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Diffraction Grating

Diffraction grating

In optics, a diffraction grating is a reflecting or transparent substrate whose surface contains fine parallel grooves or rulings that are equally spaced. When light is incident on a diffraction grating, diffractive and mutual interference effects occur, and light is reflected or transmitted in discrete directions, called orders. Because of their dispersive properties, gratings are commonly used in monochromators and spectrometers. These devices were first manufactured by German physicist Joseph von Fraunhofer in 1821.

Theory of operation

Gratings are usually designated by their groove density, expressed in grooves per millimeter (g/mm). The dimension and period of the grooves must be on the order of the wavelength in question. In the optical regime, in which the use of gratings is most common, this corresponds to wavelengths between 100 nm and 10 μm. In that case, the groove density can vary from a few tens of grooves per millimeter, as in echelle gratings, to a few thousands. A fundamental property of gratings is that the angle of deviation of all but one of the diffracted beams depends on the wavelength of the incident light. Therefore, a grating separates an incident beam into its constituent wavelength components, i.e., it is dispersive. Each wavelength of input beam spectrum is sent into a different direction, producing a rainbow of colors under white light illumination. This is visually similar to the operation of a prism, although the mechanism is very different. prism 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.]] When a beam is incident on a grating with an angle θi (measured from the normal of the grating), it is diffracted into several beams. The beam that corresponds to direct transmission (or specular reflection in the case of a reflection grating) is called the zero order, and is noted m = 0. The other orders correspond to diffracted angles that deviate from the one predicted by geometrical optics, and are represented by non-zero integers m. For a groove period a and an incident wavelengh λ, the grating equation gives the value of the diffracted angle θm(λ) in the order m: : a \left( \sin - \sin \right) = m \lambda Note that m can be positive or negative, resulting in diffracted orders on both sides of the zero order beam. The diffracted beams corresponding to consecutive orders may overlap, depending on the spectral content of the incident beam and the grating density. The higher the spectral order, the greater the overlap into the next order. The grating equation shows that the angles of the diffracted orders only depend on the grooves' period, and not on their shape. By controlling the cross-sectional profile of the grooves, it is possible to concentrate most of the diffracted energy in a particular order for a given wavelength. A triangular profile is commonly used. This technique is called blazing. The incident angle and wavelength for which the diffraction is most efficient are often called blazing angle and blazing wavelength. The efficiency of a grating may also depend on the polarization of the incident light.

Fabrication

Originally, high-resolution gratings were ruled using high-quality ruling engines whose construction was a large undertaking. Later, photolithographic techniques allowed gratings to be created from a holographic interference pattern. Holographic gratings have sinusoidal grooves and may not be as efficient as ruled gratings, but are often preferred in monochromators because they lead to much less stray light. A copying technique allows high quality replicas to be made from master gratings, thereby lowering fabrication costs. Another method for manufacturing diffraction gratings uses a photosensitive gel sandwiched between two substrates. A holographic interference pattern exposes the gel which is later developed. These gratings, called volume phase holography diffraction gratings have no physical grooves, but instead a periodic modulation of the refractive index within the gel. This removes much of the surface scattering effects typically seen in other types of gratings. These gratings also tend to have higher efficiencies, and allow for the inclusion of complicated patterns into a single grating.

Examples

scattering Diffraction gratings are often used in monochromators and other optical instruments. Ordinary pressed CD and DVD media are every-day examples of diffraction gratings and can be used to demonstrate the effect by shining an ordinary laser pointer onto the surface. This is a side effect of their manufacture, as one surface of a CD has many small pits in the plastic, arranged within concentric rings; that surface has a thin layer of metal applied to make the pits more visible. The structure of a DVD, while it may have more than one pitted surface, and all pitted surfaces are inside the disc, is optically similar. Diffraction gratings are also present in nature. For example, the iridescent colors of peacock feathers, mother-of-pearl, butterfly wings, and some other insects are caused by very fine regular structures that diffract light, splitting it into its component colors.

References


- Adapted from a public domain entry in Federal Standard 1037C.
- National Optical Astronomy Observatories entry regarding volume phase holography gratings.
- Palmer, Christopher, Diffraction Grating Handbook, 6th edition, Newport Corporation (2005). Category:Diffraction ja:回折格子

Reflection (physics)

Reflection is the abrupt change in direction of a wave front at an interface between two dissimilar media so that the wave front returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. Reflection of light may be specular (that is, mirror-like) or diffuse (that is, not retaining the image, only the energy) depending on the nature of the interface. Whether the interfaces consists of dielectric-conductor or dielectric-dielectric, the phase of the reflected wave may or may not be inverted.

Specular (mirror-like) reflection

phase A mirror provides the most common model for specular light reflection and consists of a glass sheet in front of a metallic coating where the reflection actually occurs. It is also possible for reflection to occur from the surface of transparent media, such as water or glass. In the diagram, a light ray PO strikes a vertical mirror at point O, and the reflected ray is OQ. By projecting an imaginary line through point O perpendicular to the mirror, known as the normal, we can measure the angle of incidence, θi and the angle of reflection, θr. The law of reflection states that θi = θr, or in other words, the angle of incidence equals the angle of reflection. In fact, reflection of light may occur whenever light travels from a medium of a given refractive index into a medium with a different refractive index. In the most general case, a certain fraction of the light is reflected from the interface, and the remainder is refracted. Solving Maxwell's equations for a light ray striking a boundary allows the derivation of the Fresnel equations, which can be used to predict how much of the light is reflected, and how much is refracted in a given situation. Total internal reflection of light from a denser medium occurs if the angle of incidence is above the critical angle. When light reflects off a material denser (with higher refractive index) than the external medium, it undergoes a 180° phase reversal. In contrast, a less dense, lower refractive index material will reflect light in phase. This is an important principle in the field of thin-film optics. For parabolic reflection, such as those used in car headlights, see paraboloid.

Other types of reflection

Diffuse reflection

(main article diffuse reflection) diffuse reflection Light bounces off in all directions due to the microscopic irregularities of the interface; this is an omnipresent phenomenon, applicable for all non-shiny objects that are not black.

Retroreflection

(main article retroreflection) Light bounces back in the direction from which it came due to the special structure of the surface.

Neutron reflection

Materials that reflect neutrons, for example beryllium, are used in nuclear reactors and nuclear weapons.

Quantum Interpretation

All interactions between light photons and matter are described as a series of absorption and emission of photons. If one examines a single molecule at the surface of a material, an arriving photon will be absorbed and almost immediately reemitted. The ‘new’ photon may be emitted in any direction, thus causing diffuse reflection. The specular reflection (following Hero's equi-angular reflection law) is a quantum mechanical effect explained as the sum of the most likely paths the photons will have taken. Light-matter interaction is a topic in Quantum Electrodynamics, and is described in detail by Richard Feynman in his book QED: The Strange Theory of Light and Matter. As the photon absorbed by the molecule may match energetic levels of the molecule (Kinetic, Rotational, Electronic or Vibrational), the photon may not be reemitted or alternatively may lose some of its energy in the process. The emitted photon will have a slightly different level of energy. These effects are known as Raman, Brillouin and Compton scattering.

See also


- Diffraction
- Reflectivity
- Refraction
- Ripple tank for a picture and description of water waves reflecting off a boundary.
- Snell's law
- Echo satellite
- Anti-reflective coating Category:Optics

Parallel (geometry)

Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The existence and properties of parallel lines are the basis of Euclid's parallel postulate. parallel postulate #When lines or planes are parallel, then every point on one is located exactly the same minimum distance from the other line or plane. #Another way of defining it is that any two parallel lines or planes, if extended to infinity in both directions, will never intersect. This second definition carries the condition that the extension must occur only in one additional dimension: In other words, parallel lines must be located in the same plane, and parallel planes must be located in the same three-dimensional space. A parallel combination of a line and a plane may be located in the same three-dimensional space. #A third definition is: if two lines are both intersected by a third line (a transversal) in the same plane, and the angles of intersection are equal, then the two lines are parallel. Lines parallel to each other have the same gradient. Compare to perpendicular. Category:Elementary geometry Category:Orientation ja:平行

Diffraction

Diffraction is the bending and spreading of waves when they meet an obstruction. It can occur with any type of wave, including sound waves, water waves, and electromagnetic waves such as light and radio waves. Diffraction also occurs when any group of waves of a finite size is propagating; for example, a narrow beam of light waves from a laser must, because of diffraction of the beam, eventually diverge into a wider beam at a sufficient distance from the laser. As a simple example of diffraction, if you speak into one end of a cardboard tube, the sound waves emerging from the other end spread out in all directions, rather than propagating in a straight line like a stream of water from a garden hose.

Introduction

Diffraction is one particular type of wave interference, caused by the partial obstruction or lateral restriction of a wave. Not all interference is diffraction; for example, sound waves emitted by two stereo speakers will interfere with each other if they are of the same frequency and have a definite phase relationship, but this is not diffraction. Diffraction will not occur if the wave is not coherent, and diffraction effects become weaker (and ultimately undetectable) as the size of obstruction is made larger and larger compared to the wavelength. In well-defined cases, a diffraction pattern may be observed. Diffraction is not the same as refraction, although both are phenomena in which a wave does not propagate in a single direction. Refraction is not an interference phenomenon, and, e.g., can occur without coherence. It is the diffraction of "particles," such as electrons, which stood as one of the powerful arguments in favor of quantum mechanics. It is possible to observe diffraction of particles such as neutrons or electrons and hence we are able to infer the existence of wave-particle duality. Indeed, this diffraction is a useful tool; the wavelengths of these particle-waves are small enough that they are used as probes of the atomic structure of crystals. See electron diffraction and neutron diffraction.
image:doubleslitdiffraction.png
Double-slit diffraction


image:Laserdiffraction.jpg
Double-slit diffraction
(red laser light)

image:Diffraction2vs5.jpg
2-slit and 5-slit diffraction
The most conceptually simple example of diffraction is double-slit diffraction in which both slits have relatively narrow widths compared to the wavelength of the wave. Suppose, for the sake of visualization, that these are water waves. After passing through the slits, two overlapping patterns of semicircular ripples are formed, as shown in the first figure. Where a crest overlaps with a crest, a double-height crest will be formed; this is constructive interference. Constructive interference also occurs where a trough overlaps another trough. However, when a trough and a crest overlap, they cancel out; the interference is destructive. The second figure shows the result of this process with light waves of a single wavelength originating from a laser. The constructive-interference locations are called maxima, because they have maximum brightness. The destructive-interference locations are the minima. Historically, the first proof that light was a wave phenomenon came from the double-slit experiment of Thomas Young.

General facts about diffraction

Several qualitative observations can be made:
- When the dimensions of the diffracting object are reduced, the angular spacing of the diffraction pattern is increased in inverse proportion. (More precisely, this is true of the sines of the angles.)
- The diffraction angles are invariant under scaling; that is, they depend only on the ratio of the wavelength to a dimension, a, of the diffracting object.
- When the diffracting object is repeated, the effect is to narrow each maximum, concentrating its energy within a narrower range of angles. The third figure, for example, shows a comparison of a double-slit pattern with a pattern formed by five slits, both sets of slits having the same spacing, a, between the center of one slit and the next.

Mathematical description

It is mathematically easier to consider the case of far-field or Fraunhofer diffraction, where the diffracting obstruction is many wavelengths distant from the point at which the wave is measured. The more general case is known as near-field or Fresnel diffraction, and involves more complex mathematics. As the observation distance is increased the results predicted by the Fresnel theory converge towards those predicted by the simpler Fraunhofer theory. This article considers far-field diffraction, which is commonly observed in nature. Quantitatively, the angular positions of the minima in multiple-slit diffraction are given by the equation : \sin \theta = \frac m, where m is an integer that labels the order of each minimum. The central maximum is two orders wide, however, so m = 0, θ = 0 is the absolute maximum of the distribution and intensity functions. This is a form of Bragg's law (see below).
image:diffraction1.png
Graph and image

Quantitative analysis of single-slit diffraction

As an example, we will now derive an exact equation for the intensity of the diffraction pattern as a function of angle in the case of single-slit diffraction. We will start with a mathematical representation of Huygens' principle. Consider a monochromatic complex plane wave \Psi^\prime of wavelength λ incident on a slit of width a. Let the slit lie in the x′-y′ plane, with its center at the origin. Then we shall assume that diffraction generates a complex wave ψ, traveling radially in the r direction away from the slit, and this is given by: :\Psi = \int_ \frac \Psi^\prime e^\,dslit let (x′,y′,0) be a point inside the slit over which we are integrating; and let (x,0,z) be the location at which we are computing the intensity of the diffraction pattern. The slit extends from x^\prime=-a/2 to +a/2\,, and from y'=-\infty to \infty. The distance r from the slot is: :r = \sqrt :r = z \left(1 + \frac\right)^\frac We assume Fraunhofer diffraction, so that z >> \big|\left(x - x^\prime\right)\big|. In other words, the distance to the target is much larger than the diffraction width on the target. By the binomial expansion rule, ignoring terms quadratic and higher, we can estimate our quantity on the right to be: :r \approx z \left( 1 + \frac \frac \right) :r \approx z + \frac We see that our 1/r in front of the equation is non-oscillatory, i.e. its contribution to the magnitude of the intensity is small compared to our exponential factors. Therefore, we will lose little accuracy by approximating it as z. To make things cleaner, we will use a placeholder 'C' to denote constants in our equation. It is important to keep in mind that C can contain imaginary numbers, thus our wave function will be complex, however at the end, we will bracket our ψ, which will eliminate any imaginary components. Now, in Fraunhoffer diffraction, kx^/z is small, so e^\frac \approx 1. The same approximation holds for e^\frac. Thus, taking C = \Psi^\prime \sqrt, we have: Now we note that \sin x = \frac and \sin \theta = \frac. \Psi = C \frac Now, substituting in \frac = k, the intensity I of the diffracted waves at an angle θ is given by: where the sinc function is given by sinc(x) = sin(x)/x.

Quantitative analysis of n-slit diffraction

Let us again start with the mathematical representation of Huygens' principle. :\Psi = \int_ \frac \Psi^\prime e^\,dslit Consider n slits in the prime plane of the equal size (a, \infty, 0) and spacing d spread along the x′ axis. As above, the distance r from the slit 1 is: :r = z \left(1 + \frac\right)^\frac To generalize this to n slits, we make the observation that while z and y remain constant, x′ shifts by :x_^ = x_0^\prime - j d Thus :r_j = z \left(1 + \frac\right)^\frac and the sum of all n contributions to the wave function is: :\Psi = \sum_^ C \int_^ e^\frac e^\frac \,dx^\prime Again noting that \frac is small, so e^\frac \approx 1, we have: Now, we can use the following identity \sum_^ e^ = \frac. Substituting into our equation, we find: We now make our k substitution as before and represent all non-oscillating constants by the I_0 variable as in the 1-slit diffraction and bracket the result. Remember that :\langle e^ \Big| e^\rangle\ = e^0 = 1 This allows us to discard the tailing exponent and we have our answer: :I\left(\theta\right)\, :=I_0 \left[ \operatorname \left( \frac \sin \theta \right) \right]^2 :\left[\frac\right]^2

Other cases

Bragg diffraction

Diffraction from multiple slits, as described above, is similar to what occurs when waves are scattered from a periodic structure, such as atoms in a crystal or rulings on a diffraction grating. Each scattering center (e.g., each atom) acts as a point source of spherical wavefronts; these wavefronts undergo constructive interference to form a number of diffracted beams. The direction of these beams is described by Bragg's law: : m \lambda = 2 d \sin \theta,\, where λ is the wavelength, d is the distance between scattering centers, θ is the angle of diffraction and m is an integer known as the order of the diffracted beam. Bragg diffraction is used in X-ray crystallography to deduce the structure of a crystal from the angles at which X-rays are diffracted from it. Since the diffraction angle θ is dependent on the wavelength λ, diffaction gratings impart angular dispersion on a beam of light. The most common demonstration of Bragg diffraction is the spectrum of colors seen reflected from a compact disc: the closely-spaced tracks on the surface of the disc form a diffraction grating, and the individual wavelengths of white light are diffracted at different angles from it, in accordance with Bragg's law.

Diffraction limit of telescopes

compact disc of the binary star zeta Boötis.]] For diffraction through a circular aperture, there is a series of concentric rings surrounding a central Airy disc. The mathematical result is similar to a radially symmetric version of the equation given above in the case of single-slit diffraction. A wave does not have to pass through an aperture to diffract; for example, a beam of light of a finite size also undergoes diffraction and spreads in diameter. This effect limits the minimum size d of spot of light formed at the focus of a lens, known as the diffraction limit: : d = 2.44 \lambda \frac,\, where λ is the wavelength of the light, f is the focal length of the lens, and a is the diameter of the beam of light, or (if the beam is filling the lens) the diameter of the lens. (See Rayleigh criterion). By use of Huygens' principle, it is possible to compute the diffraction pattern of a wave from any arbitrarily shaped aperture. If the pattern is observed at a sufficient distance from the aperture, it will appear as the two-dimensional Fourier transform of the function representing the aperture.

See also


- Atmospheric diffraction
- Electron diffraction
- Neutron diffraction

External links


- [http://www.falstad.com/wave2d/ 2-D wave java applet] displays diffraction patterns of various slit configurations.
- [http://www.falstad.com/diffraction/ Diffraction java applet] displays diffraction patterns of various 2-D apertures.
- [http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm Diffraction Limited Photography] understanding how airy disks, lens aperture and pixel size limit the absolute resolution of any camera. Category:Optics Category:Wave mechanics ja:回折

Interference

Interference is the superposition of two or more waves resulting in a new wave pattern. As most commonly used, the term usually refers to the interference of waves which are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Two non-monochromatic waves are only fully coherent with each other if they both have exactly the same range of wavelengths and the same phase differences at each of the constituent wavelengths. The principle of superposition of waves states that the resultant displacement at a point is equal to the sum of the displacements of different waves at that point. If a crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant wave amplitude is greater. If a crest of a wave meets a trough then they interfere destructively, and the overall amplitude is decreased. Interference is involved in Thomas Young's double-slit experiment where two beams of light which are coherent with each other interfere to produce an interference pattern (the beams of light both have the same wavelength range and at the center of the interference pattern they have the same phases at each wavelength, as they both come from the same source). More generally, this form of interference can occur whenever a wave can propagate from a source to a destination by two or more paths of different length. Two or more sources can only be used to produce interference when there is a fixed phase relation between them, but in this case the interference generated is the same as with a single source; see Huygens' principle. When a single source interferes with itself, the principle of conservation of energy dictates that the energy "missing" from the darkened regions of an interference pattern where destructive interference has taken place will be found in the brightened portions where constructive interference has taken place. Light from any source can be used to obtain interference patterns, for example, Newton's rings can be produced with sunlight. However, in general white light is less suited for producing clear interference patterns, as it is a mix of a full spectrum of colours, that each have different spacing of the interference fringes. Sodium light is close to monochromatic and is thus more suitable for producing interference patterns. Most suitable is laser light because that is almost perfectly monochromatic.

Constructive and destructive interference

laser When two waves superimpose, the resulting waveform depends on the frequency, (or wavelength) amplitude and relative phase of the two waves. If the two waves have the same amplitude A and wavelength the resultant waveform will have amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase. Consider two waves that are in phase,with amplitudes A1 and A2. Their troughs and peaks line up and the resultant wave will have amplitude A = A1 + A2. This is known as constructive interference. If the two waves are 180° out of phase, then one wave's crests will coincide with another wave's troughs and so will tend to cancel out. The resultant amplitude is A = |A1 − A2|. If A1 = A2 the resultant amplitude will be zero. This is known as destructive interference.

See also


- Beat (acoustics)
- Moiré pattern
- Interferometer

External links


- [http://www.falstad.com/ripple/ex-2source.html Java demonstration of interference] Category:Optics Category:Wave mechanics ja:干渉 (物理学)

Discrete

The word discrete comes from the Latin word discretus which means separate. It is used with different meanings in different contexts:
- In perception, a discrete entity is something that can be perceived individually and not as connected to, or part of something else.
- In topology, a branch of mathematics, a discrete space is a topological space in which all sets are open, and a discrete set is a set of isolated points.
- In discrete mathematics, without notion of continuity, a discrete set is a countable set; this concept is also important for combinatorics, probability theory, and statistical theory.
- In discrete mathematics and in theoretical computer science, the abstract world is usually modeled as a discrete space with discrete time.
- In electrical engineering, discrete means having separate electronic components, such as individual resistors and inductors. This is the opposite of integrated circuitry.
- In audio engineering, discrete means having separate and independent channels of audio, as opposed to matrixed stereo or quadrophonic, or other multi-channel sound.
- A discrete signal in information theory and signal processing
- In music, a discrete pitch is one with a steady frequency, rather than an indiscrete gliding, glissando or portamento, pitch. Discrete is not the same thing as discreet.

Dispersion (optics)

In optics, dispersion is a phenomenon that causes the separation of a wave into spectral components with different frequencies, due to a dependence of the wave's speed on its frequency. It is most often described in light waves, though it may happen to any kind of wave that interacts with a medium or can be confined to a waveguide, such as sound waves. There are generally two sources of dispersion: material dispersion, which comes from a frequency-dependent response of a material to waves; and waveguide dispersion, which comes because the transverse mode solutions for waves confined laterally within a finite waveguide generally depend upon the frequency (i.e. on the relative size of the wave, the wavelength, and that of the waveguide). A related phenomenon is that of modal dispersion, which comes about if a signal consists of a superposition of multiple modes at each frequency—because different modes generally travel at different speeds, dispersion of temporal features (and thus signal degradation) results. A special case of this is polarization mode dispersion (PMD), which comes from a superposition of two modes that normally travel at the same speed due to symmetry (e.g. two orthogonal polarizations in a waveguide of circular or square cross-section), but which travel at different speeds due to random imperfections that break the symmetry.

Material dispersion in optics

polarization mode dispersion In optics, the phase velocity of a wave v in a given uniform medium is given by: :v = \frac where c is the speed of light in a vacuum and n is the refractive index of the medium. In general, the refractive index is some function of the frequency ν of the light, thus n = n(ν), or alternately, with respect to the wave's wavelength n = n(λ). The wavelength dependency of a material's refractive index is usually quantified by an empirical formula, the Cauchy or Sellmeier equations. The most commonly seen consequence of dispersion in optics is the separation of white light into a color spectrum by a prism. From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted will also vary with wavelength, causing an angular separation of the colors known as angular dispersion. For visible light, most transparent materials (e.g. glasses) have: :1 or alternatively: :\frac < 0, that is, refractive index n decreases with increasing wavelength λ. At the interface of such a material with air or vacuum (index of ~1), Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle \arcsin(\sin(\theta)/n). Thus, blue light, with a higher refractive index, will be bent more strongly than red light, resulting in the well-known rainbow pattern.

Group and phase velocity

Another consequence of dispersion manifests itself as a temporal effect. The formula above, v = c / n calculates the phase velocity of a wave; this is the velocity at which the phase of any one frequency component of the wave will propagate. This is not the same as the group velocity of the wave, which is the rate that changes in amplitude (known as the envelope of the wave) will propagate. The group velocity vg is related to the phase velocity by, for a homogeneous medium (here \lambda is the wavelength in vacuum, not in the medium): :v_g = c \left[ n - \lambda \frac \right]^. The group velocity vg is often thought of as the velocity at which energy or information is conveyed along the wave. In most cases this is true, and the group velocity can be thought of as the signal velocity of the waveform. In some unusual circumstances, where the wavelength of the light is close to an absorption resonance of the medium, it is possible for the group velocity to exceed the speed of light (vg > c), leading to the conclusion that superluminal (faster than light) communication is possible. In practice, in such situations the distortion and absorption of the wave is such that the value of the group velocity essentially becomes meaningless, and does not represent the true signal velocity of the wave, which stays less than c. The group velocity itself is usually a function of the wave's frequency. This results in group velocity dispersion (GVD), which causes a short pulse of light to spread in time as a result of different frequency components of the pulse travelling at different velocities. GVD is often quantified as the group delay dispersion parameter (again, this formula is for a uniform medium only): :D = - \frac \left( \frac \right) . If D is less than zero, the medium is said to have normal, or positive dispersion. If D is greater than zero, the medium has anomalous, or negative dispersion. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components travel slower than the lower frequency components. The pulse therefore becomes positively chirped, or up-chirped, increasing in frequency with time. Conversely, if a pulse travels through an anomalously dispersive medium, high frequency components travel faster than the lower ones, and the pulse becomes negatively chirped, or down-chirped, decreasing in frequency with time. The result of GVD, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fiber, since if dispersion is too high, a group of pulses representing a bit-stream will spread in time and merge together, rendering the bit-stream unintelligible. This limits the length of fiber that a signal can be sent down without regeneration. One possible answer to this problem is to send signals down the optical fibre at a wavelength where the GVD is zero (e.g. around ~1.3-1.5 μm in silica fibres), so pulses at this wavelength suffer minimal spreading from dispersion—in practice, however, this approach causes more problems than it solves because zero GVD unacceptably amplifies other nonlinear effects (such as Four wave mixing). Another possible option is to use soliton pulses in the regime of anomalous dispersion, a form of optical pulse which uses a nonlinear optical effect to self-maintain its shape—solitons have the practical problem, however, that they require a certain power level to be maintained in the pulse for the nonlinear effect to be of the correct strength. Instead, the solution that is currently used in practice is to perform dispersion compensation, typically by matching the fiber with another fiber of opposite-sign dispersion so that the dispersion effects cancel; such compensation is ultimately limited by nonlinear effects such as self phase modulation, which interact with dispersion to make it very difficult to undo. Dispersion control is also important in lasers that produce short pulses. The overall dispersion of the optical resonator is a major factor in determining the duration of the pulses emitted by the laser. A pair of prisms can be arranged to produce net negative dispersion, which can be used to balance the usually positive dispersion of the laser medium. Diffraction gratings can also be used to produce dispersive effects; these are often used in high-power laser amplifier systems. Recently, an alternative to prisms and gratings has been developed: chirped dispersive mirrors. These dielectric mirrors are coated so that different wavelengths have different penetration lengths, and therefore different group delays. The coating layers can be tailored to achieve a net negative dispersion.

Dispersion in gemology

In the technical terminology of gemology, dispersion is the difference in the refractive index of a material at the B and G Fraunhofer wavelengths of 686.7 nm and 430.8 nm and is meant to express the degree to which a prism cut from the gemstone shows fire or color. Dispersion is a material property. Fire depends on the dispersion, the cut angles, the lighting environment, the refractive index, and the viewer.

Related topics


- Abbe number
- Group delay

External links


- [http://ioannis.virtualcomposer2000.com/spectroscope/characteristics.html Optical Characteristics of the SF10 Crystal Prism]
- [http://ioannis.virtualcomposer2000.com/spectroscope/deviationangle.html Deviation Angle for a Prism] Category:Optics

Spectrometer

:For Acoustic uses in spectrographs of sound waves, see below. A spectrometer is an optical instrument used to measure properties of light over a specific portion of the electromagnetic spectrum. The variable measured is most often the light's intensity but could also, for instance, be the polarization state. The independent variable is usually the wavelength of the light, normally expressed as some fraction of a meter, but sometimes expressed as some unit directly proportional to the photon energy, such as wavenumber or electron volts, which has a reciprocal relationship to wavelength. A spectrometer is used in spectroscopy for producing spectral lines and measuring their wavelengths and intensities. Spectrometer is a term that is applied to instruments that operate over a very wide range of wavelengths, from gamma rays and X-rays into the far infrared. In general, any particular instrument will operate over a small portion of this total range because of the different techniques used to measure different portions of the spectrum. Below optical frequencies (that is, at microwave, radio, and audio frequencies), the spectrum analyzer is a closely related electronic device.

Spectroscopes

Spectrometers known as spectroscopes are used in spectroscopic analysis to identify materials. Spectroscopes are used often in astronomy and some branches of chemistry. Early spectroscopes were simply a prism with graduations marking wavelengths of light. Modern spectroscopes generally use a diffraction grating, a movable slit, and some kind of photodetector, all automated and controlled by a computer. The spectroscope was invented by Gustav Robert Georg Kirchhoff and Robert Wilhelm Bunsen. When a material is heated to incandescence it emits light that is characteristic of the atomic makeup of the material. Particular light frequencies give rise to sharply defined bands on the scale which can be thought of as fingerprints. For example, the element sodium has a very characteristic double yellow band known as the Sodium D-lines at 588.9950 and 589.5924 nanometers, the colour of which will be familiar to anyone who has seen a low pressure sodium vapor lamp. In the original spectroscope design in the early 19th century, light entered a slit and a collimating lens transformed the light into a thin beam of parallel rays. The light was then passed through a prism (in hand-held spectroscopes, usually an Amici prism) that refracted the beam into a spectrum because different wavelengths were refracted different amounts because of dispersion. This image is then viewed through a tube with a scale that was transposed upon the spectral image, enabling its direct measurement. With the development of photographic film, the more accurate spectrograph was created. It was based on the same principle as the spectroscope, but it had a camera in place of the viewing tube. In recent years the electronic circuits built around the photomultiplier tube have replaced the camera, allowing real-time spectrographic analysis with far greater accuracy. Arrays of photosensors are also used in place of film in spectrographic systems. Such spectral analysis, or spectroscopy, has become an important scientific tool for analyzing the composition of unknown material and for studying astronomical phenomena and testing astronomical theories. See also:
- Spectroscopy
- Fourier spectrometer
- Mass spectrometer
- Monochromator
- Colorimeter

Spectrographs

A spectrograph is an instrument that transforms an incoming time-domain waveform into a frequency spectrum, or generally a sequence of such spectra. There are several kinds of machines referred to as spectrographs, depending on the precise nature of the waves.

Optical uses

frequency spectrums that is used for identifying rocks.]] In optics, a spectrograph separates incoming light according to its wavelength and records the resulting spectrum in some detector. It is a type of spectrometer and superseded the spectroscope for scientific applications. In astronomy, spectrographs are widely used. These are installed at the focus of a telescope which may be either in a ground-based observatory or in a spacecraft. The Mars Exploration Rovers each contained a Mini-TES - a Miniature Thermal Emission Spectrometer (i.e. infrared spectrometer). The first spectrographs used photographic paper as the detector. The star spectral classification and discovery of the main sequence, Hubble's law and the Hubble sequence were all made with spectrographs that used photographic paper. The plant pigment phytochrome was discovered using a spectrograph that used living plants as the detector. More recent spectrographs use electronic detectors, such as CCDs which can be used for both visible and UV light. The exact choice of detector depends on the wavelengths of light to be recorded.

Acoustic uses

UV] In acoustics, a spectrograph converts a sound wave into a sound spectrogram. The first acoustic spectrograph was developed during World War II at Bell Telephone Laboratories, and was widely used in speech science, acoustic phonetics and audiology research, before eventually being superseded by digital signal processing techniques.

External links


- [http://www.scienceofspectroscopy.info The Science of Spectroscopy] - supported by NASA, includes OpenSpectrum, a Wiki-based learning tool for spectroscopy that anyone can edit
- [http://ioannis.virtualcomposer2000.com/spectroscope/ A Short Study of the Characteristics of Two Lab Spectroscopes] Category:Spectroscopy Category:Observational astronomy Spectrometer

Joseph von Fraunhofer

Joseph von Fraunhofer (March 6, 1787 – June 7, 1826) was a German physicist. When Fraunhofer became an orphan at the age of 11, he started working as an apprentice to a harsh glassmaker named Philipp Anton Weichelsberger. In 1801 the workshop in which he was working collapsed and he was buried in the rubble. The rescue operation was led by Maximilian IV Joseph, Prince Elector of Bavaria (the future Maximilian I Joseph). The prince entered Fraunhofer's life, providing him with books and forcing his employer to allow the young Fraunhofer time to study. After eight months of study, Fraunhofer went to work at the Optical Institute at Benediktbeuren, a secularised Benedectine monastery devoted to glass-making. There he discovered how to make the world's finest optical glass and invented incredibly precise methods for measuring dispersion. In 1818 he became the director of the Optical Institute. Due to the fine optical instruments he had developed, Bavaria overtook England as the centre of the optics industry. Even the likes of Michael Faraday were unable to produce glass that could rival Fraunhofer's. In 1814 Fraunhofer was the first to investigate seriously the absorption lines in the solar spectrum that were ultimately explained by Kirchhoff and Bunsen in 1859, who also invented the spectroscope. These lines are still sometimes called Fraunhofer lines in his honour. He also invented the diffraction grating and in doing so transformed spectroscopy from a qualitative art to a quantitative science by demonstrating how one could measure the wavelength of light accurately. He found out that the spectra of Sirius and other first-magnitude stars differed from each other and from the sun, thus founding stellar spectroscopy. Ultimately, however, his primary passion was still practical optics, once noting that "In all my experiments I could, owing to lack of time, pay attention to only those matter which appeared to have a bearing upon practical optics." His illustrious career eventually earned him knighthood and membership in the Royal Academy of Sciences, Munich. Like many glassmakers of his era who were poisoned by heavy metal vapours, Fraunhofer died young, in 1826 at the age of 37. His most valuable glassmaking recipes are thought to have gone to the grave with him.

See also


- Fraunhofer society
- Fraunhofer diffraction
- Fraunhofer line

External links


- [http://www.hao.ucar.edu/Public/education/bios/fraunhofer.html Biography of Joseph von Fraunhofer] Fraunhofer, Joseph von Fraunhofer, Joseph von Fraunhofer, Joseph von Fraunhofer, Joseph von Fraunhofer, Joseph von ja:ヨゼフ・フォン・フラウンホーファー

1821 in science

The year 1821 in science and technology included many events, some of which are listed here.

Astronomy


- Comet Encke is the second comet to be discovered to have a periodic orbit, after Comet Halley
- Alexis Bouvard detects irregularities in the orbit of Uranus

Exploration


- William Edward Parry starts his second voyage to find the Northwest Passage

Geology


- Ignatz Venetz proposes his ice age theory
- Pierre Berthier discovers bauxite
- Mary Anning finds the first ever plesiosaur fossil at Lyme Regis

Mathematics


- Augustin Louis Cauchy gives the first complete presentation of calculus using limits

Paleontology


- William Buckland finds the remains of a hyenas' den in Yorkshire, containing the bones of lions, elephants and rhinoceros

Physics


- Michael Faraday discovers electromagnetic rotation
- Thomas Johann Seebeck discovers the thermoelectric effect
- Augustin Fresnel shows that light is made up of a traverse wave motion

Awards


- Copley Medal: Edward Sabine; John Herschel

Births


- May 16 - Pafnuty Chebyshev (d. 1894), mathematician.
- August 16 - Arthur Cayley (d. 1895), mathematician.
- August 31 - Hermann von Helmholtz (d. 1894), physicist.
- October 13 - Rudolf Virchow (d. 1902), biologist.
- November 18 - Franz Bronnow (d. 1891), astronomer.

Deaths


- April 20 - Franz Karl Achard (b. 1753), chemist. Category:1821 Category:Years in science

Millimeter

To help compare different orders of magnitude this page lists lengths between 10-3 m and 10-2 m (1 mm and cm).
- Distances shorter than 1 mm
- 1.0 mm is equal to
  - 1/1000th of a metre
  - 0.039 inches
  - side of square of area 1 mm2
  - edge of cube of volume 1 mm3
- 2.54 mm — distance between pins on old DIP (dual-inline-package) electronic components
- 5 mm — length of average red ant
- 7.62 mm — common military ammunition size
- Distances longer than 1 cm

See also


- Orders of magnitude (length) -03 ja:1 E-3 m

Wavelength

:For the album by Van Morrison, see Wavelength (album). The wavelength is the distance between repeating units of a wave pattern. It is commonly designated by the Greek letter lambda (λ). In a sine wave, the wavelength is the distance between the midpoints of the wave: Image:Wavelength.png The x axis represents distance, and I would be some varying quantity at a given point in time as a function of x, for instance air pressure for a sound wave or strength of the electric or magnetic field for light. Wavelength λ has an inverse relationship to frequency f, the number of peaks to pass a point in a given time. The wavelength is equal to the speed of the wave type divided by the frequency of the wave. When dealing with electromagnetic radiation in a vacuum, this speed is the speed of light c, for signals (waves) in air, this is the speed of sound in air. The relationship is given by: : \lambda = \frac where: :λ = wavelength of a sound wave or electromagnetic wave :c = speed of light in vacuum = 299,792.458 km/s ~ 300,000 km/s = 300,000,000 m/s or :c = speed of sound in air = 343 m/s at 20 °C (68 °F) :f = frequency of the wave in 1/s = Hz For radio waves this relationship is approximated with the formula: wavelength λ (in metres) = 300 / frequency (in megahertz).
For sound waves this relationship is approximated with the formula: wavelength λ (in metres) = 333 / frequency (in hertz). When light waves (and other electromagnetic waves) enter a medium, their wavelength is reduced by a factor equal to the refractive index n of the medium but the frequency of the wave is unchanged. The wavelength of the wave in the medium, λ' is given by: : \lambda^\prime = \frac where: :λ0 is the vacuum wavelength of the wave Wavelengths of electromagnetic radiation, no matter what medium they are travelling through, are usually quoted in terms of the vacuum wavelength, although this is not always explicitly stated. Louis de Broglie discovered that all particles with momentum have a wavelength associated with their quantum mechanical wavefunction, called the de Broglie wavelength.

See also


- amplitude
- periodic function

External link


- [http://www.sengpielaudio.com/calculator-wavelength.htm Conversion: Wavelength to frequency and vice versa - The calculator] Category:Length Category:Wave mechanics ko:파장 ja:波長 th:ความยาวคลื่น

Dispersion (optics)

In optics, dispersion is a phenomenon that causes the separation of a wave into spectral components with different frequencies, due to a dependence of the wave's speed on its frequency. It is most often described in light waves, though it may happen to any kind of wave that interacts with a medium or can be confined to a waveguide, such as sound waves. There are generally two sources of dispersion: material dispersion, which comes from a frequency-dependent response of a material to waves; and waveguide dispersion, which comes because the transverse mode solutions for waves confined laterally within a finite waveguide generally depend upon the frequency (i.e. on the relative size of the wave, the wavelength, and that of the waveguide). A related phenomenon is that of modal dispersion, which comes about if a signal consists of a superposition of multiple modes at each frequency—because different modes generally travel at different speeds, dispersion of temporal features (and thus signal degradation) results. A special case of this is polarization mode dispersion (PMD), which comes from a superposition of two modes that normally travel at the same speed due to symmetry (e.g. two orthogonal polarizations in a waveguide of circular or square cross-section), but which travel at different speeds due to random imperfections that break the symmetry.

Material dispersion in optics

polarization mode dispersion In optics, the phase velocity of a wave v in a given uniform medium is given by: :v = \frac where c is the speed of light in a vacuum and n is the refractive index of the medium. In general, the refractive index is some function of the frequency ν of the light, thus n = n(ν), or alternately, with respect to the wave's wavelength n = n(λ). The wavelength dependency of a material's refractive index is usually quantified by an empirical formula, the Cauchy or Sellmeier equations. The most commonly seen consequence of dispersion in optics is the separation of white light into a color spectrum by a prism. From Snell's law it can be seen that the angle of refraction of light in a prism depends on the refractive index of the prism material. Since that refractive index varies with wavelength, it follows that the angle that the light is refracted will also vary with wavelength, causing an angular separation of the colors known as angular dispersion. For visible light, most transparent materials (e.g. glasses) have: :1 or alternatively: :\frac < 0, that is, refractive index n decreases with increasing wavelength λ. At the interface of such a material with air or vacuum (index of ~1), Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle \arcsin(\sin(\theta)/n). Thus, blue light, with a higher refractive index, will be bent more strongly than red light, resulting in the well-known rainbow pattern.

Group and phase velocity

Another consequence of dispersion manifests itself as a temporal effect. The formula above, v = c / n calculates the phase velocity of a wave; this is the velocity at which the phase of any one frequency component of the wave will propagate. This is not the same as the group velocity of the wave, which is the rate that changes in amplitude (known as the envelope of the wave) will propagate. The group velocity vg is related to the phase velocity by, for a homogeneous medium (here \lambda is the wavelength in vacuum, not in the medium): :v_g = c \left[ n - \lambda \frac \right]^. The group velocity vg is often thought of as the velocity at which energy or information is conveyed along the wave. In most cases this is true, and the group velocity can be thought of as the signal velocity of the waveform. In some unusual circumstances, where the wavelength of the light is close to an absorption resonance of the medium, it is possible for the group velocity to exceed the speed of light (vg > c), leading to the conclusion that superluminal (faster than light) communication is possible. In practice, in such situations the distortion and absorption of the wave is such that the value of the group velocity essentially becomes meaningless, and does not represent the true signal velocity of the wave, which stays less than c. The group velocity itself is usually a function of the wave's frequency. This results in group velocity dispersion (GVD), which causes a short pulse of light to spread in time as a result of different frequency components of the pulse travelling at different velocities. GVD is often quantified as the group delay dispersion parameter (again, this formula is for a uniform medium only): :D = - \frac \left( \frac \right) . If D is less than zero, the medium is said to have normal, or positive dispersion. If D is greater than zero, the medium has anomalous, or negative dispersion. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components travel slower than the lower frequency components. The pulse therefore becomes positively chirped, or up-chirped, increasing in frequency with time. Conversely, if a pulse travels through an anomalously dispersive medium, high frequency components travel faster than the lower ones, and the pulse becomes negatively chirped, or down-chirped, decreasing in frequency with time. The result of GVD, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fiber, since if dispersion is too high, a group of pulses representing a bit-stream will spread in time and merge together, rendering the bit-stream unintelligible. This limits the length of fiber that a signal can be sent down without regeneration. One possible answer to this problem is to send signals down the optical fibre at a wavelength where the GVD is zero (e.g. around ~1.3-1.5 μm in silica fibres), so pulses at this wavelength suffer minimal spreading from dispersion—in practice, however, this approach causes more problems than it solves because zero GVD unacceptably amplifies other nonlinear effects (such as Four wave mixing). Another possible option is to use soliton pulses in the regime of anomalous dispersion, a form of optical pulse which uses a nonlinear optical effect to self-maintain its shape—solitons have the practical problem, however, that they require a certain power level to be maintained in the pulse for the nonlinear effect to be of the correct strength. Instead, the solution that is currently used in practice is to perform dispersion compensation, typically by matching the fiber with another fiber of opposite-sign dispersion so that the dispersion effects cancel; such compensation is ultimately limited by nonlinear effects such as self phase modulation, which interact with dispersion to make it very difficult to undo. Dispersion control is also important in lasers that produce short pulses. The overall dispersion of the optical resonator is a major factor in determining the duration of the pulses emitted by the laser. A pair of prisms can be arranged to produce net negative dispersion, which can be used to balance the usually positive dispersion of the laser medium. Diffraction gratings can also be used to produce dispersive effects; these are often used in high-power laser amplifier systems. Recently, an alternative to prisms and gratings has been developed: chirped dispersive mirrors. These dielectric mirrors are coated so that different wavelengths have different penetration lengths, and therefore different group delays. The coating layers can be tailored to achieve a net negative dispersion.

Dispersion in gemology

In the technical terminology of gemology, dispersion is the difference in the refractive index of a material at the B and G Fraunhofer wavelengths of 686.7 nm and 430.8 nm and is meant to express the degree to which a prism cut from the gemstone shows fire or color. Dispersion is a material property. Fire depends on the dispersion, the cut angles, the lighting environment, the refractive index, and the viewer.

Related topics


- Abbe number
- Group delay

External links


- [http://ioannis.virtualcomposer2000.com/spectroscope/characteristics.html Optical Characteristics of the SF10 Crystal Prism]
- [http://ioannis.virtualcomposer2000.com/spectroscope/deviationangle.html Deviation Angle for a Prism] Category:Optics

Electromagnetic spectrum

s
SX = Soft X-Rays
EUV = Extreme ultraviolet
NUV = Near ultraviolet
Visible light
NIR = Near infrared
MIR = Moderate infrared
FIR = Far infrared

Radio waves:
EHF = Extremely high frequency (Microwaves)
SHF = Super high frequency (Microwaves)
UHF = Ultrahigh frequency
VHF = Very high frequency
HF = High frequency
MF = Medium frequency
LF = Low frequency
VLF = Very low frequency
VF = Voice frequency
ELF = Extremely low frequency]] The electromagnetic spectrum is the range of all possible electromagnetic radiation. Also, the "electromagnetic spectrum" (usually just spectrum) of an object is the range of electromagnetic radiation that it emits, reflects, or transmits. The electromagnetic spectrum, shown in the table, extends from frequencies used in the electric power grid (at the long-wavelength end) to gamma radiation (at the short-wavelength end), covering wavelengths from thousands of kilometres down to fractions of the size of an atom, though in principle the spectrum is actually infinite. Electromagnetic energy at a particular wavelength λ (in vacuum) has an associated frequency ν and photon energy E. Thus, the electromagnetic spectrum may be expressed equally well in terms of any of these three quantities. They are related according to the equations: :\lambda = \frac \,\! and :E=h\nu \,\! where:
- c is the speed of light, 299792458 m/s (c \approx 3 \cdot 10^8 \ \mbox/\mbox = 300,000 \ \mbox/\mbox).
- h is Planck's constant, (h \approx 6.626069 \cdot 10^ \ \mbox \cdot \mbox \approx 4.13567 \ \mathrm \mbox/\mbox).

Spectra of objects

Nearly all objects in the universe emit, reflect and/or transmit some light. The distribution of this light along the electromagnetic spectrum (called the spectrum of the object) is determined by the object's composition. Several types of spectra can be distinguished depending upon the nature of the radiation coming from an object:
- If the spectrum is composed primarily of thermal radiation emitted by the object itself, an emission spectrum occurs.
  - Some bodies emit light more or less according to the blackbody spectrum.
- If the spectrum is composed of background light, parts of which the object transmits and parts of which it absorbs, an absorption spectrum occurs. Electromagnetic spectroscopy is the branch of physics that deals with the characterization of matter by its spectra.

Classification systems

While the classification scheme is generally accurate, in reality there is often some overlap between neighboring types of electromagnetic energy. For example, SLF radio waves at 60 Hz may be received and studied by astronomers, or may be ducted along wires as electric power. Also, some low-energy gamma rays actually have a longer wavelength than some high-energy X-rays. This is possible because "gamma ray" is the name given to the photons generated from nuclear decay or other nuclear and subnuclear processes, whereas X-rays on the other hand are generated by electronic transitions involving highly energetic inner electrons. Therefore the distinction between gamma ray and X-ray is related to the radiation source rather than the radiation wavelength. Generally, nuclear transitions are much more energetic than electronic transitions, so usually, gamma-rays are more energetic than X-rays. However, there are a few low-energy nuclear transitions (e.g. the 14.4 keV nuclear transition of Fe-57) that produce gamma rays that are less energetic than some of the higher energy X-rays. Use of the radio frequency spectrum is regulated by governments. This is called frequency allocation.

Electric energy

Electrical energy covers the low-frequency, long-wavelength end of the spectrum. The radiation is usually ducted along 2-wire and 3-wire transmission lines and sent to various devices besides antennas. At zero frequency the energy is emitted by batteries and DC power supplies, while at 50 Hz and 60 Hz it is produced by rotary magnetic generators and ducted through the international power grids. At frequencies between 20 Hz to 30 kHz the EM energy is translated to and from acoustic energy and is distributed over telephone lines, as well as being used to operate loudspeakers for public address or in music systems. Note that other than its frequency, there is no functional difference between the VHF energy guided along a television coaxial cable, versus the 60 Hz travelling along the cord leading to a light bulb. When connected to the appropriate antenna, both will radiate into space.

Radio frequency

telephone lines Radio waves generally are utilized by antennas of appropriate size, with wavelengths ranging from hundreds of meters to about one millimeter. They are used for transmission of data, via modulation. Television, mobile phones, wireless networking and amateur radio all use radio waves.

Microwaves

The super high frequency (SHF) and extremely high frequency (EHF) of Microwaves come next. Microwaves are waves which are typically short enough to employ tubular metal waveguides of reasonable diameter. Microwave energy is produced with klystron and magnetron tubes, and with solid state diodes such as Gunn and IMPATT devices. Microwaves are absorbed by molecules that have a dipole moment in liquids. In a microwave oven, this effect is used to heat food. Low-intensity microwave radiation is used in Wi-Fi. It should be noted that an average microwave oven in active condition is, in close range, powerful enough to cause interference with poorly shielded electromagnetic fields such as those found in mobile medical devices and cheap consumer electronics.

Terahertz radiation

This is a region of the light spectrum between far infrared and microwaves. Until recently, the range was rarely studied and few sources existed for microwave energy at the high end of the band (sub-millimeter waves or so-called terahertz waves), but applications are now appearing. The proposed WiMAX standard for wireless networking, a long-range enhancement of Wi-Fi, lies within this region. Scientists are also looking to apply Terahertz technology in the armed forces, where high frequency waves will be sent at enemy troops to incapacitate them.

Infrared radiation

The infrared part of the electromagnetic spectrum covers the range from roughly 300 GHz (1 mm) to 400 THz (750 nm). It can be divided into three parts:
- Far-infrared, from 300 GHz (1 mm) to 30 THz (10 μm). The lower part of this range may also be called microwaves. This radiation is typically absorbed by so-called rotational modes in gas-phase molecules, by molecular motions in liquids, and by phonons in solids. The water in the Earth's atmosphere absorbs so strongly in this range that it renders the atmosphere effectively opaque. However, there are certain wavelength ranges ("windows") within the opaque range which allow partial transmission, and can be used for astronomy. The wavelength range from approximately 200 μm up to a few mm is often referred to as "sub-millimeter" in astronomy, reserving far infrared for wavelengths below 200 μm.
- Mid-infrared, from 30 to 120 THz (10 to 2.5 μm). Hot objects (black-body radiators) can radiate strongly in this range. It is absorbed by molecular vibrations, that is, when the different atoms in a molecule vibrate around their equilibrium positions. This range is sometimes called the fingerprint region since the mid-infrared absorption spectrum of a compound is very specific for that compound.
- Near-infrared, from 120 to 400 THz (2,500 to 750 nm). Physical processes that are relevant for this range are similar to those for visible light.

Visible radiation (light)

Color Wavelength interval Frequency interval
violet ~ 380 to 430 nm ~ 790 to 700 THz
blue ~ 430 to 500 nm ~ 700 to 600 THz
cyan ~ 500 to 520 nm ~ 600 to 580 THz
green ~ 520 to 565 nm ~ 580 to 530 THz
yellow ~ 565 to 590 nm ~ 530 to 510 THz
orange ~ 590 to 625 nm ~ 510 to 480 THz
red ~ 625 to 740 nm ~ 480 to 405 THz
Continuous spectrum
Image:Spectrum441pxWithnm.png
The spectrum of visible light
Designed for monitors with gamma 1.5.
After infrared comes visible light. This is the range in which the sun and stars similar to it emit most of their radiation. It is probably not a coincidence that the human eye is sensitive to the wavelengths that the sun emits most strongly. Visible light (and near-infrared light) is typically absorbed and emitted by electrons in molecules and atoms that move from one energy level to another. The light we see with our eyes is really a very small portion of the electromagnetic spectrum. A rainbow shows the optical (visible) part of the electromagnetic spectrum; infrared (if you could see it) would be located just beyond the red side of the rainbow with ultraviolet appearing just beyond the violet end.

Ultraviolet light

Next comes ultraviolet. This is radiation whose wavelength is shorter than the violet end of the visible spectrum. Being very energetic, UV can break chemical bonds, make molecules unusually reactive or ionize them, in general changing their mutual behavior. Sunburn, for example, is caused by the disruptive effects of UV radiation on skin cells, which can even cause skin cancer, if the radiation damages the complex DNA molecules in the cells (UV radiation is a proven mutagen). The Sun emits a large amount of UV radiation, which could quickly turn Earth into a barren desert, but most of it is absorbed by the atmosphere's ozone layer before reaching the surface.

X-rays

After UV come X-rays. Hard X-rays are of shorter wavelengths than soft X-rays. X-rays are used for seeing through some things and not others, as well as for high-energy physics and astronomy. Neutron stars and accretion disks around black holes emit X-rays, which enable us to study them.

Gamma rays

After hard X-rays come gamma rays. These are the most energetic photons, having no lower limit to their wavelength. They are useful to astronomers in the study of high-energy objects or regions and find a use with physicists thanks to their penetrative ability and their production from radioisotopes. The wavelength of gamma rays can be measured with high accuracy by means of Compton scattering. Note that there are no defined boundaries between the types of electromagnetic radiation. Some wavelengths have a mixture of the properties of two regions of the spectrum. For example, red light resembles infra-red radiation in that it can resonate some chemical bonds.

See also


- Spectroscopy
- Electromagnetic spectroscopy
- Radiant energy
- Bandplan

External links


- [http://www.ntia.doc.gov/osmhome/allochrt.html U.S. Frequency Allocation Chart] - Covering the range 3 kHz to 300 GHz (from Department of Commerce)
- [http://strategis.ic.gc.ca/epic/internet/insmt-gst.nsf/vwapj/spectallocation.pdf/%24FILE/spectallocation.pdf Canadian Table of Frequency Allocations] (from Industry Canada)
- [http://www.ofcom.org.uk/static/archive/ra/topics/spectrum-strat/future/strat02/strategy02app_b.pdf UK frequency allocation table] (from Ofcom, which inherited the Radiocommunications Agency's duties, pdf format)
- [http://www.scienceofspectroscopy.info The Science of Spectroscopy] - supported by NASA, includes OpenSpectrum, a Wiki-based learning tool for spectroscopy that anyone can edit
- [http://www.e-builds.com/EM%20spectrum/ An EM Spectrum Overview in Flash] by e-builds ja:電磁スペクトル

Prism (optics)

:For other senses of this word, see prism (disambiguation). prism (disambiguation) In optics, a prism is a device used to refract light, reflect it or break it up (to disperse it) into its constituent spectral colours (colours of the rainbow). The traditional geometrical shape is that of a triangular prism, with a triangular base and rectangular sides. Some types of optical prisms are not in fact in the shape of geometric prisms. As light moves from one medium (e.g. air) to another denser medium (the glass of the prism), it is slowed down and as a result either bent (refracted) or reflected. The angle that the beam of light makes with the interface as well as the refractive indices of the two media determine whether it is reflected or refracted, and by how much (see refraction, total internal reflection). Reflective prisms are used to reflect light, for instance in binoculars, since they are easier to manufacture than mirrors. Dispersive prisms are used to break up light into its constituent spectral colours because the refractive index depends on frequency (see dispersion); the white light entering the prism is a mixture of different frequencies, each of which gets bent slightly differently. Blue light is slowed down more than red light and will therefore be bent more than red light. There are also polarizing prisms (also known as birefringent prisms) which can split a beam of light into components of varying polarization. Isaac Newton first thought that prisms split colours out of colourless light. Newton placed a second prism such that a separated colour would pass through it and found the colour unchanged. He concluded that prisms separate colours. He also used a lens and a second prism to recompose the rainbow into white light.

Types of prisms

Reflective prisms


- Pentaprism
- Porro prism
- Porro-Abbe prism
- Abbe-Koenig prism
- Schmidt-Pechan prism
- Dove prism
- Dichroic prism
- Amici roof prism

Dispersive prisms


- Triangular prism
- Abbe prism
- Pellin-Broca prism
- Amici prism

Polarizing prisms


- Nicol prism
- Wollaston prism
- Rochon prism
- Glan-Foucault prism
- Glan-Taylor prism
- Glan-Thompson prism

See also


- Prism (geometry)
- Triangular prism (geometry)

External links


- [http://ioannis.virtualcomposer2000.com/spectroscope/ Geometry of Two Prism Spectroscopes] Category:Optical devices ja:プリズム

Specular reflection

Specular reflection is the perfect, mirror-like reflection of light from a surface, in which light from a single incoming direction is reflected onto a single outgoing direction. Such behaviour is described by the law of reflection, which states that the direction of outgoing reflected light and the direction of incoming light make the same angle with respect to the surface normal; this is commonly stated as \theta _i = \theta _r. This is in contrast to diffuse reflection, where incoming light is reflected in all directions equally. The most familiar example of the distinction between specular and diffuse reflection would be matte and glossy paints. Matte paints have a higher proportion of diffuse reflection, while glossy paints have a greater proportion of specular reflection. Specular reflection and diffuse reflection are simply approximations. In reality, surfaces exhibit a continuum of modes of reflection between these two. Specular reflection is very important for making good [http://www.amasci.com/amateur/holo1.html scratch holograms], which are optically similar to Benton Rainbow Holograms (AKA: "White Light Holograms"); see also [http://www.amasci.com/amateur/hand1.html SPIE article] and the [http://amasci.com/amateur/holohint.html FAQ], and the main Wikipedia Holography entry. Category:Optics

Polarization

In electrodynamics, polarization (also spelled polarisation) is a property of waves, such as light and other electromagnetic radiation. Unlike more familiar wave phenomena such as waves on water or sound waves, electromagnetic waves are three-dimensional, and it is their vector nature that gives rise to the phenomenon of polarization.

Theory

Basics - plane waves

The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation to most light waves. A plane wave is one where the direction of the magnetic and electric fields are confined to a plane perpendicular to the propagation direction. Simply because the plane is two-dimensional, the electric vector in the plane at a point in space can be decomposed into two orthogonal components. Call these the x and y components (following the conventions of analytic geometry). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner, the two components have exactly the same frequency. However, these components have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time in the fixed plane we are talking about. By considering the shape traced out in a fixed plane by the electric vector as such a plane wave passes over it (a Lissajous figure), we obtain a description of the polarization state. The following figures show some examples of the evolution of the electric field vector (blue) with time, along with its x and y components (red/left and green/right) and the path made by the vector in the plane (purple):
Lissajous figure
Circular
Lissajous figure
Elliptical

Consider first the special case (left) where the two orthogonal components are in phase. In this case the strength of the two components are always equal or related by a constant ratio, so the direction of the electric vector (the vector sum of these two components) will always fall on a single line in the plane. We call this special case linear polarization. The direction of this line will depend on the relative amplitude of the two components. This direction can be in any angle in the plane, but the direction never varies. Now consider another special case (center), where the two orthogonal components have exactly the same amplitude and are exactly ninety degrees out of phase. In this case one component is zero when the other component is at maximum or minimum amplitude. Notice that there are two possible phase relationships that satisfy this requirement. The x component can be ninety degrees ahead of the y component or it can be ninety degrees behind the y component. In this special case the electric vector in the plane formed by summing the two components will rotate in a circle. We call this special case circular polarization. The direction of rotation will depend on which of the two phase relationships exists. We call these cases right-hand circular polarization and left-hand circular polarization, depending on which way the electric vector rotates. All the other cases, that is where the two components are not in phase and either do not have the same amplitude and/or are not ninety degrees out of phase (e.g. right) are called elliptical polarization because the sum electric vector in the plane will trace out an ellipse (the "polarization ellipse"). ellipse The use of plane polarized waves as a basis to decompose light waves is not essential; waves of opposite circular polarization can similarly be combined to yield any kind of polarization. The plane polarization decomposition is natural when dealing with reflection from surfaces, birefringent materials, or synchrotron radiation. The circularly polarized modes are a most useful basis set for the study of light propagation in stereoisomers - see, e.g. [http://bio.classes.ucsc.edu/bio100/LECTNOTES/CHIRAL/chirality.PDF].

Incoherent radiation

In nature, electromagnetic radiation is often produced by a large ensemble of individual radiators, producing waves independently of each other. This type of light is termed incoherent. In general there is no single frequency but rather a spectrum of different frequencies present, and even if filtered to an arbitrarily narrow frequency range, there may not be a consistent state of polarization. However, this does not mean that polarization is only a feature of coherent radiation. Incoherent radiation may show statistical correlation between the components of the electric field, which can be interpreted as partial polarization. In general it is possible to describe an observed wave field as the sum of a completely incoherent part (no correlations) and a completely polarized part. One may then describe the light in terms of the degree of polarization, and the parameters of the polarization ellipse.

Parameterizing polarization

correlation For ease of visualization, polarization states are often specified in terms of the polarization ellipse, specifically its orientation and elongation. A common parameterization uses the azimuth angle, ψ (the angle between the major semi-axis of the ellipse and the x-axis) and the ellipticity, ε (the ratio of the two semi-axes). Ellipticity is used in preference to the more common geometrical concept of eccentricity, which is of limited physical meaning in the case of polarization. An ellipticity of zero corresponds to linear polarization and an ellipticity of 1 corresponds to circular polarization. The arctangent of the ellipticity, χ = tan−1 ε (the "ellipticity angle"), is also commonly used. An example is shown in the diagram to the right. Full information on a completely polarized state is also provided by the amplitude and phase of oscillations in two components of the electric field vector in the plane of polarization. This representation was used above to show how different states of polarization are possible. The amplitude and phase information can be conveniently represented as a two-dimensional complex vector (the Jones vector): : \mathbf = \begin a_1 e^ \\ a_2 e^ \end . Notice that the product of a Jones vector with a complex number of unit modulus gives a different Jones vector representing the same ellipse, and thus the same state of polarization. The physical electric field, as the real part of the Jones vector, would be altered but the polarization state itself is independent of absolute phase. Note also that the basis vectors used to represent the Jones vector need not represent linear polarization states (i.e. be real). In general any two orthogonal states can be used, where an orthogonal vector pair is formally defined as one having a zero inner product. A common choice is left and right circular polarizations, for example to model the different propagation of waves in two such components in circularly birefringent media (see below) or signal paths of coherent detectors sensitive to circular polarization.
inner product Reflection of a plane wave from a surface perpendicular to the page. The p-components of the waves are in the page, while the s components are perpendicular to it.
Regardless of whether polarization ellipses are represented using geometric parameters or Jones vectors, implicit in the parameterization is the orientation of the coordinate frame. This permits a degree of freedom, namely rotation about the propagation direction. When considering light that is propagating parallel to the surface of the Earth, the terms "horizontal" and "vertical" polarization are ofte