Kramers-Kronig dispersion relations

From these relations we see that the width and shift of the power spectrum and consequently the spectroscopic lines are related through the Kronig-Kramers dispersion relations. Exactly the same arguments apply to the Laplace transform of the time-correlation function, H(/co). The real and imaginary parts, C H(co) and C"//(/(0), are related by Kramers-Kronig dispersion relation. 

The Kramers-Kronig dispersion relations between the real and imaginary parts of the dielectric permittivity can be written as follows [11] ... 

It is also shown how x(< ) is related to the temporal behaviour of the dielectric polarization follomng the sudden application, or removal, of an electric field. Various forms of the Kramers-Kronig dispersion relations are introduced for y (o>) and x C") aod for a number of functions of The section closes with the ddOnition of the frequency-dependent complex refractive index n() = n(cu) — and a discussion of its relation... 

One may deduce from equation (32) the well-known Kramers-Kronig dispersion relations which may be written in the following form ... 

This equation effectively connects the alternating and after-effect solutions provided the response is linear. We may now make use of the Kramers-Kronig dispersion relations [66,67] to rewrite equations (C.ll) and (C.12) as... 

Scattering theory has very general validity. It is based on the existence of a Schrodinger-type equation and is consistent with causality requirements through the Kramers-Kronig dispersion relations. It is widely used outside atomic physics for the description of all resonance phenomena. There is therefore some advantage in using it in atomic physics it ensures unification and is more transparent to reseachers from other fields. 

K. Krishnan, Applications of the Kramers-Kronig Dispersion Relations to the Analysis of FTIR Specular Reflectance Spectra, Fl lR/IR Notes 51, Biorad Digilab Division, Cambridge, MA, August 1987. 

Polarization and absorption are interconnected by the Kramers-Kronig dispersion relation (cf. e.g. Tauc (1965))... 

The equations (3.36a) and (3.37) are the Kramers-Kronig dispersion relations. They relate absorption and dispersion through the complex refractive index n =n — k =n — ia/(2ko). 

Actually, the real part a u) and the imaginary part a"(a ) are not independent, but related by the Kramers-Kronig dispersion relations . These have the following forms... 

The absorption coefficient a(w) and the refractive index n(w) are related by the Kramers-Kronig dispersion relation, see (3.36b, 37b) in Sect. 3.1. 

One can demonstrate that causaUty implies that the real x jg k, oj) and imaginary x gik, co) parts of the linear susceptibiUty XAS k, (d) are coimected by the Kramers-Kronig dispersion relations... 

Therefore, by determining the phase change 8[2 upon reflection, the optical constants can be calculated. Since phase angle and reflectivity are related to each other by the Kramers-Kronig dispersion relation... 

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