electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength...
15 KB (1,864 words) - 17:22, 10 October 2023
relationship: the frequency dispersion relation ω 2 = Ω 2 ( k ) . {\displaystyle \omega ^{2}=\Omega ^{2}(k).\,} The dispersion relation has two solutions: ω = +Ω(k)...
30 KB (3,374 words) - 02:45, 29 May 2024
Phonon polariton (section Dispersion relation)
transverse optical phonons, this is due to the particular form of the dispersion relation of the phonon and photon and their interaction. Photons consist of...
18 KB (2,527 words) - 18:25, 12 October 2024
In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called...
27 KB (4,096 words) - 21:45, 23 August 2024
Capillary wave (section Dispersion relation)
result from coalescence of smaller wind-caused ripple-waves. The dispersion relation describes the relationship between wavelength and frequency in waves...
18 KB (1,434 words) - 19:37, 16 August 2024
general, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for...
33 KB (3,428 words) - 21:30, 13 October 2024
A nonlinear dispersion relation (NDR) is a dispersion relation that assigns the correct phase velocity v 0 {\displaystyle v_{0}} to a nonlinear wave structure...
9 KB (1,688 words) - 08:28, 15 July 2024
Density of states (section Dispersion relations)
DOS as a function of the wave vector, the system-specific energy dispersion relation between E and k must be known. In general, the topological properties...
36 KB (5,578 words) - 07:50, 15 October 2024
wavelength: Dispersion (optics), for light waves Dispersion (water waves), for water waves Acoustic dispersion, for sound waves Dispersion relation, the mathematical...
3 KB (422 words) - 16:58, 29 October 2023
Phonon (section Dispersion relation)
of the acoustic dispersion relation, ∂ωk/∂k (see group velocity.) At low values of k (i.e. long wavelengths), the dispersion relation is almost linear...
47 KB (6,913 words) - 21:30, 12 October 2024
Surface plasmon (section Dispersion relation)
the dispersion relation (relation between frequency and wavevector) is the same as in free space. At a higher frequency, the dispersion relation bends...
13 KB (1,394 words) - 11:55, 18 May 2024
Smith–Purcell effect (section Dispersion relation)
Coulomb field of the induced charges at the grating boundaries. The dispersion relation for the Smith–Purcell effect (SPE) is given as follows: λ = L n (...
6 KB (810 words) - 17:34, 29 November 2023
Effective mass (solid-state physics) (section Simple case: parabolic, isotropic dispersion relation)
empirically measured parameter, carrier mobility. In general the dispersion relation cannot be approximated as parabolic, and in such cases the effective...
26 KB (3,717 words) - 20:05, 25 March 2024
identical, as both are examples of a massless Bose gas with a linear dispersion relation. For a cube of side-length L {\displaystyle L} , the resonating modes...
47 KB (9,148 words) - 14:58, 4 October 2024
Ion acoustic wave (section Dispersion relation)
in the numerator can be ignored. We derive the ion acoustic wave dispersion relation for a linearized fluid description of a plasma with electrons and...
10 KB (2,461 words) - 13:07, 27 November 2023
ω = 2πf. In all media, frequency and wavevector are related by a dispersion relation, ω = ω(k), and the group velocity can be written: v g = d ω ( k )...
14 KB (1,840 words) - 22:18, 15 July 2024
Clavin–Garcia equation (redirect from Clavin–Garcia dispersion relation)
Clavin–Garcia equation or Clavin–Garcia dispersion relation provides the relation between the growth rate and the wave number of the perturbation superposed...
4 KB (632 words) - 20:42, 17 July 2024
Magnetosonic wave (section Dispersion relation)
The fast and slow magnetosonic waves are defined by a bi-quadratic dispersion relation that can be derived from the linearized MHD equations. Derivation...
14 KB (2,191 words) - 07:27, 22 June 2024
free-space. The dispersion relation is plotted in Figure 3. At low k, the SPP behaves like a photon, but as k increases, the dispersion relation bends over...
39 KB (5,101 words) - 20:23, 15 August 2024
pressure gradient) a type of wave, named Langmuir wave, is excited. The dispersion relation is: ω 2 = ω p e 2 + 3 C e 2 k 2 {\displaystyle \omega ^{2}=\omega...
8 KB (1,336 words) - 23:23, 29 June 2024
§ Proof of the general case for a proof of this relation). An example assuming a parabolic dispersion relation for the density of states and the Maxwell–Boltzmann...
14 KB (1,938 words) - 06:03, 12 January 2024
Wave equation (section Dispersion relation)
varies with the wavelength of the wave, which is reflected by a dispersion relation ω = ω ( k ) , {\displaystyle \omega =\omega (\mathbf {k} ),} where...
60 KB (10,757 words) - 16:20, 20 September 2024
Graphene (section Dispersion relation)
phonon modes: two linear dispersion relation dispersion relation in-plane modes (LA, TA) and one quadratic dispersion relation out-of-plane mode (ZA)....
265 KB (27,761 words) - 02:47, 15 October 2024
Group velocity (section Dispersion)
function ω(k), which gives ω as a function of k, is known as the dispersion relation. If ω is directly proportional to k, then the group velocity is exactly...
25 KB (3,501 words) - 11:31, 17 September 2024
Kramers–Kronig relations (redirect from Kramers-Krönig relation)
data. Dispersion (optics) Linear response function Numerical analytic continuation John S. Toll (1956). "Causality and the Dispersion Relation: Logical...
23 KB (3,018 words) - 13:18, 9 July 2024
Faber–Jackson relation provided the first empirical power-law relation between the luminosity L {\displaystyle L} and the central stellar velocity dispersion σ {\displaystyle...
6 KB (938 words) - 16:12, 21 August 2024
Slow light (section Material dispersion)
dispersion, i.e., peaks in the dispersion relation. Schemes are generally grouped into two categories: material dispersion and waveguide dispersion....
20 KB (2,496 words) - 16:22, 3 October 2024
both the linear dispersion relation of photons and constant dispersion of charge waves by the avoided crossing between the two dispersion lines of polaritons...
5 KB (1,172 words) - 14:57, 8 October 2024
follows. The dispersion relation determines how electrons respond to forces (via the concept of effective mass). A dispersion relation is the relationship...
15 KB (1,956 words) - 19:26, 9 February 2024
π-band approximation, using a conventional tight-binding model, the dispersion relation (restricted to first-nearest-neighbor interactions only) that produces...
44 KB (5,083 words) - 23:14, 4 August 2024