Gradient index lenses are optical lenses — often planar — which are used in specialized applications.

Gradient index (or GRIN) optics encompasses optical effects produced by gradual variation of the refractive index of a material. Use of these materials results in the possible construction of uniquely-shaped lenses which lack the typical aberrations present in conventional spherical lenses. An excellent example of a gradient index optical system is the human eye. The refractive index of the eye lens varies from 1.406 in the center to 1.386 in the outer layers, allowing humans to see images with both good resolution and low aberration. The refractive index of the vitreous humour within the eye is typically around 1.3.

The parts of the eye and their respective refractive indices.

Image credit: ScubaGeek

Refractive Index Explained

The refractive index of a material describes how light propagates through the material when compared to the speed of light through a vacuum. Refractive index is defined as:

where:

n = refractive index

c = speed of light in a vacuum

v = speed of light through the substance/material

Therefore, taking the example of the typical vitreous humour index of 1.3, this value states that light moves 1.3 times faster through water than it does through the vitreous humour. While almost all refractive indices are greater than 1, it is possible for specialized materials to have indices less than 1 due to the fact that the index measures the phase velocity — not the true propagation speed — of light.

The table below lists common GRIN lens materials and their refractive indices. Material subtypes within each table entry limit the listed index range; for example, while both of their indices lie within the range of optical glass materials, flint glass and borosilicate glass have the differing ranges of 1.523-1.925 and 1.470, respectively. A material's refractive index also determines its optimal wavelength range. Substances with indices between 1 and 2 — namely glass and plastics — are most suitable for the visible spectrum (380 to 750 nm), while those greater than 2 — zinc selenide and especially germanium — are more appropriate for infrared (750 to 2500 nm) applications.

Gradient Index Lens Operation

GRIN lenses are manufactured by using various methods — among them neutron irradiation, chemical vapor deposition, and ion exchange — to create a variable refractive index on the lens's surface. By precisely varying the refractive index of the surface, gradient index lenses are able to continuously bend light within the lens until the light rays focus on the focal point behind the lens. This contrasts with conventional spherical lenses, which bend light only twice: when the waves meet the surface of the lens and when they exit the back of the lens.

A comparison of a positive GRIN lens (left) and a conventional lens.

Image credit: Grintech

Like most optical lenses, gradient index lenses can be positive (converging) or negative (diverging). The GRIN lens image above shows a converging lens, while the one below shows a negative one.

Image credit: Grintech

Applications

GRIN lenses are useful in any application requiring a flat lens, including photocopiers and scanners. They are especially useful in fiber optics: a flat lens can easily be connected to optical fiber in order to provide collimated output.

A GRIN lens within a fiber optic collimator. Image credit: Thorlabs

Specifications

Optical Surface Quality

A gradient index lens's surface quality rating is based on the MIL-0-131830A(1963) standard. The standard specifies two different types of surface defects:

• Scratches are defects with lengths many times their widths.
• Digs are defects with nearly equal lengths and width.

Surface quality ratings consist of two numbers separated by a hyphen, as in x-y. The x in this formula refers to the maximum allowable width of a scratch — expressed in tenths of a micron — while the y refers to the maximum width of a dig, expressed in hundredths of a millimeter. For example, a lens with a 20-10 scratch/dig rating specifies that any scratches have a maximum width of .002 millimeters (2 microns), while any digs must not exceed .10 mm in width. Smaller numbers are desirable for both specifications. 

Flatness

Optics manufacturers often specify optical surface flatness using a "peak to valley" (P-V) measurement. This value is the difference between the relative highest and lowest points of the optical surface. P-V is expressed as a ratio of a set wavelength, as shown in the table below. When expressed as a fraction, a higher denominator indicates better quality.

References

Grintech - Gradient Index Optics