Dispersion relations


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Dispersion relations

Relations between the real and imaginary parts of a response function. A response function relates a cause and its effect through an integral equation. The term dispersion refers to the fact that the index of refraction of a medium is a function of frequency. In 1926 H. A. Kramers and R. Kronig showed that the imaginary part of an index of refraction (that is, the absorptivity) determines the real part (that is, the refractivity); this is called the Kramers-Kronig relation. The term dispersion relation is now used for the analogous relation between the real and imaginary parts of the values of any response function.

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
This study adopts the approach of immersed plate for acquiring dispersion relations for three-dimensional waveguide of rectangular cross-section immersed in perfect fluid using SAFE procedure.
Caption: Figure 2: Dispersion relations [omega](q) of Cu and Ni calculated using the present theory compared to the experimental values (Expt.) [23].
DSR type theories predict a modified dispersion relation compared to usual dispersion relation of special relativity.
Two dispersion relations (9) and (25) are transcendent equations in which the wave frequency, [omega], is a complex quantity: Re([omega]) + Im([omega]), while the axial wave number, [k.sub.z], is a real variable.
For Figure 1, with wave vectors [[bar.k].sup.i.sup.TE] = [??][k.sup.TE.sub.0x] + [??][k.sup.TE.sub.y] (incident) and [[bar.k].sub.r.sup.TE] = [??][k.sup.TE.sub.0x] + [??][k.sup.TE.sub.y] (reflection) in the isotropic medium and [[bar.k].sub.t.sup.TE] = [??][k.sup.TE.sub.tx] (transmission) in the biaxial anisotropic medium, the dispersion relations can be expressed as
5.1 Dispersion relation for case of electrically open circuit
In this paper, wave dispersion relations of single anisotropic layer were presented.
Implementation of this ultimately leads to the evolution of a set of four homogeneous equations, followed by the dispersion relation (as obtained by collecting the coefficients of unknown constants) given as
The calculated lattice constant, bulk modulus, magnetic moment, electronic band structure, Fermi surface, and phonon dispersion relations are discussed in Section 3.
Depine, "Uniaxial dielectric media with hyperbolic dispersion relations," Microwave Opt.