Uniaxial vs Biaxial Crystal: Key Differences Explained

This article compares uniaxial and biaxial crystals, highlighting their key differences, types, and uses.

Uniaxial Crystal

• These crystals are characterized by one optical axis and two principal refractive indices.
• Examples: Calcite, KDP (Potassium Dihydrogen Phosphate), quartz, rutile.
• When light passes through a uniaxial crystal, it splits into two rays:
  • Ordinary ray (o-ray): Passes through the crystal without deviation.
  • Extraordinary ray (e-ray): Deviates at the air-crystal interface.

Positive Uniaxial Crystal vs. Negative Uniaxial Crystal

alt: Positive uniaxial crystal vs Negative uniaxial crystal

When light propagates through a uniaxial crystal, the wavefronts of the o-ray and e-ray form Huygens’ wave surfaces. The relationship between the velocities of these rays determines the type of uniaxial crystal.

• Case 1: Positive Uniaxial Crystal
  • Vo > Ve (no < ne) in all directions except along the optical axis. (Vo = velocity of o-ray, Ve = velocity of e-ray, no = refractive index of o-ray, ne = refractive index of e-ray)
  • The spherical wavefront of the o-ray is outside the elliptical wavefront of the e-ray.
  • The two wavefronts touch at two diametrically opposite points on the optical axis.
  • Examples: Quartz, rutile.
• Case 2: Negative Uniaxial Crystal
  • Vo < Ve (no > ne).
  • The elliptical wavefront of the e-ray is outside the spherical wavefront of the o-ray.
  • Examples: Calcite, KDP.

Factors Affecting Double Refraction:

The double refraction properties in birefringent crystals depend on:

• Polarization state of the incoming light ray.
• Incidence angle of the light ray.
• Orientation of the crystal’s optical axis with respect to its surface plane.

Biaxial Crystal

• These crystals are characterized by two optical axes and three principal refractive indices.
• Examples: Mica, lead oxide, topaz.
• Biaxial crystals are also birefringent.
• When light passes through a biaxial crystal, it splits into two e-rays. These rays have different directions and speeds.
• Examples: Crystalline structures like orthorhombic, monoclinic, or triclinic.