Birefringence and Crystal Optics

Birefringent crystals have a refractive index that depends on the polarization and direction of light, splitting a beam into two with different velocities.

Definition

The dependence of a medium's refractive index on the polarization direction and propagation direction of light, which causes light to split into ordinary and extraordinary components travelling at different speeds.

Scope

This topic covers the propagation of light in optically anisotropic media. It includes the dielectric tensor and the index ellipsoid, ordinary and extraordinary rays, uniaxial and biaxial crystals, the phase retardation accumulated between orthogonal components, double refraction and walk-off, optical activity and circular birefringence, and field-induced anisotropy through the electro-optic and photoelastic effects. It explains how anisotropic materials transform polarization and underlies wave plates, polarizing prisms, and electro-optic modulators.

Core questions

• Why do anisotropic crystals refract light into two beams?
• How is the optical behaviour of a crystal captured by the index ellipsoid?
• What distinguishes uniaxial from biaxial crystals?
• How do external fields induce or change birefringence?

Key concepts

• birefringence
• ordinary and extraordinary rays
• index ellipsoid
• uniaxial and biaxial crystals
• optic axis
• phase retardation
• optical activity
• electro-optic effect

Key theories

Index ellipsoid and double refraction

In an anisotropic crystal the refractive index for a given polarization and direction is read from the index ellipsoid, producing distinct ordinary and extraordinary waves that refract differently and accumulate a relative phase.

Electro-optic effect

An applied electric field alters the index ellipsoid of certain crystals, changing their birefringence in proportion to the field (Pockels effect) or its square (Kerr effect), the basis of fast optical modulators.

Clinical relevance

Birefringence is the contrast mechanism in polarized-light microscopy used to identify crystals in joint fluid, such as the negatively birefringent urate crystals of gout and positively birefringent calcium pyrophosphate of pseudogout, and to assess collagen and amyloid in tissue sections.

History

Bartholin reported double refraction in calcite in 1669, and Huygens analysed it with his wave construction, noting the two distinct wavefronts. Fresnel's transverse-wave theory in the 1820s gave a full account of birefringence, and the electro-optic effects were characterized later by Kerr and Pockels.

Key figures

• Erasmus Bartholin
• Christiaan Huygens
• Augustin-Jean Fresnel

Seminal works

• bornwolf1999
• hecht2017

Frequently asked questions

Why does a calcite crystal show a double image?

Calcite is birefringent, so light entering it splits into ordinary and extraordinary rays that refract at different angles and emerge separated, producing two displaced images of whatever is viewed through the crystal.

What is optical activity?

Optical activity is a form of circular birefringence in which a medium, such as a sugar solution or quartz, rotates the plane of linearly polarized light because it transmits left- and right-circular polarizations at slightly different speeds.