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Group-velocity Dispersion
In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the inverse of group velocity of light in a material with respect to angular frequency, : \text(\omega_0) \equiv \frac \left( \frac \right)_, where \omega and \omega_0 are angular frequencies, and the group velocity v_g(\omega) is defined as v_g(\omega) \equiv \partial \omega / \partial k. The units of group-velocity dispersion are imesup>2/ istance often expressed in fs2/ mm. Equivalently, group-velocity dispersion can be defined in terms of the medium-dependent wave vector k(\omega) according to : \text(\omega_0) \equiv \left( \frac\right)_, or in terms of the refractive index n(\omega) according to : \text(\omega_0) \equiv \frac \left(\frac\right)_ + \frac\left( \frac\right)_. Applications Group-velocity dispersion is most commo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes the behaviour of visible light, visible, ultraviolet, and infrared light. Light is a type of electromagnetic radiation, and other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for by using the Classical electromagnetism, classical electromagnetic description of light, however complete electromagnetic descriptions of light are often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of Ray (optics), rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dispersion (optics)
Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium. Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, and in gravity waves (ocean waves). Within optics, dispersion is a property of telecommunication signals along transmission lines (such as microwaves in coaxial cable) or the Pulse (signal processing), pulses of light in optical fiber. In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive Prism (optics), prism and in chromatic aberration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Velocity
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope (waves), envelope'' of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a capillary wave. The expanding ring of waves is the wave group or wave packet, within which one can discern individual waves that travel faster than the group as a whole. The amplitudes of the individual waves grow as they emerge from the trailing edge of the group and diminish as they approach the leading edge of the group. History The idea of a group velocity distinct from a wave's phase velocity was first proposed by William Rowan Hamilton, W.R. Hamilton in 1839, and the first full treatment was by John Strutt, 3rd Baron Rayleigh, Rayleigh in his "Theory of Sound" in 1877. Definition and interpretation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Frequency
In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves). Angular frequency (or angular speed) is the magnitude of the pseudovector quantity '' angular velocity''. (UP1) Angular frequency can be obtained multiplying '' rotational frequency'', ''ν'' (or ordinary ''frequency'', ''f'') by a full turn (2 radians): . It can also be formulated as , the instantaneous rate of change of the angular displacement, ''θ'', with respect to time, ''t''. (11 pages) Unit In SI[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Femtosecond
A femtosecond is a unit of time in the International System of Units (SI) equal to 10 or of a second; that is, one quadrillionth, or one millionth of one billionth, of a second. A femtosecond is to a second, as a second is to approximately 31.69 million years. For context, a ray of light travels approximately 0.3 μm (micrometers) in 1 femtosecond, a distance comparable to the diameter of a virus.Compared with overview in: The first to make femtosecond measurements was the Egyptian Nobel Laureate Ahmed Zewail, for which he was awarded the Nobel Prize in Chemistry in 1999. Professor Zewail used lasers to measure the movement of particles at the femtosecond scale, thereby allowing chemical reactions to be observed for the first time. The word ''femtosecond'' is formed by the SI prefix ''femto'' and the SI unit ''second''. Its symbol is fs. A femtosecond is equal to 1000 attoseconds, or 1/1000 picosecond. Because the next higher SI unit is 1000 times larger, times of 10� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Millimetre
330px, Different lengths as in respect of the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is between 1 metre to 1 millimetre. The millimetre (American and British English spelling differences#-re, -er, international spelling; International System of Units, SI unit symbol mm) or millimeter (American and British English spelling differences#-re, -er, American spelling) is a Units of measurement, unit of length in the International System of Units (SI), equal to one thousandth of a metre, which is the SI base unit of length. Therefore, there are one thousand millimetres in a metre, and there are ten millimetres in a centimetre. One millimetre is equal to micrometres or nanometres. Since an inch is officially defined as exactly 25.4 millimetres, a millimetre is equal to exactly (≈ 0.03937) of an inch. Definition Since 1983, the metre has been defined as "the length of the path travelled by light in vacuum during a time interval of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refraction, refracted, when entering a material. This is described by Snell's law of refraction, , where and are the angle of incidence (optics), angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices and . The refractive indices also determine the amount of light that is reflectivity, reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel equations) and Brewster's angle. The refractive index, n, can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chirp
A chirp is a signal in which the frequency increases (''up-chirp'') or decreases (''down-chirp'') with time. In some sources, the term ''chirp'' is used interchangeably with sweep signal. It is commonly applied to sonar, radar, and laser systems, and to other applications, such as in spread-spectrum communications (see chirp spread spectrum). This signal type is biologically inspired and occurs as a phenomenon due to dispersion (a non-linear dependence between frequency and the propagation speed of the wave components). It is usually compensated for by using a matched filter, which can be part of the propagation channel. Depending on the specific performance measure, however, there are better techniques both for radar and communication. Since it was used in radar and space, it has been adopted also for communication standards. For automotive radar applications, it is usually called linear frequency modulated waveform (LFMW). In spread-spectrum usage, surface acoustic wave (S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bandwidth-limited Pulse
A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth. Bandwidth-limited pulses have a constant phase across all frequencies making up the pulse. Optical pulses of this type can be generated by mode-locked lasers. Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation. The length of a pulse thereby is determined by its spectral components, which include not just their relative intensities, but also the relative positions ( spectral phase) of these spectral components. For different pulse shapes, the minimum duration-bandwidth product is different. The duration-bandwidth product is minimal for zero phase-modulation. For example, \mathrm pulses have a minimum duration-bandwidth product of 0.315 while gaussian pulses have a minimum value of 0.441. A bandwidth-limited pulse ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally more accurate as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek alphabet, Greek letter Sigma, σ (sigma), for the population standard deviation, or the Latin script, Latin letter ''s'', for the sample standard deviation. The standard deviation of a random variable, Sample (statistics), sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bandwidth-limited Pulse
A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth. Bandwidth-limited pulses have a constant phase across all frequencies making up the pulse. Optical pulses of this type can be generated by mode-locked lasers. Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation. The length of a pulse thereby is determined by its spectral components, which include not just their relative intensities, but also the relative positions ( spectral phase) of these spectral components. For different pulse shapes, the minimum duration-bandwidth product is different. The duration-bandwidth product is minimal for zero phase-modulation. For example, \mathrm pulses have a minimum duration-bandwidth product of 0.315 while gaussian pulses have a minimum value of 0.441. A bandwidth-limited pulse ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
