Birefringent Materials

Crystalline materials may have different indices of refraction associated with different crystallographic directions. A common situation with mineral crystals is that there are two distinct indices of refraction, and they are called birefringent materials. If the y- and z- directions are equivalent in terms of the crystalline forces, then the x-axis is unique and is called the optic axis of the material. The propagation of light along the optic axis would be independent of its polarization; it's electric field is everywhere perpendicular to the optic axis and it is called the ordinary- or o-wave. The light wave with E-field parallel to the optic axis is called the extraordinary- or e-wave. Birefringent materials are used widely in optics to produce polarizing prisms and retarder plates such as the quarter-wave plate. Putting a birefringent material between crossed polarizers can give rise to interference colors.

A widely used birefringent material is calcite . Its birefringence is extremely large, with indices of refraction for the o- and e-rays of 1.6584 and 1.4864 respectively.

Crystallographic Origins of Birefringence

The property called birefringence has to do with anisotropy in the binding forces between the atoms forming a crystal, so it can be visualized as the atoms having stronger "springs" holding them together in some crystalline directions. A useful situation with mineral crystals occurs when there are two distinct indices of refraction, and they are called birefringent materials. This is associated with uniaxial crystals, which belong to the hexagonal, tetragonal, and trigonal crystal systems. In a uniaxial crystal, there is one direction such that any light in that direction in the crystal has the same speed, regardless of its state of polarization. This direction is called the optic axis. The remaining crystal systems (orthorhombic, monoclinic, and triclinic) have two optic axes and are said to be biaxial.

Some Birefringent Materials

Two indices of refraction characterize birefringent materials. Such materials form uniaxial crystals, and may be characterized as positive or negative uniaxial crystals based on the comparison of the indices.

Tourmaline	1.669	1.638
Calcite	1.6584	1.4864
Quartz	1.5443	1. 5534
Sodium Nitrate	1.5854	1. 3369
Ice	1.309	1.313
Rutile (TiO2 )	2.616	2.903

Calcite

The indices of refraction for the o- and e-rays are 1.6584 and 1.4864 respectively. This gives total internal reflection critical angles of 37.08° for the o- and 42.28° for the e-rays when in contact with air. This means that for any angle between these two values, the o-ray will be totally reflected but the e-ray will be partially transmitted. This gives linear polarization since only the e-ray emerges.

Calcite is used in polarizing prisms such as the Nicol prism, the Glan-Foucault prism, and the Wollaston prism.

A simple demonstration of the large birefringence of calcite is to put a dot on a piece of paper and put the calcite crystal over it. You see two distinct dots. By putting a piece of polaroid over the crystal and rotating it, you can show that the two images of the dot are made up of light polarized at 90° with respect to each other. Rotating the polaroid will show one dot, then both in transition, and then just the second dot as you reach 90°.