Over time the account of how the Kramers–Kronig (dispersion) relations between the real and imaginary parts of response functions were derived in 1926 and 1927 has been transmogrified into anecdotes about what might have been done but was not. Although Kramers obtained both members of a pair of relations, Kronig obtained only one. Both authors appealed to specific models of an atomic gas rather...

We review the consequence of the causality in electrodynamics. The Kramers-Kronig relations are direct consequence of causality which has two ingredients: no perturbation in the remote past and irrelevance of future susceptibility to the present field. It is shown that the dielectric function obtained from the integration along the Landau contour can be derived from the Kramers-Kronig relations...

The theory of optical properties of nanoparticles is considered with the aid of dispersion relations, which are based on the Kramers-Kronig analysis. It is shown that one can utilize rather general dispersion relations, which hold for liquid matrices that contain nanoparticles. Wiener bounds incorporating the Kramers-Kronig analysis are utilized in assessment of the complex permittivity of a na...

The development of different forms of measurement models for impedance has allowed examination of key assumptions on which the use of such models to assess error structure are based. The stochastic error structures obtained using the transfer-function and Voigt measurement models were identical, even when non-stationary phenomena caused some of the data to be inconsistent with the Kramers–Kroni...

The Kramers-Kronig equations and the current methods used to apply them to electrochemical impedance spectra are reviewed. Measurement models are introduced as 'a tool for identification of the frequency-dependent error structure of impedance data and for evaluating the consistency of the data with the Kramers-Kronig relations. Through the use of a measurement model, experimental data can be ch...

We review dispersion relations, which relate the real part of the optical susceptibility (refraction) to the imaginary part (absorption). We derive and discuss these relations as applied to nonlinear optical systems. It is shown that in the nonlinear case, for self-action effects the correct form for such dispersion relations is nondegenerate, i.e. it is necessary to use multiple frequency argu...

The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exists Kramers-Kronig relations f...

Because direct measurements of the refractive index of hemoglobin over a large wavelength range are challenging, indirect methods deserve particular attention. Among them, the Kramers-Kronig relations are a powerful tool often used to derive the real part of a refractive index from its imaginary part. However, previous attempts to apply the relations to solutions of human hemoglobin have been s...