# Birefringence

The letters on a paper covered by a calcite crystal show up as doubled. This is an example of the phenomenon of birefringence (double refraction).

Birefringence, or double refraction, is the splitting of a ray of light into two rays when it passes through certain types of material, such as calcite crystals. The two rays, called the ordinary ray and the extraordinary ray, travel at different speeds. Thus the material has two distinct indices of refraction, as measured from different directions. This effect can occur only if the structure of the material is anisotropic, so that the material's optical properties are not the same in all directions.

Birefringent materials are used in many optical devices, such as wave plates, liquid crystal displays, polarizing prisms, light modulators, and color filters.

## Examples of birefringent materials

Birefringence was first described in calcite crystals by the Danish scientist Rasmus Bartholin in 1669. Since then, many birefringent crystals have been discovered.

Silicon carbide, also known as Moissanite, is strongly birefringent.

Many plastics are birefringent because their molecules are 'frozen' in a stretched conformation when the plastic is molded or extruded. For example, cellophane is a cheap birefringent material.

Cotton (Gossypium hirsutum) fiber is birefringent because of high levels of cellulosic material in the fiber's secondary cell wall.

Slight imperfections in optical fibers can cause birefringence, which can lead to distortion in fiber-optic communication.

Birefringence can also arise in magnetic (not dielectric) materials, but substantial variations in magnetic permeability of materials are rare at optical frequencies.

Birefringence can be observed in amyloid plaque deposits, such as are found in the brains of Alzheimer's victims. Modified proteins such as immunoglobulin light chains abnormally accumulate between cells, forming fibrils. Multiple folds of these fibers line up and take on a beta-pleated sheet conformation. Congo red dye intercalates between the folds and, when observed under polarized light, causes birefringence.

## Calculation of birefringence

If the material has a single axis of anisotropy, (that is, it is uniaxial), birefringence can be formalized by assigning two different refractive indices to the material for different polarizations. The birefringence magnitude is then defined by:

$\Delta n=n_e-n_o\,$

where no and ne are the refractive indices for polarizations perpendicular (ordinary) and parallel (extraordinary) to the axis of anisotropy, respectively.

## Refractive indices of birefringent materials

The refractive indices of several (uniaxial) birefringent materials are listed below (at a wavelength of about 590 nm).[1]

 Material no ne Δn beryl Be3Al2(SiO3)6 1.602 1.557 -0.045 calcite CaCO3 1.658 1.486 -0.172 calomel Hg2Cl2 1.973 2.656 +0.683 ice H2O 1.309 1.313 +0.014 lithium niobate LiNbO3 2.272 2.187 -0.085 magnesium fluoride MgF2 1.380 1.385 +0.006 quartz SiO2 1.544 1.553 +0.009 ruby Al2O3 1.770 1.762 -0.008 rutile TiO2 2.616 2.903 +0.287 peridot (Mg, Fe)2SiO4 1.690 1.654 -0.036 sapphire Al2O3 1.768 1.760 -0.008 sodium nitrate NaNO3 1.587 1.336 -0.251 tourmaline (complex silicate ) 1.669 1.638 -0.031 zircon, high ZrSiO4 1.960 2.015 +0.055 zircon, low ZrSiO4 1.920 1.967 +0.047

## Creating birefringence

While birefringence is often found naturally (especially in crystals), there are several ways to create it in optically isotropic materials.

• Birefringence results when isotropic materials are deformed such that the isotropy is lost in one direction (ie, stretched or bent).[2]
• Applying an electric field can induce molecules to line up or behave asymmetrically, introducing anisotropy and resulting in birefringence. (see Pockels effect)
• Applying a magnetic field can cause a material to be circularly birefringent, with different indices of refraction for oppositely-handed circular polarizations (see Faraday effect).

## Measuring birefringence by polarimetry

Birefringence and related optical effects (such as optical rotation and linear or circular dichroism) can be measured by measuring changes in the polarization of light passing through the material. These measurements are known as polarimetry.

A common feature of optical microscopes is a pair of crossed polarizing filters. Between the crossed polarizers, a birefringent sample will appear bright against a dark (isotropic) background.

## Biaxial birefringence

Biaxial birefringence, also known as trirefringence, describes an anisotropic material that has more than one axis of anisotropy. For such a material, the refractive index tensor n, will in general have three distinct eigenvalues that can be labeled nα, nβ and nγ.

The refractive indices of some trirefringent materials are listed below (at wavelength ~ 590 nm).[3]

 Material nα nβ nγ borax 1.447 1.469 1.472 epsom salt MgSO4•7(H2O) 1.433 1.455 1.461 mica, biotite 1.595 1.640 1.640 mica, muscovite 1.563 1.596 1.601 olivine (Mg, Fe)2SiO4 1.640 1.660 1.680 perovskite CaTiO3 2.300 2.340 2.380 topaz 1.618 1.620 1.627 ulexite 1.490 1.510 1.520

## Elastic birefringence

Another form of birefringence is observed in anisotropic elastic materials. In these materials, shear waves split according to similar principles as the light waves discussed above. The study of birefringent shear waves in the earth is a part of seismology. Birefringence is also used in optical mineralogy to determine the chemical composition, and history of minerals and rocks.

## Applications of birefringence

Birefringence is widely used in optical devices, such as liquid crystal displays, light modulators, color filters, wave plates, and optical axis gratings. It plays an important role in second harmonic generation and many other nonlinear processes. It is also utilized in medical diagnostics. Needle biopsy of suspected gouty joints will be negatively birefringent if urate crystals are present.

## Notes

1. Refraction Retrieved October 1, 2007.
2. Example Retrieved October 1, 2007.
3. Refraction Retrieved October 1, 2007.

## References

• Born, Max, and Emil Wolf. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 7th ed. Cambridge, UK: Cambridge University Press, 1999. ISBN 0521642221
• Elert, Glenn. The Physics Hypertextbook: Refraction hypertextbook.com, 2007. Retrieved April 19, 2007.
• Halliday, David, Robert Resnick, and Kenneth S. Krane. Physics. Vol. 2, 5th ed. New York: John Wiley, 2001. ISBN 0471401943
• Sharma, Kailash K. Optics: Principles and Applications. Burlington, MA: Academic Press, 2006. ISBN 0123706114