Diffraction grating
Overview
 
In optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, a diffraction grating is an optical component with a periodic structure, which splits and diffracts
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

 light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

 element. Because of this, gratings are commonly used in monochromator
Monochromator
A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input...

s and spectrometer
Spectrometer
A spectrometer is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum, typically used in spectroscopic analysis to identify materials. The variable measured is most often the light's intensity but could also, for instance, be the polarization...

s.

A photographic slide with a fine pattern of purple lines forms a complex grating.
Encyclopedia
In optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

, a diffraction grating is an optical component with a periodic structure, which splits and diffracts
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

 light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

 element. Because of this, gratings are commonly used in monochromator
Monochromator
A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input...

s and spectrometer
Spectrometer
A spectrometer is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum, typically used in spectroscopic analysis to identify materials. The variable measured is most often the light's intensity but could also, for instance, be the polarization...

s.

A photographic slide with a fine pattern of purple lines forms a complex grating. For practical applications, gratings generally have ridges or rulings on their surface rather than dark lines. Such gratings can be either transmissive or reflective. Gratings which modulate the phase rather than the amplitude of the incident light are also produced, frequently using holography
Holography
Holography is a technique that allows the light scattered from an object to be recorded and later reconstructed so that when an imaging system is placed in the reconstructed beam, an image of the object will be seen even when the object is no longer present...

.

The principles of diffraction gratings were discovered by James Gregory
James Gregory (astronomer and mathematician)
James Gregory FRS was a Scottish mathematician and astronomer. He described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions.- Biography :The...

, about a year after Newton's prism experiments, initially with artifacts such as bird feathers. The first man-made diffraction grating was made around 1785
1785 in science
The year 1785 in science and technology involved some significant events.-Aviation:* January 7 - Frenchman Jean-Pierre Blanchard and American John Jeffries travel from Dover, England to Calais, France in a gas balloon, becoming the first to cross the English Channel by air.-Biology:* Antoine...

 by Philadelphia inventor David Rittenhouse
David Rittenhouse
David Rittenhouse was a renowned American astronomer, inventor, clockmaker, mathematician, surveyor, scientific instrument craftsman and public official...

, who strung hairs between two finely threaded screws. This was similar to notable German physicist Joseph von Fraunhofer
Joseph von Fraunhofer
Joseph von Fraunhofer was a German optician. He is known for the discovery of the dark absorption lines known as Fraunhofer lines in the Sun's spectrum, and for making excellent optical glass and achromatic telescope objectives.-Biography:Fraunhofer was born in Straubing, Bavaria...

's wire diffraction grating in 1821
1821 in science
The year 1821 in science and technology involved some significant events, listed below.-Astronomy:* Johann Franz Encke calculates that Comet Encke has a periodic orbit, the second comet after Comet Halley for which this has been discovered....

.

Theory of operation

The relationship between the grating spacing and the angles of the incident and diffracted beams of light is known as the grating equation.

According to the Huygens–Fresnel principle, each point on the wavefront of a propagating wave can be considered to act as a point source, and the wavefront at any subsequent point can be found by adding together the contributions from each of these individual point sources.

An idealised grating is considered here which is made up of a set of long and infinitely narrow slits of spacing d. When a plane wave of wavelength λ is incident normally on the grating, each slit in the grating acts as a point source propagating in all directions. The light in a particular direction, θ, is made up of the interfering components from each slit. Generally, the phases of the waves from different slits will vary from one another, and will cancel one another out partially or wholly. However, when the path difference between the light from adjacent slits is equal to the wavelength, λ, the waves will all be in phase. This occurs at angles θm which satisfy the relationship dsinθm/λ=|m| where d is the separation of the slits and m is an integer. Thus, the diffracted light will have maxima at angles θm given by


It is straightforward to show that if a plane wave is incident at an angle θi, the grating equation becomes


The light that corresponds to direct transmission (or specular reflection
Specular reflection
Specular reflection is the mirror-like reflection of light from a surface, in which light from a single incoming direction is reflected into a single outgoing direction...

 in the case of a reflection grating) is called the zero order, and is denoted m = 0. The other maxima occur at angles which are represented by non-zero integers m. Note that m can be positive or negative, resulting in diffracted orders on both sides of the zero order beam.

This derivation of the grating equation has used an idealised grating. However, the relationship between the angles of the diffracted beams, the grating spacing and the wavelength of the light apply to any regular structure of the same spacing, because the phase relationship between light scattered from adjacent elements of the grating remains the same. The detailed distribution of the diffracted light depends on the detailed structure of the grating elements as well as on the number of elements in the grating, but it will always give maxima in the directions given by the grating equation.

Gratings can be made in which various properties of the incident light are modulated in a regular pattern; these include
  • transparency
    Transmittance
    In optics and spectroscopy, transmittance is the fraction of incident light at a specified wavelength that passes through a sample. A related term is absorptance, or absorption factor, which is the fraction of radiation absorbed by a sample at a specified wavelength...

     (transmission amplitude gratings)
  • reflectance
    Reflectivity
    In optics and photometry, reflectivity is the fraction of incident radiation reflected by a surface. In general it must be treated as a directional property that is a function of the reflected direction, the incident direction, and the incident wavelength...

     (reflection amplitude gratings)
  • refractive index
    Refractive index
    In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

     (phase gratings)
  • direction of optical axis
    Optical axis
    An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens or microscope.The optical axis is an imaginary line that defines the path along which light propagates through the system...

     (optical axis gratings)


The grating equation applies in all these cases.

QED

QED
Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

 (quantum electrodynamics) offers another derivation of the properties of a diffraction grating in terms of photons as particles. QED models photons as following all paths from a source to a final point, each of which has a certain probability amplitude
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number whose modulus squared represents a probability or probability density.For example, if the probability amplitude of a quantum state is \alpha, the probability of measuring that state is |\alpha|^2...

, which can be represented as a vector or complex number (equivalently), or as Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

 simply calls them in his book on QED, "arrows".

For the probability that a certain event will happen, one sums the probability amplitudes for all of the possible ways in which the event can occur, and then takes the square of the length of the result. The probability amplitude of a photon from a monochromatic source, in this case, is modeled as an arrow that spins rapidly until it is "evaluated" when the photon reaches its final point. This spinning is actually dependent on the time at which the photon would have left the monochromatic source, as the probability amplitudes of photons do not "spin" while they are in transit. For example, for the probability that light will reflect off of a mirror, one sets the photon's probability amplitude spinning as it leaves the source, follows it to the mirror, and then to its final point,even for paths that do not involve bouncing off of the mirror at equal angles. One then "evaluates" the probability amplitude at the photon's final point; next, one sums these arrows in a standard vector sum, and squares the length of the result for the probability that this photon will reflect off of the mirror. The times these paths take are what determine the angle of the probability amplitude arrow, as they 'spin' at a constant rate (which is related to the frequency of the photon).

The times of the paths near the classical reflection site of the mirror will be nearly the same, so as a result the probability amplitudes will point in nearly the same direction—thus, they will have a sizable sum. Examining the paths towards the edges of the mirror reveals that the times of nearby paths are quite different from each other, and thus we wind up summing vectors that cancel out quickly. So, there is a higher probability that light will follow a near-classical reflection path than a path further out. However, a diffraction grating can be made out of this mirror, by scraping away areas near the edge of the mirror that usually cancel nearby amplitudes out—but now, since the photons would not reflect from the scraped-off portions, the probability amplitudes which all point, for instance, to the right can have a sizable sum. Thus, this would let light of the right frequency sum to a larger probability amplitude, and as such possess a larger probability of reflecting.

This particular description involves many simplifications: a point source, a "surface" that light can reflect off of (thus neglecting the interactions with electrons) and so forth. However, this approximation is a reasonable one to illustrate a diffraction grating conceptually. Light of a different frequency can also use the same diffraction grating, but with a different final point.

Gratings as dispersive elements

The wavelength dependence in the grating equation shows that the grating separates an incident polychromatic
Polychromatic
The term polychromatic means having several colours.It is used to describe light that exhibits more than one color. In a technical respect, this can also mean that it contains radiation of more than one wavelength. The study of polychromatics is particularly useful in the production of diffraction...

 beam into its constituent wavelength components, i.e., it is dispersive
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...

. Each wavelength of input beam spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

 is sent into a different direction, producing a rainbow
Rainbow
A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc...

 of colors under white light illumination. This is visually similar to the operation of a prism, although the mechanism is very different.

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
Blazed grating
A blazed grating is a special type of diffraction grating.Blazed gratings produce maximum efficiency at a specified wavelength; that is, a diffraction grating that is "blazed at 250nm" will operate most efficiently when light with a wavelength of 250 nm passes through the grating.Like standard...

.
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. Gratings are usually designated by their groove density, the number of grooves per unit length, usually expressed in grooves per millimeter (g/mm), also equal to the inverse of the groove period. The groove period must be on the order of the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

 of interest; the spectral range covered by a grating is dependent on groove spacing and is the same for ruled and holographic gratings with the same grating constant. The maximum wavelength that a grating can diffract is equal to twice the grating period, in which case the incident and diffracted light will be at ninety degrees to the grating normal. To obtain frequency dispersion over a wider frequency one must use a prism
Prism (optics)
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

. In the optical regime, in which the use of gratings is most common, this corresponds to wavelengths between 100 nm  and 10 µm
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

. In that case, the groove density can vary from a few tens of grooves per millimeter, as in echelle gratings
Echelle grating
An echelle grating is a type of diffraction grating which is characterised by a relatively low groove density but is optimized for high diffraction orders. Echelle gratings are, like other types of diffraction grating, used in spectrometers and similar instruments, such as HARPS, and numerous...

, to a few thousands of grooves per millimeter.

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
Isotropy
Isotropy is uniformity in all orientations; it is derived from the Greek iso and tropos . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary...

 material the subwavelength gratings give rise to form birefringence, in which the material behaves as if it were birefringent.

Fabrication

Originally, high-resolution gratings were ruled using high-quality ruling engines whose construction was a large undertaking. Henry Joseph Grayson
Henry Joseph Grayson
Henry Joseph Grayson was a nurseryman and scientist, best known as the designer of a machine for ruling diffraction gratings....

 designed a machine to make diffraction gratings, succeeding with one of 120,000 lines to the inch (approx. 47 000 per cm) in 1899. Later, photolithographic
Lithography
Lithography is a method for printing using a stone or a metal plate with a completely smooth surface...

 techniques allowed gratings to be created from a holographic
Holography
Holography is a technique that allows the light scattered from an object to be recorded and later reconstructed so that when an imaging system is placed in the reconstructed beam, an image of the object will be seen even when the object is no longer present...

 interference pattern. Holographic grating
Holographic grating
A holographic grating is a type of diffraction grating formed by an interference-fringe field of two laser beams whose standing-wave pattern is exposed to a polished substrate coated with photoresist. Processing of the exposed medium results in a pattern of straight lines with a sinusoidal cross...

s have sinusoidal grooves and may not be as efficient as ruled gratings, but are often preferred in monochromator
Monochromator
A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input...

s because they lead to much less stray light
Stray light
Stray light is light in an optical system, which was not intended in the design. The light may be from the intended source, but follow paths other than intended, or it may be from a source other than the intended source...

. A copying technique allows high quality replicas to be made from master gratings of either type, 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 (or VPH diffraction gratings) have no physical grooves, but instead a periodic modulation of the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

 within the gel. This removes much of the surface scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

 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. In older versions of such gratings, environmental susceptibility was a trade-off, as the gel had to be contained at low temperature and humidity. Typically, the photosensitive substances are sealed between two substrates which make them resistant to humidity, thermal and mechanical stresses. VPH diffraction gratings are not destroyed by accidental touches and are more scratch resistant than typical relief gratings.

Semiconductor technology today is also utilized to etch holographically patterned gratings into robust materials such 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.

A new technology for grating insertion into integrated photonic lightwave circuits is digital planar holography
Digital planar holography
Digital Planar Holography is a new technology, developed recently, circa 2003, for fabricating miniature components for integrated optics. The essence of the DPH technology is embedding digital holograms, calculated in a computer, inside a planar waveguide...

 (DPH). DPH gratings are generated in computer and fabricated on one or several interfaces of an optical waveguide planar with standard micro-lithography or nano-imprinting methods, compatible with mass-production. Light propagates inside the DPH gratings, confined by the refractive index gradient, which provides longer interaction path and greater flexibility in light steering.

Examples

Diffraction gratings are often used in monochromator
Monochromator
A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input...

s, spectrometer
Spectrometer
A spectrometer is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum, typically used in spectroscopic analysis to identify materials. The variable measured is most often the light's intensity but could also, for instance, be the polarization...

s, laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

s, wavelength division multiplexing devices, optical pulse compressing devices, and many other optical instruments.

Ordinary pressed CD
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

 and DVD media are every-day examples of diffraction gratings and can be used to demonstrate the effect by reflecting sunlight off them onto a white wall. This is a side effect of their manufacture, as one surface of a CD has many small pits in the plastic, arranged in a spiral; 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.

In a standard pressed vinyl record
Gramophone record
A gramophone record, commonly known as a phonograph record , vinyl record , or colloquially, a record, is an analog sound storage medium consisting of a flat disc with an inscribed, modulated spiral groove...

 when viewed from a low angle perpendicular to the grooves, a similar but less defined effect to that in a CD/DVD is seen. This is due to viewing angle (less than the critical angle
Critical angle
Critical angle can refer to:*Critical angle the angle of incidence above which total internal reflection occurs*Critical angle of attack, in aerodynamics; the angle of attack which produces the maximum lift coefficient...

 of reflection of the black vinyl) and the path of the light being reflected due to this being changed by the grooves, leaving a rainbow relief pattern behind.

Natural gratings

Striated muscle
Striated muscle
Striated muscle tissue is a form of fibers that are combined into parallel fibers. More specifically, it can refer to:* Cardiac muscle .* Skeletal muscle* Branchiomeric muscles...

 is the most commonly found natural diffraction grating and, indeed, this has helped physiologists in determining the structure of such muscle. Aside from this, diffraction gratings are rarely present in nature. Most commonly confused with diffraction gratings are the iridescent colors of peacock feathers, mother-of-pearl, and butterfly
Butterfly
A butterfly is a mainly day-flying insect of the order Lepidoptera, which includes the butterflies and moths. Like other holometabolous insects, the butterfly's life cycle consists of four parts: egg, larva, pupa and adult. Most species are diurnal. Butterflies have large, often brightly coloured...

 wings. Iridescence is common in birds, fishes, insects, and some flowers, and is almost always caused by thin-film interference
Thin-film interference
Thin-film interference is the phenomenon that occurs when incident light waves reflected by the upper and lower boundaries of a thin film interfere with one another to form a new wave. Studying this new wave can reveal information about the surfaces from which its components reflected, including...

 rather than diffraction. Diffraction will produce the entire spectrum of colors as the viewing angle changes, whereas thin-film interference usually produces a much narrower range. The cell structures in plants and animals are usually too irregular to produce the fine slit geometry necessary for a diffraction grating. However, natural gratings do occur in some invertebrate marine animals, like the antennae of seed shrimp, and have even been discovered in Burgess Shale fossils
Burgess shale type fauna
A number of assemblages bear fossil assemblages similar in character to that of the Burgess Shale. While many are also preserved in a similar fashion to the Burgess Shale, the term "Burgess Shale type fauna" covers assemblages based on taxonomic criteria only.-Extent:The fauna of the middle...

.

Diffraction grating effects are sometimes seen in meteorology
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

. Diffraction coronas are colorful rings surrounding a source of light, such as the sun. These are usually observed much closer to the light source than halos
Halo (optical phenomenon)
A halo from Greek ἅλως; also known as a nimbus, icebow or gloriole) is an optical phenomenon produced by ice crystals creating colored or white arcs and spots in the sky. Many are near the sun or moon but others are elsewhere and even in the opposite part of the sky...

, and are caused by very fine particles, like water droplets, ice crystals, or smoke particles in a hazy sky. When the particles are all nearly the same size they diffract the incoming light at very specific angles. The exact angle depends on the size of the particles. Diffraction coronas are commonly observed around light sources, like candle flames or street lights, in the fog. Cloud iridescence
Cloud iridescence
thumb|260px|Cloud iridescenceCloud iridescence is the occurrence of colors in a cloud similar to those seen in oil films on puddles, and is similar to irisation. It is a fairly uncommon phenomenon, most often observed in altocumulus, cirrocumulus and lenticular clouds, and very rarely in Cirrus...

is caused by diffraction, occurring along coronal rings when the particles in the clouds are all uniform in size.

External links

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