FACTOID # 1: Idaho produces more milk than Iowa, Indiana and Illinois combined.

 Home Encyclopedia Statistics States A-Z Flags Maps FAQ About

 WHAT'S NEW

SEARCH ALL

Search encyclopedia, statistics and forums:

(* = Graphable)

Encyclopedia > Dispersion (optics)
Dispersion of a light beam in a prism.

In optics, dispersion is a phenomenon that causes the separation of a wave into spectral components with different wavelengths, due to a dependence of the wave's speed on its wavelength. It is most often described in light waves, but it may happen to any kind of wave that interacts with a medium or can be confined to a waveguide, such as sound waves. Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature. Image File history File links from en:Image:Prism1. ... For the book by Sir Isaac Newton, see Opticks. ... A wave is a disturbance that propagates through space or spacetime, transferring energy and momentum and sometimes angular momentum. ... The wavelength is the distance between repeating units of a wave pattern. ... This article does not cite any references or sources. ... Look up waveguide in Wiktionary, the free dictionary. ... Sound is a disturbance of mechanical energy that propagates through matter as a longitudinal wave, and therefore is a mechanical wave. ...

There are generally two sources of dispersion: material dispersion and waveguide dispersion. Material dispersion comes from a frequency-dependent response of a material to waves. For example, material dispersion leads to undesired chromatic aberration in a lens or the separation of colors in a prism. Waveguide dispersion occurs when the speed of a wave in a waveguide (such as an optical fiber) depends on its frequency for geometric reasons, independent of any frequency dependence of the materials from which it is constructed. This type of dispersion leads to signal degradation in telecommunications because the varying delay in arrival time between different components of a signal "smears out" the signal in time. Chromatic aberration is caused by the dispersion of the lens material, the variation of its refractive index n with the wavelength of light. ... A lens. ... For the optical prism, see Triangular prism (optics). ... Optical fibers An optical fiber (or fibre) is a glass or plastic fiber designed to guide light along its length by confining as much light as possible in a propagating form. ... Copy of the original phone of Alexander Graham Bell at the MusÃ©e des Arts et MÃ©tiers in Paris Telecommunication is the transmission of signals over a distance for the purpose of communication. ...

## Material dispersion in optics GA_googleFillSlot("encyclopedia_square");

The variation of refractive index vs. wavelength for various glasses. The wavelengths of visible light are shaded in red.

The phase velocity of a wave v in a given uniform medium is given by The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ...

$v = frac{c}{n}$

where c is the speed of light in a vacuum and n is the refractive index of the medium. A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic... The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ...

In general, the refractive index is some function of the frequency f of the light, thus n = n(f), 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 wavelength is the distance between repeating units of a wave pattern. ... A plot of refactive index vs. ... A plot of the refractive index vs. ...

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. Alternate meanings: White (disambiguation) White is a color (more accurately it contains all the colors of the spectrum and is sometimes described as an achromatic color&#8212;black is the absence of color) that has high brightness but zero hue. ... The visible spectrum is the portion of the optical spectrum (light or electromagnetic spectrum) that is visible to the human eye. ... Diagram of a triangular prism, dispersing light Lamps as seen through a prism. ... Refraction of light at the interface between two media of different refractive indices, with n2 > n1. ... The straw seems to be broken, due to refraction of light as it emerges into the air. ...

For visible light, most transparent materials (e.g. glasses) have:

$1 < n(lambda_{rm red}) < n(lambda_{rm yellow}) < n(lambda_{rm blue}) ,$

or alternatively:

$frac{{rm d}n}{{rm d}lambda} < 0,$

that is, refractive index n decreases with increasing wavelength λ. In this case, the medium is said to have normal dispersion. Whereas, if the index increases with increasing wavelength the medium has anomalous dispersion.

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 (θ) / n) . Thus, blue light, with a higher refractive index, will be bent more strongly than red light, resulting in the well-known rainbow pattern. A surface normal, or just normal to a flat surface is a three-dimensional vector which is perpendicular to that surface. ... Full featured double rainbow in Wrangell-St. ...

## 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 λ is the wavelength in vacuum, not in the medium): In physics, velocity is defined as the rate of change of displacement or the rate of displacement. ... This article is about a portion of a periodic process. ... The group velocity of a wave is the velocity with which the variations in the shape of the waves amplitude (known as the modulation or envelope of the wave) propagate through space. ... Amplitude is a nonnegative scalar measure of a waves magnitude of oscillation, that is, magnitude of the maximum disturbance in the medium during one wave cycle. ...

$v_g = c left[ n - lambda frac{dn}{dlambda} right]^{-1}.$

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 signal velocity of a wave is the speed at which a pulse travels through a medium. ... Absorption, in optics, is the process by which the energy of a photon is taken up by another entity, for example, by an atom whose valence electrons make a transition between two electronic energy levels. ...

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):

$D = - frac{lambda}{c} left( frac{d^2 n}{d lambda^2} right).$

If D is less than zero, the medium is said to have positive dispersion. If D is greater than zero, the medium has 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. FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... This article or section does not cite its references or sources. ... This article or section does not cite its references or sources. ...

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. Optical fibers An optical fiber (or fibre) is a glass or plastic fiber designed to guide light along its length by confining as much light as possible in a propagating form. ... The chemical compound silicon dioxide, also known as silica, is the oxide of silicon, chemical formula SiO2. ... For the meaning of fiber in nutrition, see dietary fiber. ... Four Wave Mixing is an intermodulation distortion in optical systems, similar to the third order intercept in electrical systems. ... In optics, the term soliton is used to refer any optical field that does not change during propagation because of a delicate balance between nonlinear and linear effects in the medium. ... Nonlinear optics is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization P responds nonlinearly to the electric field E of the light. ... Self-phase modulation (SPM) is a nonlinear optical effect of light-matter interaction. ...

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 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. Experiment with a laser (likely an argon type) (US Military) In physics, a laser is a device that emits light through a specific mechanism for which the term laser is an acronym: light amplification by stimulated emission of radiation. ... In optics, an ultrashort pulse of light is an electromagnetic pulse whose time duration is on the order of the femtosecond ( second). ... A laser system generally consists of three important parts: An energy source (usually referred to as the pump or pump source); A gain medium or laser medium; A mirror, or system of mirrors, forming an optical resonator. ... If a shaft of light entering a prism is sufficiently narrow, a spectrum results. ... The intensity pattern formed on a screen by diffraction from a square aperture Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. ... Curb, gutter, and grating covering a storm drain A grating is any regularly spaced collection of essentially identical, parallel, elongated elements. ... A chirped mirror is a dielectric mirror with chirped spaces between the dielectric layers (stack). ...

## Dispersion in waveguides

Optical fibers, which are used telecommunications, are among the most abundant types of waveguides. Dispersion in these fibers are one of the limiting factors that determine how much data can be transported on a single fiber. Fiber Optic strands An optical fiber in American English or fibre in British English is a transparent thin fiber for transmitting light. ...

The transverse modes for waves confined laterally within a waveguide generally have different speeds (and field patterns) depending upon the frequency (that is, on the relative size of the wave, the wavelength, compared the size of the waveguide). A transverse mode of a beam of electromagnetic radiation is a particular intensity pattern of radiation measured in a plane perpendicular (i. ... Look up waveguide in Wiktionary, the free dictionary. ... The wavelength is the distance between repeating units of a wave pattern. ...

A similar phenomenon is modal dispersion, caused by a waveguide having multiple modes at a given frequency, each with a different speed. A special case of this is polarization mode dispersion (PMD), which comes from a superposition of two modes that travel at different speeds due to random imperfections that break the symmetry of the waveguide. Multimode distortion is a distortion mechanism occurring in multimode fibers and other waveguides, in which the signal is spread in time because the propagation velocity of the optical signal is not the same for all modes. ... Polarization mode dispersion (PMD) is a form of modal dispersion where two different polarizations of light in a waveguide, which normally travel at the same speed, travel at different speeds due to random imperfections and asymmetries, causing random spreading of optical pulses. ...

## 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. Technical terminology is the specialised vocabulary of a profession or of some other activity to which a group of people dedicate significant parts of their lives (for instance, hobbies or a particular segment of industry). ... Gemology (gemmology outside the United States) is the science, art and profession of identifying and evaluating gemstones. ... Solar Fraunhofer lines In physics and optics, the Fraunhofer lines are a set of spectral lines named for the German physicist Joseph von Fraunhofer (1787--1826). ... The wavelength is the distance between repeating units of a wave pattern. ... A nanometre (American spelling: nanometer, symbol nm) is a unit of length in the metric system, equal to one thousand-millionth of a metre, which is the current SI base unit of length. ... A selection of gemstone pebbles made by tumbling rough rock with abrasive grit, in a rotating drum. ...

## Dispersion in imaging

In photographic and microscopic lenses, dispersion causes chromatic aberration, distorting the image, and various techniques have been developed to counteract it. Chromatic aberration is caused by the dispersion of the lens material, the variation of its refractive index n with the wavelength of light. ...

In physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material is a measure of the materials dispersion (variation of refractive index with wavelength). ... In physics, and in particular in optics, the study of waves and digital signal processing, the term group delay has the following meanings: 1. ... The relation between the energy of a system and its corresponding momentum is known as its dispersion relation. ...

Results from FactBites:

 The Effects of Dispersion on High-speed Fiber Optic Data Transmission: Fiber Bandwidth isn't Infinite (2355 words) Dispersion was initially a problem when the first optical fibers, multimode step-index fiber, were introduced. Chromatic dispersion is the result of material dispersion, waveguide dispersion, or profile dispersion. The laser is 0.1 nm wide with a center wavelength of 1550 nm and a fiber dispersion of 17 ps/nm/km.
 Dispersion (optics) (1468 words) In optics, dispersion is a phenomenon that causes the separation of a wave into spectral components with different wavelengths, due to a dependence of the wave's speed on its wavelength. The overall dispersion of the optical resonator is a major factor in determining the duration of the pulses emitted by the laser. 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.
More results at FactBites »

Share your thoughts, questions and commentary here