Why do birefringence materials have 2 refractive indices?

Question

Why do birefringence materials have 2 refractive indices? In other words, what causes the material to have 2 refractive indices?

Answer 1

In a solid, crystal structure, atoms may be arranged in different ways in different directions. When light enters the crystal, you can decompose its electric field alongside those directions, and its projections will be affected by the crystal differently (depending on the crystal, there will be two or three different refractive indices).

All of this comes down to symmetries of the action of the crystal on electromagnetic waves. If this action is isotropic, there won't be any birefringence (only one refractive index), if one symmetry is lost a second index can appear, and so on. A symmetry can break because the crystal has different regularities in its principal directions, because you apply some anisotropic influence. Examples:

• external pressure: some crystals can become birefringent when you compress them
• electric field: see Kerr effect

Answer 2

Birefringence materials have two refractive indices because they have anisotropic properties.

The anisotropy of a material can be described by the difference in the strength and direction of the chemical bonds between the atoms or molecules in the material. As a result of this anisotropy, the electrons in the material are distributed differently in different directions, and this leads to a different index of refraction for light traveling in different directions through the material.

Hence, birefringence is caused by different physical and/or chemical properties of the material in different directions. The birefringence can be induced by the

• Faraday effect (magnetic)
• Stress effect
• Kerr effect (nonlinear optics)
• Acousto-optic wave
• Electro-optic field
• Heating
• Metamaterials

Answer 3

I prefer to think of light always as a stream of photons. Each quantum of light in the stream has an oscillating magnetic and an oscillating electric field component. Their oscillation directions are perpendicular to each other, but together they are equally distributed through 360° in space. This applies to thermal light sources, i.e. non-polarised light.

Light (always considered as zillions of photons with their oscillating field components) can be easily polarised. Slits in foils are sufficient for this, which reflect some of the photons and cause a rotation and alignment of the field components for the other photons.

Almost exactly the same thing happens in the birefringent material. Only instead of one polarisation, the crystal lattice acts like two polarisation foils. The field components of the photons are aligned in two directions. The right combination of lattice structure (distance of the atoms from each other), frequency of the photon field components and speed of light in the medium direct the photons in two directions and thereby polarise the currents.