Kramers–Kronig Relation for Attenuated Total Reflection from a Metal–Dielectric Interface Where Surface Plasmon Polaritons Are Excited

The applicability of the Kramers–Kronig relation for attenuated total reflection (ATR) from a metal–dielectric interface that can excite surface plasmon polaritons (SPP) is theoretically investigated. The plasmon-induced attenuation of reflected light can be taken as the resonant absorption of light through a virtual absorptive medium. The optical phase shift of light reflected from the SPP-generating interface is calculated using the KK relation, for which the spectral dependence of ATR is used at around the plasmonic resonance. The KK relation-calculated phase shift shows good agreement with that directly obtained from the reflection coefficient, calculated by a field transfer matrix formula at around the resonance. This indicates that physical causality also produces the spectral dependence of the phase of the leakage field radiated by surface plasmons that would interfere with the reflected part of light incident to the interface. This is analogous with optical dispersion in an absorptive medium where the phase of the secondary field induced by a medium polarization, which interferes with a polarization-stimulating incident field, has a spectral dependence that stems from physical causality.

Correlations, response, and dissipation

This chapter studies how systems wiggle, and how they respond and dissipate energy when kicked. The wiggling fluctuations are described using correlation functions, the yielding and dissipation are described using susceptibilities. The intricate relations between these quantities are explored using the Onsager regression hypothesis, fluctuation--response and fluctuation--dissipation theorems, and the Kramers--Krönig relation derived from causality (the response cannot precede the kick). The powerful tools of linear response theory described here are basic tools in our exploration of materials with scattering of sound, light, X-rays, and neutrons, and have become our primary description of the behavior of materials. Exercises describe applications to noise in nanojunctions, humans on subways, magnetic spins, molecular dynamics and Ising models, liquids and magnets, materials at critical points, and fluctuations in the early Universe.

A Review Of The Linear Response Function In Condensed Matter Physics And Their Application In Some Elementary Processes

Linear response theory in quantum theory with its linear response function and its quantization process has been formulated. The relation between the linear response function with its generalized susceptibility, its symmetry properties, and its analyticity has been studied. These properties produce the dispersion relation or Kramers-Kronig relation. The explicit form of the quantum response function and generalized susceptibility also been reviewed. Applications of linear response functions have been described for three elementary processes. The process discussed is the magnetic field disturbance in the magnetic system that generates magnetic susceptibility, and the electric field disturbance in the electrical system that generates electrical conductivity tensor and the ferromagnet Heisenberg that generates its generalized susceptibility.

Особенности оптических и энергетических свойств тонких пленок CdSe

The paper presents the results of experimental and theoretical studies of the optical and energy properties of thin CdSe films obtained by the closed space sublimation. The synthesis method, the results of structural and optical studies of thin CdSe films deposited on the surface of a quartz substrate are presented. The quality of the films was analyzed by x-ray diffraction, energy dispersive analysis and scanning electron microscopy. Within the framework of the pseudopotential method, the dynamics of changes in the parameters of the CdSe films electronic subsystem is theoretically studied. The direct-gap nature of the forbidden gap of the film is established. Based on the density of states, the genesis of the conduction band and the valence band is established. Using the Kramers – Kronig relation, we obtained spectra of optical dielectric functions, optical reflection, refractive and extinction indexes, which satisfactorily correlate with the obtained experimental data.

Dispersion analysis for wave equations with fractional Laplacian loss operators

Several wave equations for power-law attenuation have a spatial fractional derivative in the loss term. Both one-sided and two-sided spatial fractional derivatives can give causal solutions and a phase velocity dispersion which satisfies the Kramers–Kronig relation. The Chen–Holm and the Treeby–Cox equations both have the two-sided fractional Laplacian derivative, but only the latter satisfies this relation. There also exists several seemingly different expressions for the phase velocity for these equations and it is shown here that they are approximately equivalent. Causality of the Chen–Holm equation has also been a topic of some discussion and it is found that despite the lack of agreement with the Kramers–Kronig relation, it is still causal.