.

In this context one also speaks of the fast and the slow axis. An optically positive uniaxial crystal in the fast axis is perpendicular to the optical axis of the crystal, whereas the slow axis coincides with the optical axis.

The feature of the optically active substances to show a different refractive index for the left - and right-handed circularly polarized light is called circular birefringence. The circular birefringence was first described by Dominique François Jean Arago (1811 ) on quartz. However, the effect for quartz is approximately 100 times smaller than the linear birefringence. Since overlap both effects, the circular birefringence can be observed only when the linear birefringence does not occur. In the case of silica, this is the case, along the optical axis.

To calculate the rotation of a linearly polarized beam by the circular birefringence in the material, this can be described as a coherent superposition of left - and a right-handed portion with the same intensity. Both move with different phase velocity (a larger phase velocity corresponds to a smaller refractive index) through the material. The superposition of both parts after the passage again yields a linearly polarized beam. The phase difference Δφ of the two components is shown in a rotation of the plane of vibration by the angle Δφ / 2 For quartz, the angle is ± 21.7 ° / mm (quartz occurs both right-and left-handed on ). A clockwise rotation is described by a positive rotation angle and arises in the case where the refractive index is greater than that for the left-handed portion of the right-handed fraction ().

The cause of the circular birefringence in the quartz is his " helical " crystal structure. However, not only crystalline materials having a " helical " structure showing a rotary power of the polarization plane, and liquids (e.g. turpentine ) have this property. The reason for this is also in their molecular structure, which is called chirality. Further comprising a circular birefringence may be induced by a magnetic field, see the Faraday effect. This is the case for example with lead silicate glass. Comparable effects are also available for the absorption behavior of materials, see dichroism.

Tables

The tables contain data common uniaxial or biaxial systems. D is the difference of the refractive indices for the extraordinary () and the ordinary ray:

Application of birefringent materials

Birefringent materials are used eg in retardation plates and polarizers. The birefringent polarizers include the Nicol prism or Glan-Thompson prism. They make it possible to produce linearly polarized light from unpolarized light.

Wherein optical images birefringent materials can be used as an optical low-pass filter in order to reduce, for example, to occur in connection with the Bayer sensors aliasing.

Birefringence can also occur as a disturbing effect, for example, during injection molding of compact discs. The birefringence is caused by mechanical stresses in the polycarbonate layer, for example, thermal stress or shear stress of the material.

Proof of birefringent materials

The detection of a birefringent substance is carried, for example, on the polarization microscopy. Upon rotation of the sample between crossed polarizing filters, the brightness and the color of the birefringent object while optically isotropic materials show no changes in the image.

Even using the immersion method, it is possible to identify birefringent materials.