Search Results (24)

This study systematically investigates continuous and discrete spectra methodologies for determining time-domain viscoelastic response functions (creep compliance and relaxation modulus) in asphalt mixtures. Through complex modulus testing of three asphalt mixtures (base asphalt mixture, SBS-modified asphalt mixture, and crumb rubber-modified asphalt mixture), we established unified master curves using a Generalized Sigmoidal model with approximated Kramers–Kronig (K-K) relations. Discrete spectra can be obtained by Prony series of Maxwell/Kelvin modeling, while continuous spectra derived through integral transformation produced complementary response functions by numerical integration. Comparative analysis demonstrated that discrete and continuous spectra methods yield highly consistent predictions of the relaxation modulus and creep compliance within conventional time scales (10⁻⁷–10⁵ s), with significant deviations emerging only at extreme temporal extremities. Compared to discrete spectra results, material parameters (relaxation modulus and creep compliance) derived from continuous spectra methods invariably asymptotically approach upper and lower plateaus. Notably, the maximum equilibrium values derived from continuous spectra methods consistently surpassed those obtained through discrete approaches, whereas the corresponding minimum values were consistently lower. This comparative analysis highlights the inherent limitations in the extrapolation reliability of computational methodologies, particularly regarding spectra method implementation. Furthermore, within the linear viscoelastic range, the crumb rubber-modified asphalt mixtures exhibited superior low-temperature cracking resistance, whereas the SBS-modified asphalt mixtures demonstrated enhanced high-temperature deformation resistance. This systematic comparative study not only establishes a critical theoretical foundation for the precise characterization of asphalt mixture viscoelasticity across practical engineering time scales through optimal spectral method selection, but also provides actionable guidance for region-specific material selection strategies. Full article

We have estimated the intrinsic complex refractive index spectrum of a CsPbBr₃ nanocrystal. With various dilute solutions of CsPbBr₃ nanocrystals dissolved in toluene, effective refractive indices were measured at two different wavelengths using Michelson interferometry. Given the effective absorption spectrum of the solution, a full spectrum of the effective refractive index was also obtained through the Kramers–Krönig relations. Based on the Maxwell–Garnett model in the effective medium approximation, the real and imaginary spectrum of the complex refractive index was estimated for the CsPbBr₃ nanocrystal, and the dominant inaccuracy was attributed to the size inhomogeneity. Full article

In unbounded media, the acoustic attenuation as function of frequency is related to the frequency-dependent sound velocity (dispersion) via Kramers–Kronig dispersion relations. These relations are fundamentally important for better understanding of the nature of attenuation and dispersion and as a tool in physical acoustics measurements, where they can be used for control purposes. However, physical acoustic measurements are frequently carried out not in unbounded media but in acoustic waveguides, e.g., inside liquid-filled pipes. Surface acoustic waves are also often used for physical acoustics measurements. In the present work, the applicability of Kramers–Kronig relations to guided and surface waves is investigated using the approach based on the theory of functions of complex variables. It is demonstrated that Kramers–Kronig relations have limited applicability to guided and surface waves. In particular, they are not applicable to waves propagating in waveguides characterised by the possibility of wave energy leakage from the waveguides into the surrounding medium. For waveguides without leakages, e.g., those formed by rigid walls, Kramers–Kronig relations remain valid for both ideal and viscous liquids. Examples of numerical calculations of wave dispersion and attenuation using Kramers–Kronig relations, where applicable, are presented for unbounded media and for waveguides formed by two rigid walls. Full article

Polyurethane (PU) mixture, which is a new pavement mixture, exhibits different dynamic properties compared to a hot-mixed asphalt mixture (HMA). This paper analyzed whether the Kramers–Kronig (K–K) relation and thermorheologically simple properties applied to the PU mixture. Based on the results, the PU mixture exhibited thermorheologically simple properties within the test conditions. The time–temperature superposition principle (TTSP) was applicable for the PU mixture to construct a dynamic modulus master curve using the standard logistic sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak–Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The core–core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K–K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results with the test temperatures and loading frequencies. The phase angle of the PU mixture at extremely high or low test temperatures cannot be derived from the dynamic modulus data. Full article

This study presents a systematic optimization of wide-angle metamaterial long-pass (LP) edge filters based on silicon nanospheres (SiNP). Multi-layered configurations incorporating SiNP-meta-films and anti-reflection coating (ARC) elements not previously considered in the literature are explored to enhance their filter performance in both stop and pass bands. This research has successfully developed an accurate model for the effective refractive index using Kramers–Kronig relations, enabling the use of classical thin-film design software for rapid device performance optimization, which is verified by full-wave numerical software. This systematic optimization has produced highly efficient, near-shift-free long-pass metamaterial filters, evidenced by their high optical density (OD = 2.55) and low spectral shift across a wide angular range (0°–60°). These advancements herald the development of high-efficiency metamaterial optical components suitable for a variety of applications that require a consistent performance across diverse angles of incidence. Full article

Spectroscopic ellipsometry (SE), a non-invasive optical technique, is a powerful tool for characterizing surfaces, interfaces, and thin films. By analyzing the change in the polarization state of light upon reflection or transmission through a sample, ellipsometry provides essential parameters such as thin film thickness (t) and optical constants (n, k). This review article discusses the principles of ellipsometry, including the measurement of key values ∆ and Ψ, and the complex quantity ρ. The article also presents the Fresnel equations for s and p polarizations and the importance of oblique angles of incidence in ellipsometry. Data analysis in ellipsometry is explored, including the determination of bandgap and data referencing the electrical properties of materials. The article emphasizes the importance of choosing the appropriate models to fit ellipsometric data accurately, with examples of the Cauchy and Lorentz models. Additionally, the Kramers–Kronig relations are introduced, illustrating the connection between real and imaginary components of optical constants. The review underscores the significance of ellipsometry as a non-destructive and versatile technique for material characterization across a wide range of applications. Full article

Stripe rust is one of the most common diseases challenging the safe production of wheat. Rapid identification and analysis of urediospores, responsible for disease transmission, are the key to preventing and controlling stripe rust. The current spore detection is time-consuming and requires auxiliary equipment, but many optical detection methods and sensors with high efficiency, sensitivity, and detection ability have been developed and widely used. Thus, the investigation of optical parameters is the prerequisite for optical sensitive detection and is detailed in this study. Firstly, the microscopic images and surface elements of wheat stripe rust urediospores were obtained using a high-resolution electron microscope and an energy spectrum analyzer. The reflectivity and absorptivity spectra in the near-infrared band of active/inactivate urediospores were measured. Further, the optical parameters, such as reflection phase shift, complex refractive index, and dielectric constant, of the urediospores were analyzed based on electromagnetic theory and Kramers–Kronig relation. The results revealed that the urediospores have a strong tolerance to near-infrared light, and the real part of the complex refractive index n was between 1.0 and 1.4. These observations indicate that whether the spores are active or not has little effect on the real part and dielectric constant of the complex refractive index but has a significant impact on the imaginary part and extinction coefficient of the complex refractive index, and the corresponding relationship between the optical properties of urediospores and biological components was established. These findings were verified with HPLC-MS and Near-Infrared Spectroscopy Analysis Technology and lay a theoretical foundation for detecting urediospores of wheat stripe rust by using optical sensors. The study provides a reference for the analysis of optical characteristics of other biological samples. Full article

We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two Noether-conserved quantities of a system: its Hamiltonian and its entropy production. In natural units, when complexified, the one is simply the Wick-rotated complex conjugate of the other. A Hilbert transform relation is constructed in the formalism of quantitative geometrical thermodynamics, which enables system irreversibility to be handled analytically within a framework that unifies both the microscopic and macroscopic scales, and which also unifies the treatment of both reversibility and irreversibility as complementary parts of a single physical description. In particular, the thermodynamics of two unitary entities are considered: the alpha particle, which is absolutely stable (that is, trivially reversible with zero entropy production), and a black hole whose unconditional irreversibility is characterized by a non-zero entropy production, for which we show an alternate derivation, confirming our previous one. The thermodynamics of a canonical decaying harmonic oscillator are also considered. In this treatment, the complexification of time also enables a meaningful physical interpretation of both “imaginary time” and “imaginary energy”. Full article

We explored spectral diversity in infrared (IR, 4–25 μm) imaginary (k) and real (n) indices of refraction (optical constants) for 26 surface soils that originated from global dust entrainment regions. The k spectra were derived from optical transmission spectra of KBr pellets containing dispersed dust and the n spectra were estimated with the subtractive Kramers–Kronig (SKK) method. We compared k and n obtained by this study with previously published values. Our optical constants from the KBr technique are comparable in magnitude and spectral shape to those from previous studies that used dust aerosols re-suspended in a chamber. This suggests that the SKK method can offer a reliable mechanism for measuring IR spectra of both optical constants for soils. The soils used here exhibit additional spectral variability compared with past studies. We note that the appearance and the shift in positions of the strongest absorption peaks are due to combinations of silicates with overlapping absorption, rather than being related to a single mineral. We note that all dust optical constants have substantially lower magnitudes compared to those of pure minerals. Our results can improve estimates of mineral dust radiative effects and support quantification of surface mineral estimates using satellite and ground-based remote sensing. Full article

The characterization of electromagnetic metamaterials (MMs) plays a fundamental role in their engineering processes. To this end, the Nicolson–Ross–Weir (NRW) method is intensively used to recover the effective parameters of MMs, even though this is affected by the branch ambiguity problem. In this paper, we face this issue in the context of global analytic functions and Riemann surfaces. This point of view allows us to rigorously demonstrate the mathematical foundations of an algorithmic approach for avoiding the branch ambiguity problem, in which the phase unwrapping method is merged with K-K relations for recovering the effective parameters of an MM. In addition, exploiting the intimate relationship between the K-K relations and the Hilbert transform, a simple variant of the above algorithm is presented. Full article

We experimentally demonstrate the spectral blue shift of surface plasmon resonance through the resonant coupling between quantum dots (QDs) and surface plasmons, surprisingly in contrast to the conventionally observed red shift of plasmon spectroscopy. Multimode optical fibers are used for extended resonant coupling of surface plasmons with excited states of QDs adsorbed to the plasmonic metal surface. The long-lived nature of excited QDs permits QD-induced negative change in the local refractive index near the plasmonic metal surface to cause such a blue shift. The analysis utilizes the physical causality-driven optical dispersion relation, the Kramers–Kronig (KK) relation, attempting to understand the abnormal behavior of the QDs-induced index dispersion extracted from blue shift measurement. Properties of QDs’ gain spectrally resonating with plasmons can account for such blue shift, though their absorbance properties never allow the negative index change for the blue shift observed according to the KK relation. We also discuss the limited applicability of the KK relation and possible QDs gain saturation for the experiment–theory disagreement. This work may contribute to the understanding of the photophysical properties critical for plasmonic applications, such as plasmonic local index engineering required in analyte labeling QDs coupled with plasmons for biomedical imaging or assay. Full article

Coherent detection provides the optimum performance for free space optical (FSO) communication systems. However, such detection systems are expensive and require digital phase noise compensation. In this paper, the transmission performance of long-haul FSO system for ground-to-satellite communication based on a Kramers–Kronig (KK) transceiver is evaluated. KK transceivers utilize inexpensive direct detection receivers and the signal phase is retrieved from the received current using the well-known KK relations. KK transceivers are not sensitive to the laser phase noise and, hence, inexpensive lasers with large linewidths can be used at the transmitter. The transmission performance of coherent and KK transceivers is compared in various scenarios such as satellite-to-ground, satellite-to-satellite, and ground-to-satellite for weak, moderate, and strong turbulence. The results show that the transmission performance of a system based on the KK transceiver is comparable to that based on a coherent transceiver, but at a significantly lower system cost and complexity. It is shown that in the absence of turbulence, the coherent receiver has a ~3 dB performance advantage over the KK receiver. However, in the presence of strong turbulence, this performance advantage becomes negligible. Full article

We comprehensively review several general methods and analytical tools used for causality evaluation of photonic materials. Our objective is to call to mind and then formulate, on a mathematically rigorous basis, a set of theorems which can answer the question whether a considered material model is causal or not. For this purpose, a set of various distributional theorems presented in literature is collected as the distributional version of the Titchmarsh theorem, allowing for evaluation of causality in complicated electromagnetic systems. Furthermore, we correct the existing material models with the use of distribution theory in order to obtain their causal formulations. In addition to the well-known Kramers–Krönig (K–K) relations, we overview four further methods which can be used to assess causality of given dispersion relations, when calculations of integrals involved in the K–K relations are challenging or even impossible. Depending on the given problem, optimal approaches allowing us to prove either the causality or lack thereof are pointed out. These methodologies should be useful for scientists and engineers analyzing causality problems in electrodynamics and optics, particularly with regard to photonic materials, when the involved mathematical distributions have to be invoked. Full article

Fluoride host materials doped with trivalent cerium ions have previously been demonstrated as successful laser materials in the ultraviolet wavelength region. However, the nonlinear optical properties of the fluoride hosts in this wavelength region have not been investigated yet, although nonlinearity could result in undesirable effects such as self-focusing and pulse distortion when these fluoride materials are used as gain media in high-power, ultrashort pulse laser oscillator and amplifier systems. In this work, the nonlinear refractive index of lithium calcium aluminum fluoride (LiCaAlF₆), lithium strontium aluminum fluoride (LiSrAlF₆), lanthanum fluoride (LaF₃), and yttrium lithium fluoride (YLiF₄) fluoride host materials are determined using the Kramers–Krönig relation model in the ultraviolet wavelength region. Self-focusing conditions, particularly at the peak laser emission wavelength of these materials, are further analyzed. Results show that LiCaAlF₆ has the smallest nonlinear refractive index and self-focusing, making it an ideal host material under the conditions of ultrashort pulse and ultrahigh-power laser generation. Full article

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. Full article