Related papers: Numerical Approximation of Kramers-Kronig Relation…
The principle of causality leads to linear Kramers-Kronig relations (KKR) that relate the real and imaginary parts of the complex modulus $G^{*}$ through integral transforms. Using the multiple integral generalization of the Boltzmann…
A complex-analytic structure within the unit disk of the complex plane is presented. It can be used to represent and analyze a large class of real functions. It is shown that any integrable real function can be obtained by means of the…
We have developed a conceptually new type of ellipsometry which allows the determination of the complex refractive index by simultaneously measuring the unpolarized normal-incidence reflectivity relative to the vacuum and to another…
We introduce a systematic approach that enables two robust methods for performing terahertz time-domain spectroscopy in reflection geometry. Using the Kramers-Kronig relations in connection to accurate experimental measurements of the…
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…
The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for sub-micron separations.…
Kramers-Kronig (KK) analysis has been widely used to extract the optical conductivity spectrum from a broad range of reflectance spectrum obtained from far-infrared to ultraviolet frequency ranges. In this study, we present how measurement…
Past work has considered the analytic properties of the reflection coefficient for a metal-backed slab. The primary result established a fundamental relationship for the minimal layer thickness to bandwidth ratio achievable for an absorber.…
The Krein transform is the real counterpart of the Cayley transform and gives a one-to-one correspondence between the positive relations and symmetric contractions. It is treated with a slight variation of the usual one, resulting in an…
Metamorphic testing is a testing method for problems without test oracles. Integration testing allows for detecting errors in complex systems that may not be found during the testing of their components. In this paper, we propose a novel…
The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of…
The intensity relations for electromagnetic transition rates in the rotational coupling scheme have been a basic tool to understand the properties of nuclear collective rotations. In particular the correction terms to the leading-order…
We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic…
An optical field is described by the amplitude and phase, and thus has a complex representation described in the complex plane. However, because the only thing we can measure is the amplitude of the complex field on the real axis, it is…
We describe an approach to online analysis of micro-rheology data using a multi-scale time-correlation method. The method is particularly suited to process high-volume data streams and compress the relevant information in real time. Using…
In a recent work, S.A.R. Horsley and coworkers [Nature Photon 9, 436-439 (2015)] showed rather interestingly that planar dielectric media, for which the real and imaginary parts of the dielectric permittivity are related by spatial…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
The modern framework of state transformers, i. e., the first Kraus representation of quantum measurement, is introduced and related both to the known textbook concepts and to measurement-interaction evolution (the second Kraus…
We present the first analysis of harmonic generation data where the full potential of the generalized nonlinear Kramers-Kronig (K-K) relations and sum rules is exploited. We consider two published sets of wide spectral range experimental…
A broad class of planar dielectric media with complex permittivity profiles that are fully invisible, for both left and right incidence sides, is introduced. Such optical media are locally isotropic, non-magnetic and belong to the recently…