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Ultrafast Spectroscopy
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 to ... [...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] |
Ferenc Krausz
Ferenc Krausz (born 17 May 1962) is a Hungaro-Austrian physicist working in Attosecond physics, attosecond science. He is a director at the Max Planck Institute of Quantum Optics and a professor of experimental physics at the Ludwig Maximilian University of Munich in Germany. His research team has generated and measured the first attosecond pulse (physics), light pulse and used it for capturing electrons' motion inside atoms, marking the birth of attophysics. In 2023, jointly with Pierre Agostini and Anne L'Huillier, he was awarded the Nobel Prize in Physics. Academic career From 1981 until 1985 Krausz studied theoretical physics at Eötvös Loránd University and electrical engineering at the Technical University of Budapest in Hungary. From 1987 to 1991 he graduated with a Doctor of Philosophy, PhD at the Technical University of Vienna, in Austria, and from 1991 to 1993 he also did his habilitation there. 1996–1998 he became associate professor, from 1999 until 2004 profess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Spectral Density
In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f 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 any sort of signal (including 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 (PSD, 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 PSD then refers to the spectral energy distribution that would be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Signal
In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components. The real and imaginary parts of an analytic signal are real-valued functions related to each other by the Hilbert transform. The analytic representation of a real-valued function is an ''analytic signal'', comprising the original function and its Hilbert transform. This representation facilitates many mathematical manipulations. The basic idea is that the negative frequency components of the Fourier transform (or spectrum) of a real-valued function are superfluous, due to the Hermitian symmetry of such a spectrum. These negative frequency components can be discarded with no loss of information, provided one is willing to deal with a complex-valued function instead. That makes certain attributes of the function more accessible and facilitates the derivation of modulation and demodulation techniques, such as single-sideband. As long as the manip ... [...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] |
Instantaneous Phase
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a ''complex-valued'' function ''s''(''t''), is the real-valued function: :\varphi(t) = \arg\, where arg is the Argument (complex analysis), complex argument function. The instantaneous frequency is the temporal rate of change of the instantaneous phase. And for a ''real-valued'' function ''s''(''t''), it is determined from the function's analytic signal, analytic representation, ''s''a(''t''): :\begin \varphi(t) &= \arg\ \\[4pt] &= \arg\, \end where \hat(t) represents the Hilbert transform of ''s''(''t''). When ''φ''(''t'') is constrained to its principal value, either the interval or , it is called ''wrapped phase''. Otherwise it is called ''unwrapped phase'', which is a continuous function of argument ''t'', assuming ''s''a(''t' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envelope (waves)
In physics and engineering, the envelope of an oscillating signal is a smooth curve outlining its extremes. The envelope thus generalizes the concept of a constant amplitude into an instantaneous amplitude. The figure illustrates a modulated sine wave varying between an ''upper envelope'' and a ''lower envelope''. The envelope function may be a function of time, space, angle, or indeed of any variable. In beating waves A common situation resulting in an envelope function in both space ''x'' and time ''t'' is the superposition of two waves of almost the same wavelength and frequency: : \begin F(x, \ t) & = \sin \left[ 2 \pi \left( \frac - ( f + \Delta f )t \right) \right] + \sin \left[ 2 \pi \left( \frac - ( f - \Delta f )t \right) \right] \\[6pt] & \approx 2\cos \left[ 2 \pi \left( \frac - \Delta f \ t \right) \right] \ \sin \left[ 2 \pi \left( \frac - f \ t \right) \right] \end which uses the trigonometric formula for the Trigonometric identity#Product-to-sum an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function (mathematics), function of the base form f(x) = \exp (-x^2) and with parametric extension f(x) = a \exp\left( -\frac \right) for arbitrary real number, real constants , and non-zero . It is named after the mathematician Carl Friedrich Gauss. The graph of a function, graph of a Gaussian is a characteristic symmetric "Normal distribution, bell curve" shape. The parameter is the height of the curve's peak, is the position of the center of the peak, and (the standard deviation, sometimes called the Gaussian Root mean square, RMS width) controls the width of the "bell". Gaussian functions are often used to represent the probability density function of a normal distribution, normally distributed random variable with expected value and variance . In this case, the Gaussian is of the form g(x) = \frac \exp\left( -\frac \frac \right). Gaussian functions are widely used in statistics to describ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if x is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), and For example, the absolute value of 3 and the absolute value of −3 is The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. Terminology and notation In 1806, Jean-Robert Argand introduced the term ''module'', meaning ''unit of measure'' in French, specifically for the ''complex'' absolute value,Oxford English Dictionary, Draft Revision, Ju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave
In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a travelling wave; by contrast, a pair of superposition principle, superimposed periodic waves traveling in opposite directions makes a ''standing wave''. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero. There are two types of waves that are most commonly studied in classical physics: mechanical waves and electromagnetic waves. In a mechanical wave, Stress (mechanics), stress and Strain (mechanics), strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (physics), deformation (strain) in some physical medium that propa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Packet
In physics, a wave packet (also known as a wave train or wave group) is a short burst of localized wave action that travels as a unit, outlined by an Envelope (waves), envelope. A wave packet can be analyzed into, or can be synthesized from, a potentially-infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere. Any signal of a limited width in time or space requires many frequency components around a center frequency within a Bandwidth (signal processing), bandwidth inversely proportional to that width; even a gaussian function is considered a wave packet because its Fourier transform is a "packet" of waves of frequencies clustered around a central frequency. Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no #Non-dispe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
