Diffraction grating

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A very large reflecting diffraction grating.

In optics, a diffraction grating is a reflecting or transparent element, whose optical properties are periodically modulated. Most commonly the diffraction gratings are realized as fine parallel and equally spaced grooves or rulings on material surface. When light is incident on a diffraction grating, diffractive and mutual interference effects occur, and light is reflected or transmitted in discrete directions, called diffraction orders. Because of their dispersive properties, gratings are commonly used in monochromators and spectrometers. These devices were first manufactured by German physicist Joseph von Fraunhofer in 1821.

Theory of operation

Gratings are usually designated by their groove density, expressed in grooves per millimeter (g/mm). The dimension and period of the grooves must be on the order of the wavelength in question. In the optical regime, in which the use of gratings is most common, this corresponds to wavelengths between 100 nm and 10 μm. In that case, the groove density can vary from a few tens of grooves per millimeter, as in echelle gratings, to a few thousands.

A fundamental property of gratings is that the angle of deviation of all but one of the diffracted beams depends on the wavelength of the incident light. Therefore, a grating separates an incident polychromatic beam into its constituent wavelength components, i.e., it is dispersive. Each wavelength of input beam spectrum is sent into a different direction, producing a rainbow of colors under white light illumination. This is visually similar to the operation of a prism, although the mechanism is very different.

A light bulb of a flashlight seen through a transmissive grating, showing three diffracted orders. The order m = 0 corresponds to a direct transmission of light through the grating. In the first positive order (m = +1), colors with increasing wavelengths (from blue to red) are diffracted at increasing angles.

When a beam is incident on a grating with an angle θ_i (measured from the normal of the grating), it is diffracted into several beams. The beam that corresponds to direct transmission (or specular reflection in the case of a reflection grating) is called the zero order, and is denoted m = 0. The other orders correspond to diffraction angles which and are represented by non-zero integers m in the grating equation. For a groove period a and an incident wavelengh λ, the grating equation gives the value of the diffracted angle θ_m(λ) in the order m:

[ a \left( \sin - \sin \right) = m \lambda ]

The diffracted beams corresponding to consecutive orders may overlap, depending on the spectral content of the incident beam and the grating density. The higher the spectral order, the greater the overlap into the next order.

The grating equation shows that the angles of the diffracted orders only depend on the grooves' period, and not on their shape. By controlling the cross-sectional profile of the grooves, it is possible to concentrate most of the diffracted energy in a particular order for a given wavelength. A triangular profile is commonly used. This technique is called blazing. The incident angle and wavelength for which the diffraction is most efficient are often called blazing angle and blazing wavelength. The efficiency of a grating may also depend on the polarization of the incident light.

When groove spacing is less than half the wavelength of light, the only present order is the m = 0 order. Gratings with such small periodicity are called subwavelength gratings and exhibit special optical properties. Made on an isotropic material the subwavelength gratings give rise to form birefringence, in which the material behaves like birefringent.

Diffraction gratings can be produced by modulating one of the following material properties:

• transparency (transmission amplitude gratings)
• reflectance (reflection amplitude gratings)
• refractive index (phase gratings)
• direction of optical axis (optical axis gratings) (phase gratings in biferfingent materials and subwavelength gratings)

Fabrication

Originally, high-resolution gratings were ruled using high-quality ruling engines whose construction was a large undertaking. Later, photolithographic techniques allowed gratings to be created from a holographic interference pattern. Holographic gratings have sinusoidal grooves and may not be as efficient as ruled gratings, but are often preferred in monochromators because they lead to much less stray light. A copying technique allows high quality replicas to be made from master gratings, thereby lowering fabrication costs.

Another method for manufacturing diffraction gratings uses a photosensitive gel sandwiched between two substrates. A holographic interference pattern exposes the gel which is later developed. These gratings, called volume phase holography diffraction gratings have no physical grooves, but instead a periodic modulation of the refractive index within the gel. This removes much of the surface scattering effects typically seen in other types of gratings. These gratings also tend to have higher efficiencies, and allow for the inclusion of complicated patterns into a single grating. Environmental susceptibility is a trade-off, however, as the gel must be contained at low temperature and humidity.

Semiconductor technology today is also utilized to etch holographically patterned gratings into robust materials as fused silica. In this way, low stray-light holography is combined with the high efficiency of deep, etched transmission gratings, and can be incorporated into high volume, low cost semiconductor manufacturing technology.

Examples

The grooves of a compact disc can act as a grating and produce iridescent reflections.

Diffraction gratings are often used in monochromators, spectrometers, wavelength division multiplexing devices, optical pulse compressing devices, and many other optical instruments.

Ordinary pressed CD and DVD media are every-day examples of diffraction gratings and can be used to demonstrate the effect by shining an ordinary laser pointer onto the surface. This is a side effect of their manufacture, as one surface of a CD has many small pits in the plastic, arranged within concentric rings; that surface has a thin layer of metal applied to make the pits more visible. The structure of a DVD is optically similar, although it may have more than one pitted surface, and all pitted surfaces are inside the disc.

Diffraction gratings are also present in nature. For example, the iridescent colors of peacock feathers, mother-of-pearl, butterfly wings, and some other insects are caused by very fine regular structures that diffract light, splitting it into its component colors.

See also

• Diffraction

References

• Adapted from a public domain entry in Federal Standard 1037C.
• National Optical Astronomy Observatories entry regarding volume phase holography gratings.
• Palmer, Christopher, Diffraction Grating Handbook, 6th edition, Newport Corporation (2005).

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