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An incandescent light-bulb viewed through a transmissive diffraction grating.

In optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts 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 element. Because of this, gratings are commonly used in monochromators and spectrometers.

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.^[1]

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.^[2] The first man-made diffraction grating was made around 1785 by Philadelphia inventor David Rittenhouse, who strung hairs between two finely threaded screws.^[3] This was similar to notable German physicist Joseph von Fraunhofer's wire diffraction grating in 1821.^[4]

Diffraction creates the "rainbow" colors reflected from a compact disc (see Examples, below). A grating has parallel lines, while a CD has a spiral of finely-spaced data tracks. Diffraction colors also appear when one looks at a bright point source through a translucent fine-pitch umbrella-fabric covering. Decorative patterned plastic films based on reflective grating patches are very inexpensive to produce, and very commonplace.

Theory of operation

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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.

Gratings may be of the 'reflective' or 'transmissive' type, analogous to a mirror or lens respectively. A grating has a 'zero-order mode' (where m=0), in which there is no diffraction and a ray of light behaves according to the laws of reflection and refraction the same as with a mirror or lens respectively.

An idealised grating is considered here which is made up of a set of slits of spacing d, that must be wider than the wavelength of interest to cause diffraction. Assuming a plane wave of wavelength λ with normal incidence (perpendicular to the grating), each slit in the grating acts as a quasi point-source from which light propagates in all directions (although this is typically limited to a hemisphere). After light interacts with the grating, the diffracted light is composed of the sum of interfering wave components emanating from each slit in the grating. At any given point in space through which diffracted light may pass, the path length to each slit in the grating will vary. Since the path length varies, generally, so will the phases of the waves at that point from each of the slits, and thus will add or subtract from one another to create peaks and valleys, through the phenomenon of additive and destructive interference. When the path difference between the light from adjacent slits is equal to half the wavelength, λ/2, the waves will all be out of phase, and thus will cancel each other to create points of minimum intensity. Similarly, when the path difference is λ, the phases will add together and maxima will occur. The maxima occur at angles θ_m, which satisfy the relationship dsinθ_m/λ=|m| where θ_m is the angle between the diffracted ray and the grating's normal vector, and d is the distance from the center of one slit to the center of the adjacent slit, and m is an integer representing the propagation-mode of interest.

Thus, when light is normally incident on the grating, the diffracted light will have maxima at angles θ_m given by:

d\ \sin {\theta _{m}}=m\lambda

It is straightforward to show that if a plane wave is incident at any arbitrary angle θ_i, the grating equation becomes:

d\left(\sin {\theta _{i}}+\sin {\theta _{m}}\right)=m\lambda

When solved for the diffracted angle maxima, the equation is:

\theta _{m}=\arcsin {\left({\frac {m\lambda }{d}}-\sin {\theta _{i}}\right)}

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. 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 is based on 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.

Quantum electrodynamics

Quantum electrodynamics (QED) offers another derivation of the properties of a diffraction grating in terms of photons as particles (at some level). QED can be described intuitively with the path integral formulation of quantum mechanics. As such it can model photons as potentially following all paths from a source to a final point, each path with a certain probability amplitude. These probability amplitudes can be represented as a complex number or equivalent vector—or, as Richard Feynman 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 for a photon from a monochromatic source to arrive at a certain final point at a given time, in this case, can be modeled as an arrow that spins rapidly until it is evaluated when the photon reaches its final point. For example, for the probability that a photon will reflect off of a mirror and be observed at a given point a given amount of time later, 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 can then evaluate the probability amplitude at the photon's final point; next, one can integrate over all of these arrows (see vector sum), and square the length of the result to obtain the probability that this photon will reflect off of the mirror in the pertinent fashion. The times these paths take are what determine the angle of the probability amplitude arrow, as they can be said to "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 would all wind up pointing, for instance, at forty-five degrees can have a sizable sum. Thus, this would let light of the right frequency to make this happen sum to a larger probability amplitude, and as such possess a larger probability of reaching the appropriate final point.

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. The biggest simplification is perhaps in the fact that the "spinning" of the probability amplitude arrows is actually more accurately explained as a "spinning" of the source, as the probability amplitudes of photons do not "spin" while they are in transit. We obtain the same variation in probability amplitudes by allowing the time at which the photon left the source to be indeterminate, and the time of the path now tells us when the photon would have left the source, and thus what the angle of its "arrow" would be. However, this model and approximation is a reasonable one to illustrate a diffraction grating conceptually. Light of a different frequency may also reflect off of the same diffraction grating, but with a different final point.^[5]

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.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.

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. 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 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. 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 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 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 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 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 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 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. 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 (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

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

Diffraction gratings are often used in monochromators, spectrometers, lasers, 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 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 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 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.

Diffraction gratings are also used to distribute evenly the frontlight of e-readers such as the Nook Simple Touch with GlowLight.^[6]

Natural gratings

Striated muscle is the most commonly found natural diffraction grating^[7] and, indeed, this has helped physiologists in determining the structure of such muscle. Aside from this, the chemical structure of crystals can be thought of as diffraction gratings for types of electromagnetic radiation other than visible light, this is the basis for techniques such as X-ray crystallography. Most commonly confused with diffraction gratings are the iridescent colors of peacock feathers, mother-of-pearl, and butterfly wings. Iridescence is common in birds, fishes, insects, and some flowers, and is almost always caused by thin-film interference rather than diffraction.^[8] Diffraction will produce the entire spectrum of colors as the viewing angle changes, whereas thin-film interference usually produces a much narrower range.^[9] The cell structures in plants and animals are usually too irregular to produce the fine slit geometry necessary for a diffraction grating.^[10] 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.^[11]^[12]

Diffraction grating effects are sometimes seen in meteorology. 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, 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 is caused by diffraction, occurring along coronal rings when the particles in the clouds are all uniform in size.^[13]

References

↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ Letter from James Gregory to John Collins, dated 13 May 1673. Reprinted in: Correspondence of Scientific Men of the Seventeenth Century …, ed. Stephen Jordan Rigaud (Oxford, England: Oxford University Press, 1841), vol. 2, pp. 251–255, especially p. 254
↑
See:
- "An optical problem, proposed by Mr. Hopkinson, and solved by Mr. Rittenhouse," Transactions of the American Philosophical Society, vol. 2, pages 201-206 (1786).
- Thomas D. Cope (1932) "The Rittenhouse diffraction grating". Reprinted in: David Rittenhouse, The Scientific Writings of David Rittenhouse, Brooke Hindle, ed. (New York, New York: Arno Press, 1980), pages 377-382. (A reproduction of Rittenhouse's letter re his diffraction grating appears on pages 369-374.)
↑
See:
- Frauhofer. Jos. (1821) "Neue Modifikation des Lichtes durch gegenseitige Einwirkung und Beugung der Strahlen, und Gesetze derselben" (New modification of light by the mutual influence and the diffraction of [light] rays, and the laws thereof), Denkschriften der Königlichen Akademie der Wissenschaften zu München (Memoirs of the Royal Academy of Science in Munich), 8: 3-76.
- Fraunhofer, Jos. (1823) "Kurzer Bericht von den Resultaten neuerer Versuche über die Gesetze des Lichtes, und die Theorie derselben" (Short account of the results of new experiments on the laws of light, and the theory thereof) Annalen der Physik, 74(8): 337-378.
↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
↑ http://www.ifixit.com/Teardown/Nook-Simple-Touch-with-GlowLight-Teardown/9301/3
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ Nature's palette: the science of plant color By David Webster Lee - University of Chicago Press 2007 Page 255-256
↑ Nature's palette: the science of plant color By David Webster Lee - University of Chicago Press 2007 Page 255
↑ Nature's palette: the science of plant color By David Webster Lee - University of Chicago Press 2007 Page 84
↑ Nature's palette: the science of plant color By David Webster Lee - University of Chicago Press 2007 Page 41
↑ http://www.nhm.ac.uk/about-us/news/2006/mar/news_7834.html
↑ Polarized light in nature By G. P. Können - Cambridge University Press 1985 Page 72-73

Template:Refbegin

Template:FS1037C
Hutley, Michael, Diffraction Gratings (Techniques of Physics), Academic Press (1982). ISBN 0-12-362980-2
Loewen, Erwin & Evgeny Popov, Diffraction Gratings and Applications, CRC; 1 edition (1997). ISBN 0-8247-9923-2
Palmer, Christopher, Diffraction Grating Handbook, 6th edition, Newport Corporation (2005).
Greenslade, Thomas B., "Wire Diffraction Gratings," The Physics Teacher, February 2004. Volume 42 Issue 2, pp. 76–77.
Abrahams, Peter, Early Instruments of Astronomical Spectroscopy.
William E. L. Grossman, "The optical characteristics and production of diffraction gratings," Journal of Chemical Education 70:9 (Sep 1993), p. 741.
National Optical Astronomy Observatories entry on volume phase holography gratings.

Template:Refend

External links

[1] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[2] Letter from James Gregory to John Collins, dated 13 May 1673. Reprinted in: Correspondence of Scientific Men of the Seventeenth Century …, ed. Stephen Jordan Rigaud (Oxford, England: Oxford University Press, 1841), vol. 2, pp. 251–255, especially p. 254

[3] See:
"An optical problem, proposed by Mr. Hopkinson, and solved by Mr. Rittenhouse," Transactions of the American Philosophical Society, vol. 2, pages 201-206 (1786).

Thomas D. Cope (1932) "The Rittenhouse diffraction grating". Reprinted in: David Rittenhouse, The Scientific Writings of David Rittenhouse, Brooke Hindle, ed. (New York, New York: Arno Press, 1980), pages 377-382. (A reproduction of Rittenhouse's letter re his diffraction grating appears on pages 369-374.)

[4] "An optical problem, proposed by Mr. Hopkinson, and solved by Mr. Rittenhouse," Transactions of the American Philosophical Society, vol. 2, pages 201-206 (1786).

[5] Thomas D. Cope (1932) "The Rittenhouse diffraction grating". Reprinted in: David Rittenhouse, The Scientific Writings of David Rittenhouse, Brooke Hindle, ed. (New York, New York: Arno Press, 1980), pages 377-382. (A reproduction of Rittenhouse's letter re his diffraction grating appears on pages 369-374.)

[4] See:
Frauhofer. Jos. (1821) "Neue Modifikation des Lichtes durch gegenseitige Einwirkung und Beugung der Strahlen, und Gesetze derselben" (New modification of light by the mutual influence and the diffraction of [light] rays, and the laws thereof), Denkschriften der Königlichen Akademie der Wissenschaften zu München (Memoirs of the Royal Academy of Science in Munich), 8: 3-76.

Fraunhofer, Jos. (1823) "Kurzer Bericht von den Resultaten neuerer Versuche über die Gesetze des Lichtes, und die Theorie derselben" (Short account of the results of new experiments on the laws of light, and the theory thereof) Annalen der Physik, 74(8): 337-378.

[7] Frauhofer. Jos. (1821) "Neue Modifikation des Lichtes durch gegenseitige Einwirkung und Beugung der Strahlen, und Gesetze derselben" (New modification of light by the mutual influence and the diffraction of [light] rays, and the laws thereof), Denkschriften der Königlichen Akademie der Wissenschaften zu München (Memoirs of the Royal Academy of Science in Munich), 8: 3-76.

[8] Fraunhofer, Jos. (1823) "Kurzer Bericht von den Resultaten neuerer Versuche über die Gesetze des Lichtes, und die Theorie derselben" (Short account of the results of new experiments on the laws of light, and the theory thereof) Annalen der Physik, 74(8): 337-378.

[5] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[6] ttp://www.ifixit.com/Teardown/Nook-Simple-Touch-with-GlowLight-Teardown/9301/3

[7] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

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Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[8] Nature's palette: the science of plant color By David Webster Lee - University of Chicago Press 2007 Page 255-256

[9] Nature's palette: the science of plant color By David Webster Lee - University of Chicago Press 2007 Page 255

[10] Nature's palette: the science of plant color By David Webster Lee - University of Chicago Press 2007 Page 84

[11] Nature's palette: the science of plant color By David Webster Lee - University of Chicago Press 2007 Page 41

[12] ttp://www.nhm.ac.uk/about-us/news/2006/mar/news_7834.html

[13] Polarized light in nature By G. P. Können - Cambridge University Press 1985 Page 72-73

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-== Louis Vuitton Occhiali  a casa ==
+{{more footnotes|date=December 2011}}
+[[Image:Diffraction grating.jpg|thumb|right|300px|A very large reflecting diffraction grating]]
+[[File:An incandescent light-bulb viewed through a transmissive diffraction grating.jpg|thumb|An incandescent light-bulb viewed through a transmissive diffraction grating.]]
-Anche le piccole eruzioni vulcaniche come l'attività sul mt. Sant'Elena messo decenni di zolfo, carbonio e altri gas "casa verde". I social media è diventato un ottimo modo per molte persone di commercializzare il loro business. Si può fare un po 'di pubblicità gratuita [http://www.hoteloasiverde.it/web/include/datebase.asp Louis Vuitton Occhiali] su lì e si può anche ottenere comprato la pubblicità in cui le informazioni riportate sulla barra laterale di Facebook. <br><br>10. Ciao Boston (ex Bull Finch Pub) Famoso come l'ispirazione per i Saluti show televisivo, l'ex Bull Finch Pub, ora ufficialmente nota come Ciao Boston, si trova a Beacon Hill District di Boston. È andato giù un po 'l'anno scorso, ha detto Cook. Abbiamo pensato che questo sarebbe una buona posizione per provarlo. <br><br>Per Farewell La classe operaia! scritto da huitard soixante francese e confidente sartriana André Gorz, rende polso tremante lettura per il socialista sci fi. "Se l'automazione e la robotica è in grado di ridurre la quantità di ricchezza che producono, lavoro produttivo umano che una società industriale ha bisogno di un minimo assoluto ... <br><br>Come ho sottolineato [http://www.metallipressofusi.it/web_ted/include/datebase.asp Pandora Italia] prima, non è chiaro che Tim Cook capisce il problema. Egli sembra credere che Apple può continuare ad operare come ha sempre fatto, rendendo i prodotti "follemente grande", migliorando la tecnologia esistente. Purtroppo ci sono molti falsi concerti e insegnanti del cristianesimo in questo mondo che hanno dato veri credenti un involucro male. Che è triste e infelice come tante persone si perdono. <br><br>E se siete a lavoro, a casa, o ad una festa, solo perché un cookie è seduto su un tavolo in bella vista, questo non significa che devi mangiare it.Ask voi stessi perché si sta mangiando zucchero prima lo metti in bocca. Stai mangiando per abitudine? A causa delle circostanze? Per un'occasione speciale? Perché tutti gli altri è? Guardate voi stessi come un topo da laboratorio.. <br><br>I didn dire una grande differenza da quando lei controllando diolation. Dopo aver spogliato le membrane ho avuto una piccola quantità di rosso a destra sangue dopo ha fatto lo [http://www.mieascensori.com/web/client.asp Oakley Outlet] sweep / tratto (qualunque cosa in quanto ha un paio di nomi diversi), quindi i prossimi due volte [http://www.metallipressofusi.it/web_ted/include/datebase.asp Pandora Roma] sono andato in bagno ho avuto qualche colore rosso quando ho cancellato. <br><br>Conclusione L'ironia è, mentre noi tutti eccitati attraverso i nuovi formati, ho sempre un po 'emotivo su un lettore CD. Nel corso degli ultimi due anni, ho sentito solo un lettore CD finora (un entry level Krell) che mi ha affascinato e ho sentito numerose altre macchine che in genere mi ha lasciato così, a freddo.
+In [[optics]], a '''diffraction grating''' is an optical component with a periodic structure, which splits and [[diffraction|diffracts]] 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 [[dispersion (optics)|dispersive]] element. Because of this, gratings are commonly used in [[monochromator]]s and [[spectrometer]]s.
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-== Abercrombie Milano stand up comedian acclamato e di talento ==
+A [[reversal film|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 [[reflection (optics)|reflective]]. Gratings which modulate the phase rather than the amplitude of the incident light are also produced, frequently using [[holography]].<ref>{{cite journal |author= AK Yetisen, H Butt, F da Cruz Vasconcellos, Y Montelongo, CAB Davidson, J Blyth, JB Carmody, S Vignolini, U Steiner, JJ Baumberg, TD Wilkinson and CR Lowe |title=Light-Directed Writing of Chemically Tunable Narrow-Band Holographic Sensors. |journal= Advanced Optical Materials |year=2013 |doi= 10.1002/adom.201300375 |url=http://onlinelibrary.wiley.com/doi/10.1002/adom.201300375/abstract}}</ref>
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+The principles of diffraction gratings were discovered by [[James Gregory (astronomer and mathematician)|James Gregory]], about a year after Newton's prism experiments, initially with artifacts such as bird feathers.<ref>Letter from James Gregory to John Collins, dated 13 May 1673.  Reprinted in:  ''Correspondence of Scientific Men of the Seventeenth Century …'', ed. Stephen Jordan Rigaud (Oxford, England: Oxford University Press, 1841), vol. 2, pp. 251–255, especially [http://books.google.com/books?id=0h45L_66bcYC&pg=PA254 p. 254]</ref> The first man-made diffraction grating was made around [[1785 in science|1785]] by [[Philadelphia]] inventor [[David Rittenhouse]], who strung hairs between two finely threaded screws.<ref>See:
-相关的主题文章：
+*  [http://books.google.com/books?id=OLgAAAAAYAAJ&pg=PA201#v=onepage&q&f=false "An optical problem, proposed by Mr. Hopkinson, and solved by Mr. Rittenhouse,"] ''Transactions of the American Philosophical Society'', vol. 2, pages 201-206 (1786).
-  <ul>
+*  Thomas D. Cope (1932) [http://books.google.com/books?id=epgvIYkMiUIC&pg=PA377#v=onepage&q&f=false "The Rittenhouse diffraction grating"].  Reprinted in:  David Rittenhouse, ''The Scientific Writings of David Rittenhouse'', Brooke Hindle, ed. (New York, New York:  Arno Press, 1980), pages 377-382.  (A reproduction of Rittenhouse's letter re his diffraction grating appears on pages 369-374.)</ref> This was similar to notable German physicist [[Joseph von Fraunhofer]]'s wire diffraction grating in [[1821 in science|1821]].<ref>See:
+*  Frauhofer. Jos. (1821) [http://books.google.com/books?id=k-EAAAAAYAAJ&pg=RA1-PA3#v=onepage&q&f=false "Neue Modifikation des Lichtes durch gegenseitige Einwirkung und Beugung der Strahlen, und Gesetze derselben"] (New modification of light by the mutual influence and the diffraction of [light] rays, and the laws thereof), ''Denkschriften der Königlichen Akademie der Wissenschaften zu München'' (Memoirs of the Royal Academy of Science in Munich), '''8''': 3-76.
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+*  Fraunhofer, Jos. (1823) [http://gallica.bnf.fr/ark:/12148/bpt6k15083w/f353.image "Kurzer Bericht von den Resultaten neuerer Versuche über die Gesetze des Lichtes, und die Theorie derselben"] (Short account of the results of new experiments on the laws of light, and the theory thereof) ''Annalen der Physik'', '''74'''(8): 337-378.</ref>
-   <li>[http://enseignement-lsf.com/spip.php?article64#forum17548686 http://enseignement-lsf.com/spip.php?article64#forum17548686]</li>
+Diffraction creates the "rainbow" colors reflected from a compact disc (see Examples, below). A grating has parallel lines, while a CD has a spiral of finely-spaced data tracks. Diffraction colors also appear when one looks at a bright point source through a translucent fine-pitch umbrella-fabric covering. Decorative patterned plastic films based on reflective grating patches are very inexpensive to produce, and very commonplace.
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+== Theory of operation ==
+{{main|Diffraction}}
-   <li>[http://www.imc-e.net/thread-1205075-1-1.html http://www.imc-e.net/thread-1205075-1-1.html]</li>
+[[Image:Difraction grating reflecting green light.JPG|thumb|300px|A diffraction grating reflecting only the green portion of the spectrum from a room's fluorescent lighting]]The relationship between the grating spacing and the angles of the incident and diffracted beams of light is known as the '''grating equation'''.
-   <li>[http://sgwto.com/bbs/forum.php?mod=viewthread&tid=588562 http://sgwto.com/bbs/forum.php?mod=viewthread&tid=588562]</li>
+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.
- </ul>
+Gratings may be of the 'reflective' or 'transmissive' type, analogous to a mirror or lens respectively.  A grating has a 'zero-order mode' (where m=0), in which there is no diffraction and a ray of light behaves according to the laws of reflection and refraction the same as with a mirror or lens respectively.
+An idealised grating is considered here which is made up of a set of slits of spacing ''d'', that must be wider than the wavelength of interest to cause diffraction.  Assuming a plane wave of wavelength λ with [[Normal (geometry)|normal]] incidence (perpendicular to the grating), each slit in the grating acts as a quasi point-source from which light propagates in all directions (although this is typically limited to a hemisphere).  After light interacts with the grating, the diffracted light is composed of the sum of [[Interference (wave propagation)|interfering]] wave components emanating from each slit in the grating. At any given point in space through which diffracted light may pass, the path length to each slit in the grating will vary.  Since the path length varies, generally, so will the phases of the waves at that point from each of the slits, and thus will add or subtract from one another to create peaks and valleys, through the phenomenon of additive and [[destructive interference]].  When the path difference between the light from adjacent slits is equal to half the wavelength, λ/2, the waves will all be out of phase, and thus will cancel each other to create points of minimum intensity.  Similarly, when the path difference is λ, the phases will add together and maxima will occur.  The maxima occur at angles ''θ''<sub>m</sub>, which satisfy the relationship ''d''sin''θ''<sub>m</sub>/λ=|''m''| where ''θ''<sub>m</sub> is the angle between the diffracted ray and the grating's [[Normal (geometry)|normal]] vector, and ''d'' is the distance from the center of one slit to the center of the adjacent slit, and ''m'' is an [[integer]] representing the propagation-mode of interest.
+[[File:comparison_refraction_diffraction_spectra.svg|thumb|upright|Comparison of the spectra obtained from a diffraction grating by diffraction (1), and a prism by refraction (2). Longer wavelengths (red) are diffracted more, but refracted less than shorter wavelengths (violet).]]
+Thus, when light is normally incident on the grating, the diffracted light will have maxima at angles ''θ''<sub>m</sub> given by:
+:<math> d \ \sin{\theta_m} = m \lambda</math>
+It is straightforward to show that if a plane wave is incident at any arbitrary angle θ<sub>i</sub>, the grating equation becomes:
+:<math> d \left( \sin{\theta_i} + \sin{\theta_m} \right) = m \lambda</math>
+When solved for the diffracted angle maxima, the equation is:
+:<math> \theta_m = \arcsin{ \left( \frac{m \lambda}{d} - \sin{\theta_i}  \right)} </math>
+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. 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 is based on 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
+* [[Transmittance|transparency]] (transmission amplitude gratings)
+* [[Reflectivity|reflectance]] (reflection amplitude gratings)
+* [[refractive index]] (phase gratings)
+* direction of [[optical axis]] ([[optical axis grating]]s)
+The grating equation applies in all these cases.
+===Quantum electrodynamics===
+[[Quantum electrodynamics]] (QED) offers another derivation of the properties of a diffraction grating in terms of [[photons]] as particles (at some level). QED can be described intuitively with the [[path integral formulation]] of quantum mechanics. As such it can model photons as potentially following all paths from a source to a final point, each path with a certain [[probability amplitude]]. These probability amplitudes can be represented as a complex number or equivalent vector—or, as [[Richard Feynman]] 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 for a photon from a monochromatic source to arrive at a certain final point at a given time, in this case, can be modeled as an arrow that spins rapidly until it is evaluated when the photon reaches its final point. For example, for the probability that a photon will reflect off of a mirror and be observed at a given point a given amount of time later, 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 can then evaluate the probability amplitude at the photon's final point; next, one can integrate over all of these arrows (see [[vector sum]]), and square the length of the result to obtain the probability that this photon will reflect off of the mirror in the pertinent fashion. The times these paths take are what determine the angle of the probability amplitude arrow, as they can be said to "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 would all wind up pointing, for instance, at forty-five degrees can have a sizable sum. Thus, this would let light of the right frequency to make this happen sum to a larger probability amplitude, and as such possess a larger probability of reaching the appropriate final point.
+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. The biggest simplification is perhaps in the fact that the "spinning" of the probability amplitude arrows is actually more accurately explained as a "spinning" of the source, as the probability amplitudes of photons do not "spin" while they are in transit. We obtain the same variation in probability amplitudes by allowing the time at which the photon left the source to be indeterminate, and the time of the path now tells us when the photon would have left the source, and thus what the angle of its "arrow" would be. However, this model and approximation is a reasonable one to illustrate a diffraction grating conceptually. Light of a different frequency may also reflect off of the same diffraction grating, but with a different final point.<ref>{{cite book|last=Feynman|first=Richard|title=QED: The Strange Theory of Light and Matter|year=1985|publisher=Princeton University Press|location=Princeton, New Jersey}}</ref>
+==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.e., it is [[dispersion (optics)|dispersive]].  Each wavelength of input beam [[electromagnetic spectrum|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 [[triangular prism (optics)|prism]], although the mechanism is very different.
+[[Image:light-bulb-grating.png|thumb|right|300px|A light [[incandescent light bulb|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.]]
+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.
+[[File:Argon laser beam and diffraction mirror.png|thumb|An argon laser beam consisting of multiple colors (wavelengths) strikes a silicon diffraction mirror grating and is separated into several beams, one for each wavelength. The wavelengths are (left to right) 458&nbsp;nm, 476&nbsp;nm, 488&nbsp;nm, 497&nbsp;nm, 502&nbsp;nm, and 515&nbsp;nm.]]
+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 ''[[Blazed grating|blazing]].'' The incident angle and wavelength for which the diffraction is most efficient are often called ''blazing angle'' and ''blazing wavelength.''  The [[grating efficiency|efficiency]] of a grating may also depend on the [[Polarization (waves)|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]] 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 (optics)|prism]]. In the optical regime, in which the use of gratings is most common, this corresponds to wavelengths between 100 [[nanometer|nm]]  and 10 [[micrometre|µm]]. In that case, the groove density can vary from a few tens of grooves per millimeter, as in [[Echelle grating|''echelle gratings'']], 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 grating]]s and exhibit special optical properties. Made on an [[Isotropy|isotropic]] 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]] designed a machine to make diffraction gratings, succeeding with one of 120,000 lines to the inch (approx. 47&nbsp;000&nbsp;per&nbsp;cm) in 1899. Later, [[lithography|photolithographic]] techniques allowed gratings to be created from a [[holography|holographic]] interference pattern. [[Holographic grating]]s have sinusoidal grooves and may not be as efficient as ruled gratings, but are often preferred in [[monochromator]]s because they lead to much less [[stray light]]. 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]] 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. 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 optics|integrated photonic lightwave circuits]] is [[digital planar holography]] (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 ==
+[[Image:Interference-colors.jpg|thumbnail|200px|The grooves of a compact disc can act as a grating and produce [[iridescent]] reflections.]]
+Diffraction gratings are often used in [[monochromator]]s, [[spectrometer]]s, [[laser]]s, [[wavelength division multiplexing]] devices, optical [[Pulse_compression|pulse compressing]] devices, and many other optical instruments.
+Ordinary pressed [[Compact Disc|CD]] and [[Digital Video Disc|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 [[Gramophone record|vinyl record]] 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 (optics)|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.
+Diffraction gratings are also used to distribute evenly the [[frontlight]] of [[e-reader]]s such as the [[Nook Simple Touch|Nook Simple Touch with GlowLight]].<ref>http://www.ifixit.com/Teardown/Nook-Simple-Touch-with-GlowLight-Teardown/9301/3</ref>
+===Natural gratings===
+[[Striated muscle]] is the most commonly found natural diffraction grating<ref>{{cite journal|last=Baskin et al|title=LIGHT DIFFRACTION STUDY OF SINGLE SKELETAL MUSCLE FIBERS|pmc=1328609|publisher=BIoPHYs.J.|pmid=318066|doi=10.1016/S0006-3495(79)85158-9|volume=28|issue=1|date=October 1979|journal=Biophys. J.|pages=45–64|bibcode = 1979BpJ....28...45B }}</ref>  and, indeed, this has helped physiologists in determining the structure of such muscle. Aside from this, the chemical structure of crystals can be thought of as diffraction gratings for types of electromagnetic radiation other than visible light, this is the basis for techniques such as [[X-ray crystallography]]. Most commonly confused with diffraction gratings are the [[iridescent]] colors of [[peacock]] feathers, [[mother-of-pearl]], and [[butterfly]] wings. Iridescence is common in birds, fishes, insects, and some flowers, and is almost always caused by [[thin-film interference]] rather than diffraction.<ref>''Nature's palette: the science of plant color'' By David Webster Lee - University of Chicago Press 2007 Page 255-256</ref> Diffraction will produce the entire spectrum of colors as the viewing angle changes, whereas thin-film interference usually produces a much narrower range.<ref>''Nature's palette: the science of plant color'' By David Webster Lee - University of Chicago Press 2007 Page 255</ref> The cell structures in plants and animals are usually too irregular to produce the fine slit geometry necessary for a diffraction grating.<ref>''Nature's palette: the science of plant color'' By David Webster Lee - University of Chicago Press 2007 Page 84</ref> However, natural gratings do occur in some invertebrate marine animals, like the antennae of [[seed shrimp]], and have even been discovered in [[Burgess Shale type fauna|Burgess Shale fossils]].<ref>''Nature's palette: the science of plant color'' By David Webster Lee - University of Chicago Press 2007 Page 41</ref><ref>http://www.nhm.ac.uk/about-us/news/2006/mar/news_7834.html</ref>
+Diffraction grating effects are sometimes seen in [[meteorology]]. [[Corona (optical phenomenon)|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 [[halo (optical phenomenon)|halos]], 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]] is caused by diffraction, occurring along coronal rings when the particles in the clouds are all uniform in size.<ref>''Polarized light in nature'' By G. P. Können - Cambridge University Press 1985 Page 72-73</ref>
+== See also ==
+*[[Kirchhoff's diffraction formula]]
+*[[Fresnel diffraction]]
+*[[Fraunhofer diffraction]]
+*[[Fraunhofer diffraction (mathematics)]]
+*[[Angle-sensitive pixel]]
+*[[Grism]]
+*[[Henry Augustus Rowland]]
+*[[N-slit interferometric equation]]
+*[[Spider web]]
+*[[Ultrasonic grating]]
+*[[Zone plate]]
+==References==
+<references/>
+{{refbegin}}
+*{{FS1037C}}
+*Hutley, Michael, ''Diffraction Gratings (Techniques of Physics)'', Academic Press (1982). ISBN 0-12-362980-2
+*Loewen, Erwin & Evgeny Popov, ''Diffraction Gratings and Applications'', CRC; 1 edition (1997). ISBN 0-8247-9923-2
+*Palmer, Christopher, ''[http://gratings.newport.com/library/handbook/cover.asp Diffraction Grating Handbook]'', 6th edition, Newport Corporation (2005).
+*Greenslade, Thomas B., "[http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PHTEAH000042000002000076000001&idtype=cvips&gifs=Yes Wire Diffraction Gratings]," ''The Physics Teacher'', February 2004. Volume 42 Issue 2, pp.&nbsp;76–77.
+*Abrahams, Peter, ''[http://www.europa.com/~telscope/histspec.txt Early Instruments of Astronomical Spectroscopy]''.
+* William E. L. Grossman, "The optical characteristics and production of diffraction gratings," ''Journal of Chemical Education'' 70:9 (Sep 1993), p.&nbsp;741.
+*National Optical Astronomy Observatories entry on [http://www.noao.edu/ets/vpgratings/ volume phase holography gratings].
+{{refend}}
+== External links ==
+* [http://gratings.newport.com/information/gratings.asp Diffraction Gratings - The Crucial Dispersive Component]
+* [http://gratings.newport.com/handbook Diffraction Grating Handbook]
+* [http://gratings.newport.com/information/handbook/chapter2.asp Diffraction Grating Equations]
+* [http://www.calctool.org/CALC/phys/optics/grating Automatic calculation of diffraction angles based on input variables.]
+* [http://www.horiba.com/scientific/products/optics-tutorial/diffraction-gratings Optics Tutorial - Diffraction Gratings Ruled & Holographic]
+* [http://sourceforge.net/projects/gratingcalc Ray-Tracing program handling general reflective concave gratings for Windows XP and above]
+* http://demonstrations.wolfram.com/InterferenceInDiffractionGratingBeams/
+* [http://ssioptics.com/cart/index.php?dispatch=pages.view&page_id=31#concave Concave Diffraction Grating]
+[[Category:Diffraction]]
+[[Category:Optical devices]]
+[[Category:Photonics]]

Dielectric: Difference between revisions

Revision as of 19:31, 19 December 2013

Contents

Theory of operation

Quantum electrodynamics

Gratings as dispersive elements

Fabrication

Examples

Natural gratings

See also

References

External links

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Dielectric: Difference between revisions

Revision as of 19:31, 19 December 2013

Theory of operation

Quantum electrodynamics

Gratings as dispersive elements

Fabrication

Examples

Natural gratings

See also

References

External links

Navigation menu

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