Diffraction grating
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In optics, a diffraction grating is a reflecting or transparent substrate whose surface contains fine parallel grooves or rulings that are equally spaced. When light is incident on a diffraction grating, diffractive and mutual interference effects occur, and light is reflected or transmitted in discrete directions, called orders. Because of their dispersive properties, gratings are commonly used in monochromators and spectrometers.
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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 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.
When a beam is incident on a grating with an angle θi (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 noted m = 0. The other orders correspond to diffracted angles that deviate from the one predicted by geometrical optics, and are represented by non-zero integers m. For a groove period a and an incident wavelengh λ, the grating equation gives the value of the diffracted angle θm(λ) in the order m:
- <math> a \left( \sin{\theta_m(\lambda)} - \sin{\theta_i} \right) = m \lambda </math>
Note that m can be positive or negative, resulting in diffracted orders on both sides of the zero order beam.
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.
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 sandwitched between two substrates. A holographic interference pattern exposes the gel which is later developed. These gratings, called volume phase holograpy 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.
Examples
Diffraction gratings are often used in monochromators and 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 they have a thin layer of aluminium with regular grooves pressed into it in a spiral pattern.
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.
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).
