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Vector Soliton
In physical optics or wave optics, a vector soliton is a solitary wave with multiple components coupled together that maintains its shape during propagation. Ordinary solitons maintain their shape but have effectively only one (scalar) polarization component, while vector solitons have two distinct polarization components. Among all the types of solitons, optical vector solitons draw the most attention due to their wide range of applications, particularly in generating ultrafast pulses and light control technology. Optical vector solitons can be classified into temporal vector solitons and spatial vector solitons. During the propagation of both temporal solitons and spatial solitons, despite being in a medium with birefringence, the orthogonal polarizations can copropagate as one unit without splitting due to the strong cross-phase modulation and coherent energy exchange between the two polarizations of the vector soliton which may induce intensity differences between these two pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Optics
In physics, physical optics, or wave optics, is the branch of optics that studies Interference (wave propagation), interference, diffraction, Polarization (waves), polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effects such as quantum noise in optical communication, which is studied in the sub-branch of coherence theory (optics), coherence theory. Principle ''Physical optics'' is also the name of an approximation commonly used in optics, electrical engineering and applied physics. In this context, it is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory. The word "physical" means that it is more physical than geometric or ray (optics), ray optics and not that it is an exact physical theory. This approximation consists of using ray optics to estimate the field on a surface and then integral, integrating that field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillon
In physics, an oscillon is a soliton-like phenomenon that occurs in granular and other dissipative media. Oscillons in granular media result from vertically vibrating a plate with a layer of uniform particles placed freely on top. When the sinusoidal vibrations are of the correct amplitude and frequency and the layer of sufficient thickness, a localized wave, referred to as an oscillon, can be formed by locally disturbing the particles. This meta-stable state will remain for a long time (many hundreds of thousands of oscillations) in the absence of further perturbation. An oscillon changes form with each collision of the grain layer and the plate, switching between a peak that projects above the grain layer to a crater like depression with a small rim. This self-sustaining state was named by analogy with the soliton In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is , in that it preserves its shape while propagating freely, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphene
Graphene () is a carbon allotrope consisting of a Single-layer materials, single layer of atoms arranged in a hexagonal lattice, honeycomb planar nanostructure. The name "graphene" is derived from "graphite" and the suffix -ene, indicating the presence of double bonds within the carbon structure. Graphene is known for its exceptionally high Ultimate tensile strength, tensile strength, Electrical resistivity and conductivity, electrical conductivity, Transparency and translucency, transparency, and being the thinnest two-dimensional material in the world. Despite the nearly transparent nature of a single graphene sheet, graphite (formed from stacked layers of graphene) appears black because it absorbs all visible light wavelengths. On a microscopic scale, graphene is the strongest material ever measured. The existence of graphene was first theorized in 1947 by P. R. Wallace, Philip R. Wallace during his research on graphite's electronic properties, while the term ''graphen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine-Gordon Equation
The sine-Gordon equation is a second-order nonlinear partial differential equation for a function \varphi dependent on two variables typically denoted x and t, involving the wave operator and the sine of \varphi. It was originally introduced by in the course of study of surfaces of constant negative curvature as the Gauss–Codazzi equation for surfaces of constant Gaussian curvature −1 in 3-dimensional space. The equation was rediscovered by in their study of crystal dislocations known as the Frenkel–Kontorova model. This equation attracted a lot of attention in the 1970s due to the presence of soliton solutions, and is an example of an integrable PDE. Among well-known integrable PDEs, the sine-Gordon equation is the only ''relativistic'' system due to its Lorentz invariance. Realizations of the sine-Gordon equation Differential geometry This is the first derivation of the equation, by Bour (1862). There are two equivalent forms of the sine-Gordon equation. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Quantum Number
In physics, a topological quantum number (also called topological charge) is any quantity, in a physical theory, that takes on only one of a discrete set of values, due to topological considerations. Most commonly, topological quantum numbers are topological invariants associated with topological defects or soliton-type solutions of some set of differential equations modeling a physical system, as the solitons themselves owe their stability to topological considerations. The specific "topological considerations" are usually due to the appearance of the fundamental group or a higher-dimensional homotopy group in the description of the problem, quite often because the boundary, on which the boundary conditions are specified, has a non-trivial homotopy group that is preserved by the differential equations. The topological quantum number of a solution is sometimes called the winding number of the solution, or, more precisely, it is the degree of a continuous mapping. The concept of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solitary Wave (other)
In mathematics and physics, a solitary wave can refer to * The solitary wave (water waves) or wave of translation, as observed by John Scott Russell in 1834, the prototype for a soliton. * A soliton, a generalization of the wave of translation to general systems of partial differential equations * A topological defect, a generalization of the idea of a soliton to any system which is stable against decay due to homotopy theory See also *Rogue wave A rogue wave is an abnormally large ocean wave. Rogue wave may also refer to: * Optical rogue waves, are rare pulses of light analogous to rogue or freak ocean waves. * Rogue Wave Software, a software company * Rogue Wave (band), an American in ... {{mathdab zh:孤波 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Soliton
Spatial may refer to: *Dimension *Space *Three-dimensional space In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values ('' coordinates'') are required to determine the position of a point. Most commonly, it is the three- ... * Spatial (platform) See also * * {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soliton Model
The soliton hypothesis in neuroscience is a biological neuron models, model that claims to explain how action potentials are initiated and conducted along axons based on a thermodynamic theory of nerve pulse propagation. It proposes that the signals travel along the cell's cell membrane, membrane in the form of certain kinds of Solitary wave (water waves), solitary sound (or density) pulses that can be modeled as solitons. The model is proposed as an alternative to the Hodgkin–Huxley model in which action potentials: voltage-gated ion channels in the membrane open and allow sodium ions to enter the cell (inward current). The resulting decrease in membrane potential opens nearby voltage-gated sodium channels, thus propagating the action potential. The transmembrane potential is restored by delayed opening of potassium channels. Soliton hypothesis proponents assert that energy is mainly conserved during propagation except dissipation losses; Measured temperature changes are comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soliton (optics)
In optics, the term soliton is used to refer to any optical field that does not change during propagation because of a delicate balance between nonlinear and dispersive effects in the medium. There are two main kinds of solitons: * spatial solitons: the nonlinear effect can balance the dispersion. The electromagnetic field can change the refractive index of the medium while propagating, thus creating a structure similar to a graded-index fiber. If the field is also a propagating mode of the guide it has created, then it will remain confined and it will propagate without changing its shape * temporal solitons: if the electromagnetic field is already spatially confined, it is possible to send pulses that will not change their shape because the nonlinear effects will balance the dispersion. Those solitons were discovered first and they are often simply referred as "solitons" in optics. *Spatial solitons* In order to understand how a spatial soliton can exist, we have to make som ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soliton (topological)
In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in a physical system that are stable against perturbations. Solitons do not decay, dissipate, disperse or evaporate in the way that ordinary waves (or solutions or structures) might. The stability arises from an obstruction to the decay, which is explained by having the soliton belong to a different topological homotopy class or cohomology class than the base physical system. More simply: it is not possible to continuously transform the system with a soliton in it, to one without it. The mathematics behind topological stability is both deep and broad, and a vast variety of systems possessing topological stability have been described. This makes categorization somewhat difficult. Overview The original soliton was observed in the 19th century, as a solitary water wave in a barge canal. It was eventually explained by noting that the K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Q-ball
In theoretical physics, Q-ball is a type of non-topological soliton. A soliton is a localized field configuration that is stable—it cannot spread out and dissipate. In the case of a non-topological soliton, the stability is guaranteed by a conserved charge: the soliton has lower energy per unit charge than any other configuration (in physics, charge is often represented by the letter "Q", and the soliton is spherically symmetric, hence the name). Intuitive explanation A Q-ball arises in a theory of bosonic particles when there is an attraction between the particles. Loosely speaking, the Q-ball is a finite-sized "blob" containing a large number of particles. The blob is stable against fission into smaller blobs and against "evaporation" via emission of individual particles, because, due to the attractive interaction, the blob is the lowest-energy configuration of that number of particles. (This is analogous to the fact that nickel-62 is the most stable nucleus because it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peakon
In the theory of integrable systems, a peakon ("peaked soliton") is a soliton with discontinuous first derivative; the wave profile is shaped like the graph of the function e^. Some examples of non-linear partial differential equations with (multi-)peakon solutions are the Camassa–Holm shallow water wave equation, the Degasperis–Procesi equation and the Fornberg–Whitham equation. Since peakon solutions are only piecewise differentiable, they must be interpreted in a suitable weak sense. The concept was introduced in 1993 by Camassa and Holm in the short but much cited paper where they derived their shallow water equation. A family of equations with peakon solutions The primary example of a PDE which supports peakon solutions is : u_t - u_ + (b+1) u u_x = b u_x u_ + u u_, \, where u(x,t) is the unknown function, and ''b'' is a parameter. In terms of the auxiliary function m(x,t) defined by the relation m = u-u_, the equation takes the simpler form : m_t + m_x u + b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
