Crystals are categorized as both isotropic and anisotropic depending upon their optical behavior and whether or not their crystallographic axes are equivalent. All isotropic crystals have identical axes that similarly engage with light, irrespective of the crystal orientation with admire to incident light waves. Light getting into an isotropic crystal is refracted at a regular attitude and passes through the crystal at a fixed angle, having constant speed without being polarized with the aid of interaction with the electronic components of the crystalline lattice.

On the other hand, anisotropic crystals have crystallographically awesome axes and engage with light in a way that is established or depends upon the orientation of the crystalline lattice subject to the incident light. When light ray enters the optical axis of anisotropic crystals, it acts in a manner just like the interplay with isotropic crystals and passes through at one velocity. But, while light enters a non-equal axis, it is refracted into two rays. This phenomenon is explained by a term called birefringence.

Birefringence, also known as double refraction, is an optical property in which a single ray of unpolarized light getting into an anisotropic medium is divided into two rays, each going in a unique route. One ray (referred to as extraordinary ray) is bent, or refracted, at an angle as it travels through the medium; the opposite ray (called the regular ray) passes via the medium unchanged.

Double refraction may be determined by means of comparing two materials, glass and calcite. If a pencil mark is drawn upon a sheet of paper after which is protected with a chunk of glass, most effective one photograph may be seen; however, if the same paper is blanketed with a bit of calcite, and the crystal is orientated in a particular way only then marks will become visible.

Birefringence is classified as intrinsic or pressure-caused birefringence. Intrinsic birefringence is a kind of birefringence resulting from the anisotropy occurring within the crystals. The atomic arrangement of the crystal itself is the source of birefringence. Examples are calcite, tourmaline, and many others While on the other hand, pressure-induced birefringence is a kind of birefringence that is prompted due to the stresses imposed on fabric materials, including glass or plastics show stress birefringence.

Birefringence can be quantified by measuring the changes that happened in the polarization of light waves. This technique of measurement is referred to as polarimetry. A unique technique, referred to as twin polarization interferometry is used to measure the birefringence of lipid bilayers.

Applications of birefringence

Birefringence is utilized in clinical diagnostics. One powerful accent used with optical microscopes is a couple of crossed polarizing filters. Light from the source is polarized inside the x course after passing through the first polarizer. However, above the specimen, a polarizer (a so-known as an analyzer) is oriented in the y-direction. Therefore, the analyzer will accept no light from the supply, and the field will seem dark. But, areas of the sample possessing birefringence will usually couple a number of the x-polarized light into the y-polarization; those regions will then appear brilliant against the darkish historical past. Changes to this primary principle can differentiate between positive and poor birefringence.

Birefringence is extensively utilized in optical gadgets, such as liquid crystal displays, light modulators, shade filters, wave plates, and optical axis gratings. It plays an essential role in the 2nd harmonic generation and lots of different nonlinear tactics. It’s also applied in clinical diagnostics. Needle biopsy of suspected gouty joints might be negatively birefringent if urate crystals are present.

Birefringence and birefringent material
Figure 1: Birefringence and birefringent material.

Uniaxial materials

They are a class of anisotropic minerals in which all the minerals that crystallize in the tetragonal and hexagonal crystal systems are included. They are known as uniaxial due to the fact they have only one optical axis. Light traveling alongside the course of this single optical axis shows the same properties as isotropic substances in the sense that the polarization path of the light is not always modified by using passage through the crystal. 

Similarly, if the optical axis is orientated perpendicular to the microscope level with the analyzer inserted, the grain will stay extinct all through a 360-degree rotation of the stage. The single optical axis is coincident with the c-crystallographic axis in tetragonal and hexagonal minerals. For this reason, light traveling parallel to the c-axis will behave as though it has been traveling in an isotropic substance because, looking down the c-axis of tetragonal or hexagonal minerals, one sees only equal period a-axes, similar to in isometric minerals.

Biaxial materials

All minerals that crystallize within the orthorhombic, triclinic, or monoclinic crystal structures are biaxial. There are two optical axes in them that differentiate biaxial crystals from uniaxial crystals. Just Like uniaxial crystals, biaxial crystals do have indices of refraction that change between two extremes but also have a completely unique intermediate refractive index. Biaxial refractive indices are as follows: the symbol α (or X) is for the smallest refractive index, the symbol β (or Y) is for intermediate refractive index, and the symbol γ (or Z) is for the largest refractive index. The optical symmetry is equivalent to 2/m2/m2/m for all biaxial minerals, but the optical directions have various relationships to the crystallographic directions in each crystal system.

In orthorhombic crystals, the optical directions relate to the crystallographic axes in orthorhombic crystals, i.e., the direction in X and its relevant refractive index, α can be either the a, b, or c crystallographic axes, beta β and direction in Y may be parallel to a, b, c or both, and the direction Z or γ, can be parallel to either a, b, or c.

If we talk about monoclinic crystals, any one of the X (α), Y (β), or Z (γ) indices or directions are parallel with the crystallographic axis b, and the remaining two do not coincide with crystallographic directions.  No optical indices or directions are coincident with crystallographic directions in triclinic crystals. However, in some extreme cases, one of the indices might be concurrent with one of the crystallographic directions in triclinic crystals.

Further readings

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