|
Mode (electromagnetism)
The mode of electromagnetic systems describes the field pattern of the propagating waves. Some of the classifications of electromagnetic modes include; * Modes in waveguides and transmission lines. These modes are analogous to the normal modes of vibration in mechanical systems. ** Transverse modes, modes that have at least one of the electric field and magnetic field entirely in a transverse direction. *** Transverse electromagnetic mode (TEM), as with a free space plane wave, both the electric field and magnetic field are entirely transverse. *** Transverse electric (TE) modes, only the electric field is entirely transverse. Also notated as H modes to indicate there is a longitudinal magnetic component. *** Transverse magnetic (TM) modes, only the magnetic field is entirely transverse. Also notated as E modes to indicate there is a longitudinal electric component. ** Hybrid electromagnetic (HEM) modes, both the electric and magnetic fields have a component in the longitudinal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, which are distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles. Electric forces cause an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs between charged particles in relative motion. These two forces are described in terms of electromagnetic fields. Macroscopic charged objects are described in terms of Coulomb's law for electricity and Ampère's force law for magnetism; the Lorentz force describes microscopic charged particles. The electromagnetic force is responsible for ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Mode
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. The most general motion of a linear system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other. General definitions Mode In the wave theory of physics and engineering, a mode in a dynamical system is a standing wave st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transverse Mode
A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and microwaves confined to a waveguide, and also in light waves in an optical fiber and in a laser's optical resonator. Transverse modes occur because of boundary conditions imposed on the wave by the waveguide. For example, a radio wave in a hollow metal waveguide must have zero tangential electric field amplitude at the walls of the waveguide, so the transverse pattern of the electric field of waves is restricted to those that fit between the walls. For this reason, the modes supported by a waveguide are quantized. The allowed modes can be found by solving Maxwell's equations for the boundary conditions of a given waveguide. Types of modes Unguided electromagnetic waves in free space, or in a bulk isotropic dielectric, can be described as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superposition Principle
The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input ''A'' produces response ''X'', and input ''B'' produces response ''Y'', then input (''A'' + ''B'') produces response (''X'' + ''Y''). A function F(x) that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties: additivity F(x_1 + x_2) = F(x_1) + F(x_2) and homogeneity F(ax) = a F(x) for scalar . This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Longitudinal-section Mode
Longitudinal-section modes are a set of a particular kind of electromagnetic transmission modes found in some types of transmission line. They are a subset of hybrid electromagnetic modes (HEM modes). HEM modes are those modes that have both an electric field and a magnetic field component longitudinally in the direction of travel of the propagating wave. Longitudinal-section modes, additionally, have a component of either magnetic or electric field that is zero in one transverse direction. In longitudinal-section electric (LSE) modes this field component is electric. In longitudinal-section magnetic (LSM) modes the zero field component is magnetic. Hybrid modes are to be compared to transverse modes which have, at most, only one component of either electric or magnetic field in the longitudinal direction. Derivation and notation There is an analogy between the way transverse modes (TE and TM modes) are arrived at and the definition of longitudinal section modes (LSE and LS ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenfunctions
In mathematics, an eigenfunction of a linear map, linear operator ''D'' defined on some function space is any non-zero function (mathematics), function f in that space that, when acted upon by ''D'', is only multiplied by some scaling factor called an eigenvalues and eigenvectors, eigenvalue. As an equation, this condition can be written as Df = \lambda f for some scalar (mathematics), scalar eigenvalue \lambda. The solutions to this equation may also be subject to Boundary value problem#boundary value conditions, boundary conditions that limit the allowable eigenvalues and eigenfunctions. An eigenfunction is a type of eigenvalues and eigenvectors, eigenvector. Eigenfunctions In general, an eigenvector of a linear operator ''D'' defined on some vector space is a nonzero vector in the domain of ''D'' that, when ''D'' acts upon it, is simply scaled by some scalar value called an eigenvalue. In the special case where ''D'' is defined on a function space, the eigenvectors are referred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenmode Expansion
Eigenmode expansion (EME) is a computational electrodynamics modelling technique. It is also referred to as the mode matching technique or the bidirectional eigenmode propagation method (BEP method). Eigenmode expansion is a linear frequency-domain method. It offers very strong benefits compared with FDTD, FEM and the beam propagation method for the modelling of optical waveguides, and it is a popular tool for the modelling linear effects in fiber optics and silicon photonics devices. Principles of the EME method Eigenmode expansion is a technique to simulate electromagnetic propagation which relies on the decomposition of the electromagnetic fields into a basis set of local eigenmodes that exists in the cross section of the device. The eigenmodes are found by solving Maxwell's equations in each local cross-section. The method can be fully vectorial provided that the mode solvers themselves are fully vectorial. In a typical waveguide, there are a few guided modes (which pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bloch Wave
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem is named after the Swiss physicist Felix Bloch, who discovered the theorem in 1929. Mathematically, they are written where \mathbf is position, \psi is the wave function, u is a periodic function with the same periodicity as the crystal, the wave vector \mathbf is the crystal momentum vector, e is Euler's number, and i is the imaginary unit. Functions of this form are known as Bloch functions or Bloch states, and serve as a suitable basis for the wave functions or states of electrons in crystalline solids. The description of electrons in terms of Bloch functions, termed Bloch electrons (or less often ''Bloch Waves''), underlies the concept of electronic band structures. These eigenstates are written with subscripts as \psi_, where n is a discrete index, called the band index, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Mechanics
Wave mechanics may refer to: * the mechanics of waves * the application of the quantum wave equation, especially in position and momentum spaces * the resonant interaction of three or more waves, which includes the "three-wave equation" See also * Quantum mechanics * Wave equation * Quantum state * Matter wave Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffract ... Further reading * Flint H.T., (1929) ''Wave Mechanics,'' Methuen & Co. Ltd, London {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Radiation
In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ranging from radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. All forms of EMR travel at the speed of light in a vacuum and exhibit wave–particle duality, behaving both as waves and as discrete particles called photons. Electromagnetic radiation is produced by accelerating charged particles such as from the Sun and other celestial bodies or artificially generated for various applications. Its interaction with matter depends on wavelength, influencing its uses in communication, medicine, industry, and scientific research. Radio waves enable broadcasting and wireless communication, infrared is used in thermal imaging, visible light is essential for vision, and higher-energy radiation, such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
