사용자:Dltldls95/연습장

A very large reflecting diffraction grating

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

광학에서, 회절 격자 는 주기적인 구조를 갖는 광학 부품으로, 빛을 서로 다른 방향으로 진행하는 빔으로 분산시키고 회절시킨다. 이러한 빔들의 방향은 회절 격자의 배치와 빛의 파장에 영향을 받으며 회절 격자는 분산요소로 작용한다. 이러한 이유로, 회절 격자는 보편적으로 monochromator와 spectrometer에 쓰인다.

섬세한 무늬의 보라색 선을 가진 광학 조각은 복잡한 회절 격자를 형성한다. 실용적인 면에서, 회절 격자는 일반적으로 그것의 표면에 검정색 선 보다는 능선이나 rulings를 가진다. 회절 격자 중 입사광의 진폭이 아닌 상을 조절하는 종류도 있는데, 주로 홀로그래피에 쓰인다.

뉴턴의 프리즘 실험으로부터 약 1년 후, 회절 격자의 원리는 James Gregory에 의해 발견되었고, 새 깃털 등의 가공물로 시작되었다. 최초의 인간이 만든 회절 격자는 1785 에 필라델피아 의 발명가 David Rittenhouse가 만들었으며, 그는 섬세하게 만든 두 나사 사이에 자신의 머리카락을 끼웠다. 이것은 유명한 독일 물리학자 Joseph von Fraunhofer의 1821년 와이어 회절 격자와 비슷하다.

회절은 CD 표면에서 반사된 무지개빛과 같은 색을 만든다. 하나의 격자는 평행선을 가지며, CD는 그러한 데이터 트랙이 나선형으로 조밀하게 배치된 것이다. 회절 색은 반투명하며 미세한 홈을 가진 우산 직물 표면을 통해 밝은 점광원을 볼 때도 나타난다. 반사 격자들을 이용한 플라스틱 필름은 저렴하게 생산할 수 있으며, 보편적으로 쓰인다.

이론

 이 부분의 본문은 회절입니다.

A diffraction grating reflecting only the green portion of the spectrum from a room's fluorescent lighting

격자 배치 및 입사광의 각도와 회절된 빔의 각도 관계는 grating equation으로 알려져 있다.

Density plot of diffraction of grating

호이겐스-프레넬 원리에 따르면, 진행하는 파동의 파면의 각 점은 점광원으로 간주할 수 있으며, 파면의 이후 모양은 이러한 개별 점광원들의 영향을 더해서 알아낼 수 있다.

격자는 '반사'나 '통과' 타입을 가질 수 있으며, 각각 거울과 렌즈로 비유될 수 있다. 격자는 m=0일 때 '0차 모드'를 가지며, 이 때 빛은 회절 없이 거울이나 렌즈를 썼을 때와 같이 빛의 반사와 굴절법칙을 따른다.

슬릿 사이의 거리가 d인 이상적인 격자를 생각해보면, d는 회절을 일으키기 위해 대상의 파장보다 반드시 커야 한다. 파장이 lambda 인 수직 입사하는 평면파를 생각해보자(격자에 수직), 각각의 격자 안의 슬릿은 거의 점광원처럼 행동하여 빛은 모든 방향으로 진행한다 (비록 이는 전형적으로 반구로 제한되지만). 빛이 격자와 상호작용하고 나면, 회절된 빛은 격자 안의 각각의 슬릿으로부터 나온 파동 요소들의 간섭의 합으로 구성된다. 공간의 어떠한 한 점에 대해서라도 회절된 빛이 지날 때, 격자 내 각각의 슬릿을 지나는 광경로 길이는 달라진다. 대개 광경로 길이가 달라지므로, 그 점에서의 슬릿에서의 파동의 상도 달라지게 되며, 이는 보강 및 상쇄 간섭의 현상에 따라, 파동끼리의 굴곡이 서로 더해지고 빼지는 결과를 만든다. 인접한 빛 사이의 광경로차가 파장의 절반인 λ/2일 때, 위상은 완전히 정반대이며, 서로 상쇄하여 최소 강도인 점을 만들 것이다. 이와 비슷하게, 광경로차가 파장과 같은 λ일 때, 위상이 서로 더해져 최대 강도인 점을 만들 것이다. 최대점들은 θ_m에서 일어나며, 각도는 dsinθ_m/λ=|m| 관계를 만족하며 θ_m 는 회절된 빛과 격자의 법선 벡터 사이의 각이고, d는 슬릿 사이의 간격, m은 정수를 나타낸다.

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).

Intensity as heatmap for monochromatic light behind a grating

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.

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.

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 nm, 476 nm, 488 nm, 497 nm, 502 nm, and 515 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 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.

Natural gratings

Striated muscle is the most commonly found natural diffraction grating 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. Diffraction will produce the entire spectrum of colors as the viewing angle changes, whereas thin-film interference usually produces a much narrower range. The cell structures in plants and animals are usually too irregular to produce the fine slit geometry necessary for a diffraction grating. However, natural gratings do occur in some invertebrate marine animals, like the antennae of seed shrimp, and have even been discovered in Burgess Shale fossils.

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.

See also

• Angle-sensitive pixel
• Fraunhofer diffraction
• Fraunhofer diffraction (mathematics)
• Fresnel diffraction
• Grism
• Henry Augustus Rowland
• Kapitza-Dirac effect
• Kirchhoff's diffraction formula
• N-slit interferometric equation
• Spider web
• Ultrasonic grating
• Zone plate

References

•  이 문서는 다음을 포함합니다: 퍼블릭 도메인 자료 - 총무청 문서 "연방 표준 1037C".
• 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|[1], 7th edition, Richardson Gratings (2014).
• 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.

External links

• Diffraction Gratings (see and listen to Lecture 9)
• Diffraction Gratings - The Crucial Dispersive
• Optics Tutorial - Diffraction Gratings Ruled & Holographic
• Ray-Tracing program handling general reflective concave gratings for Windows XP and above
• http://demonstrations.wolfram.com/InterferenceInDiffractionGratingBeams/
• Concave Diffraction Grating