In optics, a diffraction grating is an optical component with a regular pattern, which splits 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 a dispersive element. In Optics, dispersion is the phenomenon in which the Phase velocity of a wave depends on its frequency Because of this, gratings are commonly used in monochromators and spectrometers. A monochromator is an optical device that transmits a mechanically selectable narrow band of Wavelengths of Light or other Radiation chosen from A spectrometer is an Optical instrument used to measure properties of Light over a specific portion of the Electromagnetic spectrum, typically used
A photographic slide with a fine pattern of black lines forms a simple grating. In Photography, a reversal film is a still positive image created on a transparent base using photochemical means For practical applications, gratings generally have grooves or rulings on their surface rather than dark lines. Such gratings can be either transparent or reflective. In Optics, transparency (also called pellucidity) is the Material property of allowing Reflection is the change in direction of a Wave front at an interface between two different media so that the wave front returns into the medium from which Gratings which modulate the phase rather than the amplitude of the incident light are also produced, frequently using holography. Holography (from the Greek, ὅλος - hólos whole + γραφή - grafē writing drawing is a technique that allows the
The principles of diffraction gratings were discovered by James Gregory, about a year after Newton's Prism experiments, initially with artifacts such as bird feathers. James Gregory (November 1638 &ndash October 1675 was a Scottish Mathematician and Astronomer. The first man-made diffraction grating was made around 1785 by Philadelphia inventor David Rittenhouse, who strung hairs between two finely threaded screws. The year 1785 in Science and Technology involved some significant events Philadelphia (ˌfɪləˈdɛlfiə David Rittenhouse ( April 8, 1732 June 26, 1796) was a renowned American Astronomer, Inventor, Clockmaker This was similar to notable German physicist Joseph von Fraunhofer's wire diffraction grating in 1821. Joseph von Fraunhofer ( March 6, 1787 &ndash June 7, 1826) was a German optician The year 1821 in Science and Technology involved some significant events listed below
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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. Diffraction is normally taken to refer to various phenomena which occur when a wave encounters an obstacle
When a wave propagates, each point on the wavefront can be considererd 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 of the point slits in the grating acts as a set of point sources which propagate in all directions. The light in a particular direction, θ, is made up of the interfering components from each slit. In physics interference is the addition ( superposition) of two or more Waves that result in a new wave pattern 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 which satisfy the relationship dsinθ/λ=|m| where d is the separation of the slits and m is an integer. Thus, the diffracted light will have maxima at angles θ 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 in the case of a reflection grating) is called the zero order, and is denoted m = 0. Specular reflection is the perfect Mirror -like reflection of light (or sometimes other kinds of Wave) from a surface in which light from a single incoming 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 (transmission amplitude gratings)
- reflectance (reflection amplitude gratings)
- refractive index (phase gratings)
- direction of optical axis (optical axis gratings)
The grating equation applies in all these cases. In Optics and Spectroscopy, transmittance is the fraction of incident light at a specified Wavelength that passes through a sample In photometry and Heat transfer, reflectivity is the fraction of incident radiation reflected by a surface The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium In Optics, the term optical axis is used to define a direction along which there is some degree of Rotational symmetry.
Gratings as dispersive elements
The wavelength dependence in the grating equation shows that the grating separates an incident polychromatic beam into its constituent wavelength components, i. The term polychromatic is used to described Light that exhibits more than one Color. e. , it is dispersive. In Optics, dispersion is the phenomenon in which the Phase velocity of a wave depends on its frequency Each wavelength of input beam spectrum is sent into a different direction, producing a rainbow of colors under white light illumination. The electromagnetic (EM spectrum is the range of all possible Electromagnetic radiation frequencies A rainbow is an optical and meteorological phenomenon that causes a spectrum of Light to appear in the Sky when the Sun This is visually similar to the operation of a prism, although the mechanism is very different. In Optics, a dispersive prism is a type of optical prism, normally having the shape of a geometrical triangular prism.
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. Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations 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 Millimetre ( American spelling: millimeter, symbol mm) is a unit of Length in the Metric system, equal to Periodicity is the quality of occurring at regular intervals or periods (in Time or Space) and can occur in different contexts A Clock marks The groove period must be on the order of the wavelength 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. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. 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. In the optical regime, in which the use of gratings is most common, this corresponds to wavelengths between 100 nm and 10 µm. A nanometre ( American spelling: nanometer, symbol nm) ( Greek: νάνος nanos dwarf; μετρώ metrό count) is a A micrometre ( American spelling: micrometer; symbol µm) is one millionth of a Metre, or equivalently one thousandth of a Millimetre In that case, the groove density can vary from a few tens of grooves per millimeter, as in echelle gratings, to a few thousands of grooves per millimeter. An echelle grating (from French échelle, meaning stairs or ladder is a type of Diffraction grating which is characterised by a relatively low grooves density but
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 as if it were birefringent. Isotropy is uniformity in all directions Precise definitions depend on the subject area Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray
Fabrication
Originally, high-resolution gratings were ruled using high-quality ruling engines whose construction was a large undertaking. Henry Joseph Grayson designed a machine to make diffraction gratings, succeeding with one of 120,000 lines to the inch (approx. Henry Joseph Grayson (9 May 1856 – 21 March 1918 was a designer of a machine for ruling diffraction gratings and scientist 47 000 per cm) in 1899. Later, photolithographic techniques allowed gratings to be created from a holographic interference pattern. Lithography is a method for Printing using a plate or stone with a completely smooth surface Holography (from the Greek, ὅλος - hólos whole + γραφή - grafē writing drawing is a technique that allows the 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 monochromator is an optical device that transmits a mechanically selectable narrow band of Wavelengths of Light or other Radiation chosen from 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. Photosensitivity is the amount to which an object reacts upon receiving Photons especially Visible light. 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 within the gel. The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium This removes much of the surface scattering effects typically seen in other types of gratings. Scattering is a general physical process whereby some forms of Radiation, such as Light, Sound or moving particles for example are forced to deviate from 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 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
Diffraction gratings are often used in monochromators, spectrometers, wavelength division multiplexing devices, optical pulse compressing devices, and many other optical instruments. A monochromator is an optical device that transmits a mechanically selectable narrow band of Wavelengths of Light or other Radiation chosen from A spectrometer is an Optical instrument used to measure properties of Light over a specific portion of the Electromagnetic spectrum, typically used In Fiber-optic communications wavelength-division multiplexing ( WDM) is a technology which multiplexes multiple optical carrier signals on a In fact, Dispersion Bridge technology for planar lightwave circuits, which is based on diffraction gratings, will likely displace thin-film filter technology and other bulk optics approaches to processing optical signals in both fiber to the home and wavelength division multiplexing devices.
Ordinary pressed CD 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. A Compact Disc (also known as a CD) is an Optical disc used to store digital data, originally developed for storing digital audio DVD (also known as " Digital Versatile Disc " or " Digital Video Disc " - see Etymology)is 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.
In a standard pressed vinyl record when viewed from a low angle perpendicular to the grooves, a similar but less defined effect to that seen in a CD/DVD. A gramophone This is due to viewing angle (less than the critical angle 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.
The image sensor of a digital camera has a fine pattern which can produce a diffraction artifact on the image. An image sensor is a device that converts an optical image to an electric signal Many compact digital still cameras can record Sound and moving Video as well as still Photograph. Lens flare is the light scattered in lens systems through generally unwanted image formation mechanisms such as internal reflection and Scattering from
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. Iridescence is an Optical phenomenon in which Hue changes with the angle from which a surface is viewed The term peafowl refers to Gallinaceous Birds classified within the genera Rheinardia Argusianus Afropavoand Pavo Nacre, also known as mother of pearl, is an organic-inorganic Composite material produced by some Mollusks as an inner shell layer A butterfly is an Insect of the order Lepidoptera. Like all Lepidoptera butterflies are notable for their unusual life cycle with a Insects ( Class Insecta) are a major group of Arthropods and the most diverse group of Animals on the Earth with over a million described
See also
External links
- Diffraction Grating Equations
- How to build a diffraction spectrometer
- Photograph of a lightbulb seen through a diffraction grating.
- Automatic calculation of diffraction angles based on input vatiables.
References
- Adapted from a public domain entry in Federal Standard 1037C. Henry Augustus Rowland ( November 27, 1848 &ndash April 16, 1901) was a U A zone plate is a device used to focus light Unlike lenses however zone plates use Diffraction instead of Refraction. Federal Standard 1037C, entitled Telecommunications Glossary of Telecommunication Terms is a United States Federal Standard issued by the General Services Administration
- National Optical Astronomy Observatories entry regarding volume phase holography gratings.
- Palmer, Christopher, Diffraction Grating Handbook, 6th edition, Newport Corporation (2005). [1]
- Greenslade, Thomas B. , "Wire Diffraction Gratings," The Physics Teacher, February 2004. Volume 42 Issue 2, pp. 76-77. [2]
- Abrahams, Peter Early Instruments of Astronomical Spectroscopy. [3]
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