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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 complex 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 pul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term ''Fourier ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kerr-lens Modelocking
Kerr-lens mode-locking (KLM) is a method of mode-locking lasers via the nonlinear optical Kerr effect. This method allows the generation of pulses of light with a duration as short as a few femtoseconds. The optical Kerr effect is a process which results from the nonlinear response of an optical medium to the electric field of an electromagnetic wave. The refractive index of the medium is dependent on the field strength. Because of the non-uniform power density distribution in a Gaussian beam (as found in laser resonators) the refractive index changes across the beam profile; the refractive index experienced by the beam is greater in the center of the beam than at the edge. Thus a rod of an active Kerr medium functions as a lens for high intensity light. This is called self-focusing and in extreme cases leads to material destruction. In the laser cavity short bursts of light will then be focused differently from continuous waves. To favor the pulsed mode over continuous-wave, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultrashort Pulse
In optics, an ultrashort pulse, also known as an ultrafast event, is an electromagnetic pulse whose time duration is of the order of a picosecond (10−12 second) or less. Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators. Amplification of ultrashort pulses almost always requires the technique of chirped pulse amplification, in order to avoid damage to the gain medium of the amplifier. They are characterized by a high peak intensity (or more correctly, irradiance) that usually leads to nonlinear interactions in various materials, including air. These processes are studied in the field of nonlinear optics. In the specialized literature, "ultrashort" refers to the femtosecond (fs) and picosecond (ps) range, although such pulses no longer hold the record for the shortest pulses artificially generated. Indeed, x-ray pulses with durations on the attosecond time scale have been reported. The 1999 Nobel Prize in Chemistry was awarded ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Velocity Dispersion
In optics, group velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium will affect 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, :\textrm(\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 :\textrm(\omega_0) \equiv \left( \frac\right)_, or in terms of the refractive index n(\omega) according to :\textrm(\omega_0) \equiv \frac \left(\frac\right)_ + \frac\left( \frac\right)_. Applications Group velocity dispersion is most commonly u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dispersion Management
Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns * Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variation in wages encountered in an economy *Dispersed knowledge, notion that any one person is unable to perceive all economic forces Science and mathematics Mathematics *Statistical dispersion, a quantifiable variation of measurements of differing members of a population ** Index of dispersion, a normalized measure of the dispersion of a probability distribution *Dispersion point, a point in a topological space the removal of which leaves the space highly disconnected Physics *The dependence of wave velocity on frequency or wavelength: ** Dispersion (optics), for light waves **Dispersion (water waves), for water waves **Acoustic dispersion, for sound waves **Dispersion relation, the mathematical description of dispersion in a system **Modal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dispersion (optics)
In optics, and by analogy other branches of physics dealing with wave propagation, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity to optics in particular. A medium having this common property may be termed a dispersive medium (plural ''dispersive media''). 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 pulses of light in optical fiber. Physically, dispersion translates in a loss of kinetic energy through absorption. In optics, one important and familiar consequence of dispersion is the change in the angle of refra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Phase
The power spectrum S_(f) of a time series x(t) describes the distribution of Power (physics), power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including Noise (electronics), noise) as analyzed in terms of its frequency content, is called its spectrum. When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (or simply power spectrum), which applies to signals existing over ''all'' time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The power spectral density (PSD) then refers to the spec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Component
In telecommunications, spectral component is any of the waves that range outside the interval of frequencies assigned to a signal. Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation. The length of a pulse thereby is detesitions (spectral phase) of these spectral components. See also * Spectral width In telecommunications, spectral width is the wavelength interval over which the magnitude of all spectral components is equal to or greater than a specified fraction of the magnitude of the component having the maximum value. In optical communicat ... * Bandwidth-pulse Telecommunications Fourier analysis {{Mathematics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pulse (physics)
In physics, a pulse is a generic term describing a single disturbance that moves through a transmission medium. This medium may be vacuum (in the case of electromagnetic radiation) or matter, and may be indefinitely large or finite. Pulse reflection Consider a pulse moving through a medium - perhaps through a rope or a slinky. When the pulse reaches the end of that medium, what happens to it depends on whether the medium is fixed in space or free to move at its end. For example, if the pulse is moving through a rope and the end of the rope is held firmly by a person, then it is said that the pulse is approaching a fixed end. On the other hand, if the end of the rope is fixed to a stick such that it is free to move up or down along the stick when the pulse reaches its end, then it is said that the pulse is approaching a free end. Free end A pulse will reflect off a free end and return with the same direction of displacement that it had before reflection. That is, a pulse with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The first laser was built in 1960 by Theodore H. Maiman at Hughes Research Laboratories, based on theoretical work by Charles Hard Townes and Arthur Leonard Schawlow. A laser differs from other sources of light in that it emits light which is ''coherent''. Spatial coherence allows a laser to be focused to a tight spot, enabling applications such as laser cutting and lithography. Spatial coherence also allows a laser beam to stay narrow over great distances (collimation), enabling applications such as laser pointers and lidar (light detection and ranging). Lasers can also have high temporal coherence, which allows them to emit light with a very narrow spectrum. Alternatively, temporal coherence can be used to produce ultrashort pulses of ligh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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