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The term is also used, even more specifically, to mean a "monochromatic" or sinusoidal plane wave: a travelling plane wave whose profile () is a sinusoidal function. That is, (,) = (() +) The parameter , which may be a scalar or a vector, is called the amplitude of the wave; the scalar coefficient is its "spatial frequency"; and the scalar is its "phase shift".
Sinusoidal plane wave. In physics, a sinusoidal plane wave is a special case of plane wave: a field whose value varies as a sinusoidal function of time and of the distance from some fixed plane. It is also called a monochromatic plane wave, with constant frequency (as in monochromatic radiation).
Wave equation. The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
The plane sinusoidal solution for an electromagnetic wave traveling in the z direction is for the electric field and for the magnetic field, where k is the wavenumber, is the angular frequency of the wave, and is the speed of light. The hats on the vectors indicate unit vectors in the x, y, and z directions. r = (x, y, z) is the position vector ...
The plane wave spectrum representation of a general electromagnetic field (e.g., a spherical wave) in the equation is the basic foundation of Fourier optics (this point cannot be emphasized strongly enough), because at z = 0, the equation simply becomes a Fourier transform (FT) relationship between the field and its plane wave contents (hence ...
For example, if the wave propagation is in the z-direction, both the electric field and the magnetic field lie in the xy-plane. The electric field points in a specific direction in space since it is a vector. The direction of an electromagnetic wave's electric field vector E is referred to as polarization. If the electric field oscillates in ...
The Poynting vector for a wave is a vector whose component in any direction is the irradiance (power per unit area) of that wave on a surface perpendicular to that direction. For a plane sinusoidal wave the Poynting vector is 1 / 2 Re{E × H ∗}, where E and H are due only to the wave in question, and the asterisk denotes ...
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, electric and magnetic circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such ...