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Anapole
In physics, an anapole () is a system of currents that does not radiate into the far field. The term "anapole" first appeared in the work of Zel'dovich, in which he thanks A. S. Kompaneets, who first proposed the name. An anapole is a system of currents that transforms under all transformations of the symmetry group O(3) as a certain multipole (or the corresponding vector spherical harmonic), but does not radiate to the far field. Photonics In photonics, anapoles first appeared in 2015 as zeros in the Mie-coefficient of a particular multipole in the scattering spectrum. They can also be explained as destructive interference of a "cartesian multipole" and a " toroidal multipole". The anapole state is not an eigenmode. Total scattering cross-section is not zero in the anapole state, due to the contribution of other multipoles. The terms "anapole" and toroidal moment were once used synonymously,Popov, A. I., D. I. Plokhov, and A. K. Zvezdin. "Anapole moment and spin-electric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toroidal Moment
In electromagnetism, a toroidal moment is an independent term in the multipole expansion of the electromagnetic field which is distinct from magnetic and electric multipoles. In the electrostatic multipole expansion, all charge and current distributions can be expanded into a complete set of electric and magnetic multipole coefficients. However, additional terms arise in an electrodynamic multipole expansion. The coefficients of these terms are given by the toroidal multipole moments as well as time derivatives of the electric and magnetic multipole moments. While electric dipoles can be understood as separated charges and magnetic dipoles as circular currents, axial (or electric) toroidal dipoles describe toroidal (donut-shaped) charge arrangements whereas a polar (or magnetic) toroidal dipole (also called an anapole) corresponds to the field of a solenoid bent into a torus. Classical toroidal dipole moment A complex expression allows the current density J to be written as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Current
An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge carriers, which may be one of several types of particles, depending on the Electrical conductor, conductor. In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or Electron hole, holes. In an Electrolyte#Electrochemistry, electrolyte the charge carriers are ions, while in Plasma (physics), plasma, an Ionization, ionized gas, they are ions and electrons. In the International System of Units (SI), electric current is expressed in Unit of measurement, units of ampere (sometimes called an "amp", symbol A), which is equivalent to one coulomb per second. The ampere is an SI base unit and electric current is a ISQ base quantity, base quantity in the International System of Qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Near And Far Field
The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative ''near-field'' behaviors dominate close to the antenna or scatterer, while electromagnetic radiation ''far-field'' behaviors predominate at greater distances. Far-field (electric) and (magnetic) radiation field strengths decrease as the distance from the source increases, resulting in an inverse-square law for the '' power'' intensity of electromagnetic radiation in the transmitted signal. By contrast, the near-fields and strengths decrease more rapidly with distance: The radiative field decreases by the inverse-distance squared, the reactive field by an inverse-''cube'' law, resulting in a diminished power in the parts of the electric field by an inverse fourth-power and sixth-power, respectively. The rapid drop in power contained in the near-field ensures that effects due to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yakov Zeldovich
Yakov Borisovich Zeldovich (, ; 8 March 1914 – 2 December 1987), also known as YaB, was a leading Soviet people, Soviet Physics, physicist of Belarusians, Belarusian origin, who is known for his prolific contributions in physical Physical cosmology, cosmology, physics of Plasma physics, thermonuclear reactions, combustion, and Fluid dynamics, hydrodynamical phenomena. From 1943, Zeldovich, a self-taught physicist, started his career by playing a crucial role in the development of the former Soviet atomic bomb project, Soviet program of nuclear weapons. In 1963, he returned to academia to embark on pioneering contributions on the fundamental understanding of the Black hole thermodynamics, thermodynamics of black holes and expanding the scope of physical cosmology. Biography Early life and education Yakov Zeldovich was born into a History of the Jews in Belarus, Belarusian Jewish family in his grandfather's house in Minsk. However, in mid-1914, the Zeldovich family moved to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Kompaneyets
Alexander Solomonovich Kompaneyets (Russian: Александр Соломонович Компанеец) was born on January 4, 1914, in Ekaterinoslav, Russian Empire (now Dnipro, Ukraine) and died on August 19, 1974, in Palanga, Lithuania. He was a prominent physicist, author of a number of textbooks, and collaborator on the Soviet atomic bomb project who lived mainly in Moscow. Life Kompaneyets was a student of Lev Landau in Kharkiv in the 1930s, where he dealt with solid state physics (electrical conductivity in metals and semiconductors). In 1936 he received his doctorate (candidate title) and habilitated in 1939 (Russian doctorate). He was a professor at the Institute of Chemical Physics at the Russian Academy of Sciences in Moscow (where he worked from 1946 until the end of his life) and is best known for his introductory textbook on theoretical physics. He also dealt with the physics of detonation, which he wrote about in a book with Yakov Zeldovich, and generally about ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Group
In mathematics, the orthogonal group in dimension , denoted , is the Group (mathematics), group of isometry, distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by Function composition, composing transformations. The orthogonal group is sometimes called the general orthogonal group, by analogy with the general linear group. Equivalently, it is the group of orthogonal matrix, orthogonal matrices, where the group operation is given by matrix multiplication (an orthogonal matrix is a real matrix whose invertible matrix, inverse equals its transpose). The orthogonal group is an algebraic group and a Lie group. It is compact group, compact. The orthogonal group in dimension has two connected component (topology), connected components. The one that contains the identity element is a normal subgroup, called the special orthogonal group, and denoted . It consists of all orthogonal matrices of determinant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multipole
A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, \R^3. Multipole expansions are useful because, similar to Taylor series, oftentimes only the first few terms are needed to provide a good approximation of the original function. The function being expanded may be real- or complex-valued and is defined either on \R^3, or less often on \R^n for some other Multipole expansions are used frequently in the study of electromagnetic and gravitational fields, where the fields at distant points are given in terms of sources in a small region. The multipole expansion with angles is often combined with an expansion in radius. Such a combination gives an expansion describing a function throughout three-dimensional space. The multipole expansion is expressed as a sum of terms with progressively finer angular featu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Spherical Harmonics
In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields. The components of the VSH are complex-valued functions expressed in the spherical coordinate basis vectors. Definition Several conventions have been used to define the VSH. We follow that of Barrera ''et al.''. Given a scalar spherical harmonic , we define three VSH: * \mathbf_ = Y_\hat, * \mathbf_ = r\nabla Y_, * \mathbf_ = \mathbf\times\nabla Y_, with \hat being the unit vector along the radial direction in spherical coordinates and \mathbf the vector along the radial direction with the same norm as the radius, i.e., \mathbf = r\hat. The radial factors are included to guarantee that the dimensions of the VSH are the same as those of the ordinary spherical harmonics and that the VSH do not depend on the radial spherical coordinate. The interest of these new vector fields is to separate the radial dependence from the angular one when using spherical c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mie Theory
In electromagnetism, the Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the form of an infinite series of Vector spherical harmonics, spherical multipole partial waves. It is named after German physicist Gustav Mie. The term ''Mie solution'' is also used for solutions of Maxwell's equations for scattering by stratified spheres or by infinite cylinders, or other geometries where one can write separation of variables, separate equations for the radial and angular dependence of solutions. The term ''Mie theory'' is sometimes used for this collection of solutions and methods; it does not refer to an independent physical theory or law. More broadly, the "Mie scattering" formulas are most useful in situations where the size of the scattering particles is comparable to the wavelength of the light, rather ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
