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Uniform Theory Of Diffraction
In numerical analysis, the uniform theory of diffraction (UTD) is a high-frequency method for solving electromagnetic scattering problems from electrically small discontinuities or discontinuities in more than one dimension at the same point. UTD is an extension of Joseph Keller's geometrical theory of diffraction (GTD). J. B. Keller"Geometrical theory of diffraction" ''J. Opt. Soc. Am.'', vol. 52, no. 2, pp. 116–130, 1962. The uniform theory of diffraction approximates near field electromagnetic fields as quasi optical and uses knife-edge diffraction to determine diffraction coefficients for each diffracting object-source combination. These coefficients are then used to calculate the field strength and phase for each direction away from the diffracting point. These fields are then added to the incident fields and reflected fields to obtain a total solution. See also * Electromagnetic modeling Computational electromagnetics (CEM), computational electrodynamics or electrom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High Frequency
High frequency (HF) is the ITU designation for the range of radio frequency electromagnetic waves (radio waves) between 3 and 30 megahertz (MHz). It is also known as the decameter band or decameter wave as its wavelengths range from one to ten decameters (ten to one hundred meters). Frequencies immediately below HF are denoted medium frequency (MF), while the next band of higher frequencies is known as the very high frequency (VHF) band. The HF band is a major part of the shortwave band of frequencies, so communication at these frequencies is often called shortwave radio. Because radio waves in this band can be reflected back to Earth by the ionosphere layer in the atmosphere – a method known as "skip" or " skywave" propagation – these frequencies are suitable for long-distance communication across intercontinental distances and for mountainous terrains which prevent line-of-sight communications. The band is used by international shortwave broadcasting stations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, Light, (visible) light, ultraviolet, X-rays, and gamma rays. All of these waves form part of the electromagnetic spectrum. Classical electromagnetism, Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric field, electric and magnetic fields. Depending on the frequency of oscillation, different wavelengths of electromagnetic spectrum are produced. In a vacuum, electromagnetic waves travel at the speed of light, commonly denoted ''c''. In homogeneous, isotropic media, the oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave. The position of an electromagnetic wave w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called ''diffuse reflections'' and unscattered reflections are called ''specular'' (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, a pioneer in light scattering researc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph Keller
Joseph Bishop Keller (July 31, 1923 – September 7, 2016) was an American mathematician who specialized in applied mathematics. He was best known for his work on the "geometrical theory of diffraction" (GTD). Early life and education Born in Paterson, New Jersey on July 31, 1923, Keller attended Eastside High School (Paterson, New Jersey), Eastside High School, where he was a member of the math team. After earning his undergraduate degree in 1943 at New York University, Keller obtained his PhD in 1948 from NYU under the supervision of Richard Courant. He was a Professor of Mathematics in the Courant Institute at New York University until 1979. Then he was Professor of Mathematics and Mechanical Engineering at Stanford University until 1993, when he became professor emeritus. Research Keller worked on the application of mathematics to problems in science and engineering, such as wave propagation. He contributed to the Einstein–Brillouin–Keller method for computing eigen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Near-field Optics
Near-field optics is that branch of optics that considers configurations that depend on the passage of light to, from, through, or near an element with subwavelength features, and the coupling of that light to a second element located a subwavelength distance from the first. The barrier of spatial resolution imposed by the very nature of light itself in conventional optical microscopy contributed significantly to the development of near-field optical devices, most notably the near-field scanning optical microscope, or NSOM. The relatively new optical science of dressed photons (DPs) can also find its origin in near-field optics. Size constraints The limit of optical resolution in a conventional microscope, the so-called diffraction limit, is in the order of half the wavelength of the light used to image. Thus, when imaging at visible wavelengths, the smallest resolvable features are several hundred nanometers in size (although point-like sources, such as quantum dots, can be res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi Optical
Quasioptics concerns the propagation of electromagnetic radiation where the wavelength is comparable to the size of the optical components (e.g. lenses, mirrors, and apertures) and hence diffraction effects may become significant. It commonly describes the propagation of Gaussian beams where the beam width is comparable to the wavelength. This is in contrast to geometrical optics, where the wavelength is small compared to the relevant length scales. Quasioptics is so named because it represents an intermediate regime between conventional optics and electronics, and is often relevant to the description of signals in the far-infrared or terahertz region of the electromagnetic spectrum. It represents a simplified version of the more rigorous treatment of physical optics. Quasi-optical systems may also operate at lower frequencies such as millimeter wave, microwave, and even lower. See also *Optoelectronics Optoelectronics (or optronics) is the study and application of electronic d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knife-edge Diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word ''diffraction'' and was the first to record accurate observations of the phenomenon in 1660. In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The characteristic bending pattern is most pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture that is comparable in size to its wavelength, as shown in the inserted image. This is due to the addition, or interference, of different points on the wavefront (or, equivalently, each wavelet) that travel by paths of diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase (waves)
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or 2\pi as the variable t completes a full period. This convention is especially appropriate for a sinusoidal function, since its value at any argument t then can be expressed as \phi(t), the sine of the phase, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.) Usually, whole turns are ignored when expressing the phase; so that \phi(t) is also a periodic function, with the same period as F, that repeatedly scans the same range of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Modeling
Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment. It typically involves using computer programs to compute approximate solutions to Maxwell's equations to calculate antenna performance, electromagnetic compatibility, radar cross section and electromagnetic wave propagation when not in free space. A large subfield is ''antenna modeling'' computer programs, which calculate the radiation pattern and electrical properties of radio antennas, and are widely used to design antennas for specific applications. Background Several real-world electromagnetic problems like electromagnetic scattering, electromagnetic radiation, modeling of waveguides etc., are not analytically calculable, for the multitude of irregular geometries found in actual devices. Computational numerical techniques can overcome the inability to derive closed f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biot–Tolstoy–Medwin Diffraction Model
In applied mathematics, the Biot–Tolstoy–Medwin (BTM) diffraction model describes edge diffraction. Unlike the uniform theory of diffraction (UTD), BTM does not make the high frequency assumption (in which edge lengths and distances from source and receiver are much larger than the wavelength). BTM sees use in acoustic simulations. Impulse response The impulse response according to BTM is given as follows:Calamia 2007, p. 183. The general expression for sound pressure is given by the convolution integral : p(t) = \int_0^\infty h(\tau) q (t - \tau) \, d \tau where q(t) represents the source signal, and h(t) represents the impulse response at the receiver position. The BTM gives the latter in terms of * the source position in cylindrical coordinates ( r_S, \theta_S, z_S ) where the z-axis is considered to lie on the edge and \theta is measured from one of the faces of the wedge. * the receiver position ( r_R, \theta_R, z_R ) * the (outer) wedge angle \theta_W and from th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Differential Equations
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Numerical may refer to: * Number * Numerical digit * Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
