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For electromagnetic waves in vacuum, the angular frequency is proportional to the wavenumber: =. This is a linear dispersion relation, in which case the waves are said to be non-dispersive. [1] That is, the phase velocity and the group velocity are the same:
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
A. R. Forouhi and I. Bloomer deduced dispersion equations for the refractive index, n, and extinction coefficient, k, which were published in 1986 [1] and 1988. [2] The 1986 publication relates to amorphous materials, while the 1988 publication relates to crystalline.
The dispersion relation is: ω 2 = ω p e 2 + 3 C e 2 k 2 {\displaystyle \omega ^{2}=\omega _{pe}^{2}+3C_{e}^{2}k^{2}} The first term on the right-hand side of the dispersion relation is the electron plasma oscillation related to the electric field force and the second term is related to the thermal motion of the electrons, where C e is the ...
In physics, electromagnetic radiation (EMR) is the set of waves of an electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. [ 1 ] [ 2 ] Classically , electromagnetic radiation consists of electromagnetic waves , which are synchronized oscillations of electric and magnetic fields .
The ratio between the speed of light c and the phase velocity v p is known as the refractive index, n = c / v p = ck / ω. In this way, we can obtain another form for group velocity for electromagnetics. Writing n = n(ω), a quick way to derive this form is to observe
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.