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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, Finite element method, FEM and the beam propagation method for the modelling of Waveguide (optics), 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 rigorous 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 wave ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FDTD
Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to the associated system of differential equations). Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way. The FDTD method belongs in the general class of grid-based differential numerical modeling methods ( finite difference methods). The time-dependent Maxwell's equations (in partial differential form) are discretized using central-difference approximations to the space and time partial derivatives. The resulting finite-difference equations are solved in either software or hardware in a leapfrog manner: the electric field vector components in a volume of space are solved at a given instant in time; then the magnetic fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beam Propagation Method
The beam propagation method (BPM) is an approximation technique for simulating the propagation of light in slowly varying optical waveguides. It is essentially the same as the so-called parabolic equation (PE) method in underwater acoustics. Both BPM and the PE were first introduced in the 1970s. When a wave propagates along a waveguide for a large distance (larger compared with the wavelength), rigorous numerical simulation is difficult. The BPM relies on approximate differential equations which are also called the one-way models. These one-way models involve only a first order derivative in the variable z (for the waveguide axis) and they can be solved as "initial" value problem. The "initial" value problem does not involve time, rather it is for the spatial variable z. The original BPM and PE were derived from the slowly varying envelope approximation and they are the so-called paraxial one-way models. Since then, a number of improved one-way models are introduced. They come f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waveguide (optics)
An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber waveguides, transparent dielectric waveguides made of plastic and glass, liquid light guides, and liquid waveguides. Optical waveguides are used as components in integrated optical circuits or as the transmission medium in local and long-haul optical communication systems. Optical waveguides can be classified according to their geometry (planar, strip, or fiber waveguides), mode structure (single-mode optical fiber, single-mode, multi-mode optical fiber, multi-mode), refractive index distribution (step or gradient index), and material (glass, polymer, semiconductor). Total internal reflection The basic principles behind optical waveguides can be described using the concepts of geometrical optics, geometrical or ray optics, as illustrated in the diagram. Light passing into a medium with higher refractive index bends towa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenmodes
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 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 state of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell's Equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields.''Electric'' and ''magnetic'' fields, according to the theory of relativity, are the components of a single electromagnetic field. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon. The modern form of the equations in their most common formul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-matrix
In physics, the ''S''-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the ''S''-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the ''in-states'' and the ''out-states'') in the Hilbert space of physical states. A multi-particle state is said to be ''free'' (non-interacting) if it transforms under Lorentz transformations as a tensor product, or ''direct product'' in physics parlance, of ''one-particle states'' as prescribed by equation below. ''Asymptotically free'' then means that the state has this appearance in either the distant past or the distant future. While the ''S''-matrix may be defined for any background (spacetime) that is asymptotically solvable and has no event horizons, it has a simple form in the case of the Minkowsk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, , where ''θ''1 and ''θ''2 are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices ''n''1 and ''n''2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity ( Fresnel's equations) and Brewster's angle. The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that medium is , where ''Π... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slowly Varying Envelope Approximation
In physics, slowly varying envelope approximation (SVEA, sometimes also called slowly varying asymmetric approximation or SVAA) is the assumption that the envelope of a forward-travelling wave pulse varies slowly in time and space compared to a period or wavelength. This requires the spectrum of the signal to be narrow-banded—hence it also referred to as the narrow-band approximation. The slowly varying envelope approximation is often used because the resulting equations are in many cases easier to solve than the original equations, reducing the order of—all or some of—the highest-order partial derivatives. But the validity of the assumptions which are made need to be justified. Example For example, consider the electromagnetic wave equation: :\nabla^2 E - \mu_0\, \varepsilon_0\, \frac = 0. If k0 and ''ω''0 are the wave number and angular frequency of the (characteristic) carrier wave for the signal ''E''(r,''t''), the following representation is useful: :E(\mathbf,t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Electromagnetics
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] |
Electrodynamics
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electricity and magnetism, two distinct but closely intertwined phenomena. In essence, electric forces occur between any two charged particles, causing an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs exclusively between ''moving'' charged particles. These two effects combine to create electromagnetic fields in the vicinity of charge particles, which can exert influence on other particles via the Lorentz force. At high energy, the weak force and electromagnetic force are unified as a single electroweak force. The electromagnetic force is responsible for many o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
