An optic axis is a direction within an anisotropic crystal along which light propagates without double refraction — meaning the ordinary and extraordinary rays travel at the same velocity and do not separate. The concept is fundamental to optical mineralogy and to the gemmological identification of doubly refractive species. Uniaxial crystals (those belonging to the tetragonal, hexagonal, or trigonal crystal systems) possess a single optic axis parallel to the crystallographic c-axis; biaxial crystals (those belonging to the orthorhombic, monoclinic, or triclinic systems) possess two optic axes whose orientation depends on the specific crystal's optical constants.

The physical meaning

In an anisotropic crystal, light entering the crystal in a general direction is split into two rays — the ordinary and the extraordinary — that travel at different velocities and refract at different angles. The two rays are mutually perpendicular in their vibration directions, and the difference in velocity (and therefore in refractive index) produces the optical phenomenon of birefringence. Along an optic axis, however, this splitting does not occur: the two rays travel at the same velocity, and the crystal behaves optically as if it were singly refractive.

The mathematical reason is that the refractive index of an anisotropic crystal depends on direction within the crystal, and the optic axis or axes correspond to the directions where this dependence resolves into a single refractive-index value rather than two distinct values. The Fresnel ellipsoid formalism captures this geometry, and the resulting equations show that uniaxial crystals have one such direction (the optic axis along the c-axis) while biaxial crystals have two.

Uniaxial crystals

Uniaxial crystals — those of the tetragonal, hexagonal, and trigonal systems — have an optical character determined by the symmetry of the crystal class. The single optic axis lies along the c-axis (the axis of higher symmetry), and the refractive indices in directions perpendicular to this axis are equal. The two principal refractive indices are described as the ordinary refractive index (n omega, for light vibrating perpendicular to the optic axis) and the extraordinary refractive index (n epsilon, for light vibrating parallel to the optic axis).

Common uniaxial gem species include corundum (sapphire and ruby), tourmaline, beryl (emerald and aquamarine), zircon, quartz, calcite, and apatite. Each has its own characteristic ordinary and extraordinary refractive indices, and the magnitude and sign of the difference (the birefringence) is a useful identifying property.

Biaxial crystals

Biaxial crystals — those of the orthorhombic, monoclinic, and triclinic systems — have lower crystallographic symmetry and therefore have three distinct principal refractive indices: alpha (smallest), beta (intermediate), and gamma (largest). The geometry of the optical indicatrix in this case has not one but two directions in which the indices coincide, producing the two optic axes. The angle between the two axes (the 2V angle) is characteristic of the species and is itself a useful identification property — see the separate entry on optic angle 2V for detail.

Common biaxial gem species include peridot, topaz, tanzanite, chrysoberyl, andalusite, kyanite, sphene, and most members of the feldspar family. The biaxial optical character has implications for pleochroism (the variation in colour with viewing direction), for cutting strategy (orientation of the rough to optimise face-up colour), and for laboratory identification.

Observation and identification

Identification of the optic axis is most directly accomplished by observing the interference figure under a polarising microscope or conoscope. Light from below passes through crossed polarisers, then through the crystal, then through a Bertrand lens that magnifies the image at the back focal plane of the objective. For uniaxial crystals viewed along the optic axis, the figure shows a black cross with concentric coloured rings; the cross arms remain stationary as the stage rotates. For biaxial crystals viewed close to one of the optic axes, the figure shows a single curved isogyre that rotates as the stage rotates.

This conoscope observation provides several pieces of identification information at once: optic character (uniaxial or biaxial), optic sign (positive or negative), and, for biaxial crystals, the 2V value. The technique is fundamental to laboratory gemmology and is taught as part of any rigorous gemmological education.

Optic axis and pleochroism

Pleochroism — the property of doubly refractive coloured stones to show different colours when viewed in different directions — is intimately connected to the optic axis structure. In uniaxial crystals, two pleochroic colours are observed (along and perpendicular to the optic axis). In biaxial crystals, three pleochroic colours are observed (along the three principal vibration directions, alpha, beta, and gamma). The dichroscope, a small handheld instrument that splits the field of view into the two principal pleochroic directions, is used to observe pleochroism for identification.

For cutters, the orientation of the rough relative to the optic axis is a critical decision. In tanzanite, for example, the strongest blue colour is seen along one of the principal axes, and the rough is oriented to present this colour face-up in the cut stone. Similar considerations apply to most pleochroic species.

In the trade

For working gemmologists, knowledge of the optic axis structure of a species is essential for identification, for treatment evaluation, and for understanding the behaviour of light in the cut stone. The standard gemmological curriculum includes substantial coverage of optic axes, the interference figure, and the conoscope technique, and any rigorous identification work draws on this body of knowledge.

See also uniaxial, biaxial, optic angle 2V, optic sign, conoscope, and interference figure for related entries.

Further reading

• GIA Gems & Gemology — optical mineralogy articles
• GIA — gemmological practice reference
• International Gem Society — optical character and identification