Kramers-Kronig Relations Research Articles

Demonstration of a photonic integrated circuit for quantitative phase imaging

Quantitative phase imaging (QPI) is an optical microscopy method that has been developed over nearly a century to rapidly visualize and analyze transparent or weakly scattering objects in view of biological, medical, or material science applications. The bulky nature of the most performant QPI techniques in terms of phase noise limits their large-scale deployment. In this context, the beam shaping properties of photonic chips, combined with their intrinsic compact size and low cost, could be beneficial. Here, we demonstrate the implementation of QPI with a photonic integrated circuit (PIC) used as an add-on to a standard wide-field microscope. Combining a 50 mm×50 mm footprint PIC as a secondary coherent illuminating light source with an imaging microscope objective of numerical aperture 0.45 and implementing a phase retrieval approach based on the Kramers–Kronig relations, we achieve a phase noise of 5.5 mrad and a diffraction limited spatial resolution of 400 nm. As a result, we retrieve quantitative phase images of Escherichia coli bacteria cells and monolayers of graphene patches from which we determine a graphene monolayer thickness of 0.45±0.15 nm. The current phase noise level is more than five times lower than that obtained with other state-of-the-art QPI techniques using coherent light sources and comparable to their counterparts based on incoherent light sources. The PIC-based QPI technique opens new avenues for low-phase noise, miniature, robust, and cost-effective quantitative phase microscopy.

Multi-wavelength digital holography based on Kramers–Kronig relations

We propose a multi-wavelength digital holography based on Kramers–Kronig (KK) relations, introducing a unified angle-multiplexing multi-wavelength KK model to overcome the accuracy and resolution limitations of angle-multiplexing techniques. By linking the real and imaginary parts of the multi-wavelength complex function via the KK relation, the method captures object light waves with the full effective bandwidth from a single interferogram and reference wave intensity. This method greatly improves spectral utilization and measurement accuracy in multi-wavelength interference. We use a three-wavelength multiplexing system to measure the topography of multi-step samples. The results show that our method expands the spectral range more than twice, reduces errors by 39.3%, and improves the peak signal-to-noise ratio and structural similarity index nearly three times compared to the traditional Fourier transform (FT) method. It offers a new, to the best of our knowledge, approach for high-precision multi-wavelength dynamic measurement and has the potential to overcome the limitations of multiplexing technology.

Enhanced Surface Plasmon Resonance Sensing via Kramers-Kronig Phase Extraction.

This study introduces a novel approach to enhance surface plasmon resonance (SPR) sensing using Kramers-Kronig (K-K) relations for phase extraction from reflection spectra. By applying the K-K relations, a phase shift sensitivity of 3400°/RIU is achieved improving SPR detection limits to 9 × 10-6 RIU, which is four times more sensitive than conventional methods for determining SPR peak shifts. This advancement enables more precise detection of refractive index changes in aqueous solutions, making it valuable for biosensing and environmental monitoring with spectrometers.

Computational investigation of the phase stability, electronic, optical, phonon spectrum, and elastic behavior of layered perovskites Ca2XO4 (X = Zr, Hf) for optoelectronic applications.

A significant class of solid-state materials, Ruddlesden-Popper (RP) perovskites are well-known for their rich chemical compositions that make them excellent electrocatalysts. Therefore, in this work, we conduct thorough analysis of RP perovskites, specifically Ca2XO4 (X = Zr, Hf). We delve into the structural, electronic, optical, and mechanical properties presenting their insights for the first time. Our investigations reveal that Ca2XO4 (X = Zr, Hf) exhibits stable tetragonal phase structures, with energies (E0) of - 10,522.93eV and - 33,520.14eV, respectively. The calculated in terms of the ground state determines to possess distinct values such as - 4.79 eV/atom for LiScTe2 and - 3.95 eV/atom for Ca2ZrO4 and Ca2HfO4. Notably, the semiconductor characteristics of Ca2ZrO4 and Ca2HfO4 are underscored by their respective wide direct band gap of 5.02eV and 5.30eV. Then, we discuss the optical parameters encompassing the dielectric function, absorption coefficient, optical conductivity, refractive index, and energy loss function. is described as ductile, whereas is defined as brittle. Our outcomes underscore remarkable ability of these materials to absorb ultraviolet radiation from the electromagnetic spectrum, positioning them as promising candidates for optoelectronic applications. We made these calculations by employing first-principles approach rooted in density functional theory (DFT) and utilizing the Perdew-Burke-Ernzerhof-Generalized Gradient Approximation (PBE-GGA) and Tran and Blaha-modified Becke-Johnson (TB-mBJ) functional within the WEIN2K framework. In this framework, Kramers-Kronig relations are used to obtain crucial optical parameters. Mechanical behavior is assessed by employing Voigt-Reuss-Hill approximation (VRH) fulfilling the Born's criteria which emphasizes that these materials are equally appropriate for a broad range of mechanical applications.

Nonlinear multi-image optical authentication based on QR decomposition and Kramer-Kronig relations

Abstract In this paper, a new nonlinear optical multi-image authentication scheme is proposed based on Kramers-Kronig digital holography and orthogonal triangular decomposition or QR decomposition. Here, the complex light field carrying the information of multiple images is modulated by random phase masks and propagated at certain distance. Afterwards, the QR decomposition is applied to the complex wavefront to generate the private keys and to add the non-linearity in the scheme. Next, the product of orthogonal matrix and upper triangular matrix is processed further. The obtained output is modulated by different phase masks and interfered with reference beam to record the encrypted image. For decryption, the Kramer-Kronig relation is utilized to extract the plaintext images directly with only the positive frequency part. A series of numerical simulations are conducted to validate the efficacy and robustness of proposed image authentication scheme.

Structured illumination microscopy based on Kramers-Kronig relations for quantitative phase reconstruction.

Structured illumination microscopy (SIM) is a widely applied fluorescence super-resolution imaging technique. It can also serve as high-throughput imaging in coherent imaging systems. However, coherent SIM requires additional qualitative/quantitative phase imaging methods to acquire phase information. This paper proposes a structured illumination microscopy technique based on the Kramers-Kronig relations (KK-SIM) that achieves quantitative phase imaging without the need for extra technical assistance and relies solely on the spatial-domain intensity images reconstructed through conventional SIM. KK-SIM utilizes a non-iterative approach to recover intensity into amplitude and phase, maintaining SIM's high acquisition speed and reconstruction efficiency. Our work enables high-throughput quantitative phase imaging using conventional SIM experimental setups and data post-processing, making SIM suitable for label-free, noninvasive dynamic observation.

Interface Characterization of Fusion Bonded Composites Made from Laser-Pretreated Steel and Glass Fiber-Reinforced Thermoplastics Using Electrochemical Impedance Spectroscopy

Material-hybrid designs made of metal and plastic are becoming increasingly important in the automotive and aerospace industries. They place new demands on joining technology in particular. One promising process is the fusion bonding of metals and fiber-reinforced thermoplastics. In this process, the thermoplastic matrix material of the fiber-reinforced composite component is melted and a direct adhesive bond is created with the metallic joining partner. This joining technology has already been extensively studied in the past. In particular, the interface between the joining partners has been identified as a critical factor for the long-term quality of the joint. The interface can be altered by influences during production, such as e-coat process or the effects of harsh environmental conditions during operation like corrosion and thermomechanical loads. Determining the extent of these influences on the interface condition and thus the quality of the joint is difficult, but it is essential to support the use of the joining method in safety-critical areas. Previous investigations of this joining method have mostly been carried out destructively using tensile shear tests and non-destructively using fiber optic and piezo ceramic sensors, but all approaches have only shown limited significance with regard to the metal-plastic interface in detail. Electrochemical impedance spectroscopy (EIS) as a very sensitive measurement method could represent an almost non-destructive and at the same time very sensitive alternative which is currently not reported for this use case in the literature. In previous internal investigations, we found that EIS can be used to measure layer thicknesses of up to 3.5 mm, contrary to the usual use of this test method for characterizing the properties of thin coatings, corrosion behavior and battery performance. In fusion bonding applications, typical material thicknesses of thermoplastics above the interface are around 1.5 mm and are thus well above the usual layer thicknesses of approx. 20 µm to 100 µm for typical EIS applications.This study aims to examine how EIS can be used advantageously for the interface characterization of fusion bonded specimens and up to which extent the EIS can provide a statement about the metal-plastic interface. In this study, a joint of a laser-pretreated steel and a glass fiber-reinforced PA6 is investigated. We measured specimens directly after production, after a treatment similar to an automotive e-coat process and after certain intervals of a salt spray test. Using the Kramers-Kronig transformation, the EIS data was validated and qualitatively analyzed with Nyquist and Bode diagrams, the impedance at 0.1 Hz, the maximum impedance and equivalent circuits. Tensile shear and edge shear test serve as destructive reference tests to determine strength parameters of the joints and evaluate the respective fracture patterns. This opens up the possibility to correlate the results of EIS and destructive measurements. In summary, EIS is suitable for characterizing the metal-plastic interface, even with polymer thicknesses of 1.5 mm, which are comparatively high for EIS. Due to the very low phase angle and the resulting low dielectricity of the glass fiber-reinforced thermoplastic, changes in the impedance data are directly related to the interface condition. The measured impedance spectra could be differentiated with Nyquist and Bode diagrams, the impedance at 0.1 Hz and the maximum impedance.

Interpretation of Impedance Spectra for Neural Stimulation Devices in Vitro

The interpretation of the physical properties of any given electrode device requires precise models for analyzing the impedance spectroscopy data and assessment of the data consistency with the Kramers-Kronig relations. In 1992, Shannon [1] studied the influence of charge reactions and charge density on macro electrodes and proposed safe levels of electrical stimulation for macro electrodes employed in brain stimulation. However, the current density performance of neural stimulation devices is dependent on the electrode size. By considering the contributions of both charging and faradaic current densities on the impedance spectroscopy data for microelectrode and ultra-microelectrode devices, we aim to develop accurate models and provide reliable data interpretation for the physical properties of neural stimulation devices.We conducted electrochemical impedance spectroscopy (EIS) measurement for our 32-channel ultramicroelectrode device with site diameters ranging from 5 microns to 10 microns. The experiment was performed with the Gamry Reference 600+ Potentiostat, at open circuit conditions. The three-electrode-cell configuration consists of the working electrode, an Ag/AgCl reference, and a Platinum mesh counter electrode, immersed in phosphate-buffered saline. Impedance measurements were collected at an applied AC voltage of 25 mV rms with a frequency sweep from 10 kHz to 0.2 Hz at 10 points per decade.The limits of the EIS measurements were assessed by plotting the accuracy contour plot for the Gamry Reference 600+ Potentiostat and the Reference 600+ Potentiostat connected to the 32-channel ultramicroelectrode device by a junction box. Methods for assessing potentiostat limits followed Gamry's recommendations, including open and shorted lead EIS measurements [2]. The accuracy of impedance measurement for the ultramicroelectrode device was evaluated using loops and terminal features on the device that enabled closed-circuit and open-circuit measurements, respectively.The EIS data for the smaller electrodes (with diameters of 10 microns and 5 microns) were influenced by the capacitance of the cables; whereas, the larger/reference electrode (with an area of 4004 square microns) was unaffected by cable capacitance but was affected by ohmic impedance. The impedance spectra of the ultramicroelectrode device were regressed with a measurement model program [3] to compute the stochastic error structure and obtain parameters for accurate interpretation of the electrodes’ properties. Most of the data was consistent with the Kramers-Kronig relations.The circuit element for the parasitic capacitance was added to the process model to fit the data points affected by the cable capacitance at high frequency. At open circuit, the model accounted for the constant element behavior of the electrode, and mass-transfer influenced by oxygen-reduction reactions. The capacitance of the electrodes was estimated by the application of Brug’s formula to the fitting parameters obtained from the process model analysis and the measurement model regression results. The capacitance calculated with the measurement model was consistent with the values of the parasitic capacitance obtained from the process model regression analysis.

Impedance Analysis of Ultramicroelectrodes for Neural Stimulation

Most neural stimulation techniques rely on macroelectrodes, which generate electric fields that impact neuronal groups rather than specific neurons, often resulting in unintended side effects.1,2 Ultramicroelectrodes (UMEs) offer enhanced spatial resolution, holding promise for precise targeting of specific neurons to optimize therapeutic outcomes while mitigating adverse effects. However, ultramicroelectrodes present challenges. For example, delivery of required charge may require current densities that can damage the electrode or adjacent tissue.Impedance measurements of UMEs were conducted and analyzed to understand stimulation currents and potential damage to the electrodes and tissue. The measurement-model technique was used to identify the optimal frequency range for regression analysis, to quantify the stochastic error structure, and to identify inconsistencies with the Kramers-Kronig relations. Understanding of the error structure is vital for interpretation.3 The regressions were weighted using the inverse of the variance for the stochastic error structures, and quality of fits were determined by the weighted chi-square statistic.Process modeling was used to understand and characterize the underlying physical and chemical processes that occur at the electrode-electrolyte interface and electrode-tissue interface during neural stimulation. Constant-phase element (CPE) parameters, Q and alpha, corresponding to the behavior of the electrode-tissue interface, were obtained from this model. In addition, parameters associated with a capacitive loop were identified. Work is in progress to identify the origin of this loop. References(1) Otto, K. J.; Schmidt, C. E. Neuron-Targeted Electrical Modulation. Science. March 20, 2020, pp 1303–1304. https://doi.org/10.1126/science.abb0216.(2) Orazem, M. E.; Otto, K. J., Alexander, C. L., Electrochemistry in Action-Engineering the Neuronal Response to Electrical Microstimulation. Electrochemical Society Interface 2023, 32 (1), 40–42. https://doi.org/10.1149/2.F06231IF.(3) Orazem, M. E.; Agarwal, P.; Jansen, A. N.; Wojcik, P. T.; Garcia-Rubio, L. H. Development of Physico-Chemical Models for Electrochemical Impedance Spectroscopy. Electrochim Acta 1993, 38 (14), 1903–1911.

Analyzing Experimental Data Validity and Error Structure for Second-Harmonic Nonlinear Electrochemical Impedance Spectroscopy

Second harmonic nonlinear electrochemical impedance spectroscopy (2nd-NLEIS) is a powerful and complementary technique to traditional EIS, often resolving model degeneracy issues in electroanalytical half-cell measurements and enabling better parameter assignment in two-electrode systems such as lithium-ion battery (LIB) experiments. Since the initial 2nd-NLEIS data for Li-ion batteries was reported by Murbach et al., [1] methods for testing the validity of 2nd-NLEIS datasets have been lacking. In EIS, the Kramers-Kronig (KK) relation is foundational for evaluating if experimental data meets key metrics for linearity, causality, and stationarity. [2] While the nonlinear nature of the 2nd-NLEIS response does not allow the direct application of KK relation, other approaches for data validation established in the EIS literature can be adapted to data validation and experimental error analysis in 2nd-NLEIS experiments.In this work, we provide a pathway to quantify the quality of 2nd-NLEIS data, providing better confidence in the simultaneous analysis of EIS and 2nd-NLEIS. The Data validation for 2nd-NLEIS relies on the use of a series of nonlinear Voigt elements to describe a 2nd-NLEIS spectrum, enabling a foundational assessment of data quality and stochastic error analogous to the practice in linear EIS data quality assessments. [3,4] Our method builds on prior work showing the 2nd-NLEIS Randles circuit response is directly proportional to the square of the linear EIS response. [5] By feeding the KK-transformable EIS response into the 2nd-NLEIS governing equation, we obtained a KK equivalent nonlinear transformation for the 2nd-NLEIS. That is, the 2nd-NLEIS response can be represented by the sum of M nonlinear Randles in the absence of measurement noise. Similarly, the difference between the data and fit provides a measure of the experimental noise. Overall, this work leverages methods from linear EIS and basic circuit elements we’ve developed for the 2nd-NLEIS response to provide data quality quantification of the 2nd-NLEIS data.

Optical and Plasmonic Properties of Epitaxial and Oxidative Controlled Titanium Nitride Thin Films

The present study is an effort to develop negative-permittivity, high melting point, mechanically hard, and chemically stable materials beyond commonly employed plasmonic metals such as gold and silver, which are often device incompatible in terms of real operating environments. The material studied here is titanium nitride (TiN), which possess free electron gas density similar to of gold and silver, and embodies refractory metals’ characteristics. The aforementioned advantages of TiN are taken to the next level by transforming them to oxynitrides (TiON) with a precise control in oxygen composition that can, in turn, be used to tune the electronic band structure of transition metal nitrides, opening another new dimension to transition metals nitride based plasmonics and metamaterials research. This presentation will report a pulsed laser-assisted synthesis, detailed structural characterization using x-ray diffraction (XRD), x-ray photoelectron spectroscopy (XPS), soft x-ray absorption spectroscopy (XAS), non-Rutherford Backscattering spectrometry (RBS), and plasmonic properties of three sets of TiN/TiON thin films. The first two sets of TiN films were grown 600 and 700 °C under a high vacuum condition. The third set of TiN film was grown in the presence of 5 mTorr of molecular oxygen at 700 °C. The purpose of making these three sets of TiN/TiON films was to understand the role of film crystallinity and role of oxygen content of TiN films on their optical and plasmonic properties. The results have shown that TiN films deposited in a high vacuum are metallic, have large reflectance, and high optical conductivity. The TiN films, grown in 5 mTorr, were found to be partially oxidized with room temperature resistivity nearly three times larger than those of the TiN films grown under high vacuum conditions. The optical conductivity these films were analyzed using a Kramers-Kronig transformation of reflectance and a Lorentz-Drude model; the optical conductivity determined by two different methods agrees very well, indicative of reliable estimate of the absolute value of reflectance in the first place. Then, it allows us to determine and analyze the complex dielectric function over a broad spectral range. We notice the existence of significant spectral weight below the interband absorptions, described by two Lorentzians, one around 250 cm-1 and one around 2,500 cm-1. We discuss here the dependence of the two bands on the deposition conditions and their effect on the plasmonic performances of TiN/TiON thin films, in particular on the surface plasmon polariton (SPP) and localized surface plasmon resonance (LSPR) quality factors.

(Invited) Attenuated Total Reflectance UV-Vis Spectroscopy Applied for Organic Semiconductor Films

Poly(3-hexylthiophene) (P3HT) is a p-type organic semiconductor extensively utilized in various electrochemical devices like solar cells and organic field-effect transistors owing to its outstanding solubility in a wide array of solvents and its high field-effect mobility. The packing structure and crystallinity of P3HT have a significant impact on device performance. The electronic state of P3HT is one of important properties, playing a crucial role in both fundamental understanding and practical applications. Ultraviolet-visible spectroscopy is one of the powerful techniques for investigating the electronic states within materials.In this study, ultraviolet-visible absorption spectra of P3HT films deposited on sapphire substrates were examined utilizing two spectroscopic techniques: transmission and attenuated total reflection (ATR) spectroscopies. Furthermore, a comprehensive comparative analysis was conducted between two deposition methodologies, namely casting and spin-coating methods.The ATR spectra were measured by the custom-made spectrometer, which consisted of the UV–vis–NIR spectrophotometer (V-770, JASCO) and an original ATR unit [1]. The incident light passed through a monochromator and irradiated into the sapphire ATR prism. The reflected light was detected by a photo-multiplier. The incident angle was set to 70°, and the penetration depth was approximately 50 nm or less in the measured wavelength region (200–800 nm). The original ATR unit and the commercial transmission unit could be easily exchanged, and the transmission spectra of the P3HT film fabricated on the sapphire ATR prism could be meaasured.In both the transmission spectrum (Figure 1a) and ATR spectrum (Figure 1b), the spectra of the P3HT thin films fabricated via the casting method (red lines) exhibited absorptions at longer wavelengths in contrast to the film prepared using the spin-coating method (blue lines), thus indicating that the casting method yields a more ordered structure. The spectral shapes differed between the transmission and ATR methods. To compare them, it was necessary to apply Kramers-Kronig transformation to the ATR spectra. The details will be discussed in the presentation.The ATR spectrum of the film prepared through the casting method (Figure 1b, red line) displayed distinctive absorption peaks around the 690 nm region. In the ATR spectrum of the film prepared by the spin-coating method (Figure 1b, blue line), the small absorption at the same wavelength was also observed. However, such absorption were not observed in the transmission spectra (Figure 1a). It has been reported that the absorption at around 690 nm is attributed to the high internal structural order within the single-crystalline P3HT [2]. It should be noted here that the ATR spectra strongly reflect the region near the surface of the ATR prism. Therefore, it can be assumed that the highly ordered structures of P3HT are formed near the sapphire substrate, as detected by ATR measurements.Consequently, this study revealed the structural variations in the films depending on the fabrication method using ultraviolet-visible spectroscopy. Particularly, the adoption of the ATR method enabled measurements that strongly reflected the film-substrate interface.[1] I. Tanabe, I. Imoto, D. Okaue, M. Imai, S. Kumagai, T. Makita, M. Mitani, T. Okamoto, J. Takeya and K. Fukui, Commun. Chem., 4, 88 (2021).[2] K. Rahimi, I. Botiz, J. O. Agumba, S. Motamen, N. Stingelin and G. Reiter, RSC Adv., 4, 11121 (2014). Figure 1

Inductive Behavior in Electrochemical Impedance Spectroscopy: Can We Discriminate between Adsorption and Non-Stationarity

Electrochemical impedance spectroscopy (EIS) is a widely used technique for studying electrochemical processes. EIS typically assumes a linear relationship between the applied signal (potential or current) and the measured response (current or potential). In other words, doubling the input perturbation must result in doubling the output, and the output signal must show no change in shape. However, by using “small input signals”, a linear response can be achieved. Similarly, stationarity is also a requirement for EIS measurements. In this case, several factors may be at the origin of the problem. For instance, as an electrochemical reaction progresses, the electrode surface and the surrounding electrolyte can change, affecting the resistance and capacitance, and consequently, the impedance. Temperature variations can also affect the conductivity and mobility of ions, leading to a shift in impedance as a function of the frequency. If a system is non-stationary during an impedance measurement, the measured value won't represent a single, fixed state. The impedance will depend on the time the measurement was taken. This can make it difficult to interpret the data and compare it with other measurements. Conversely, reaction mechanism involving adsorbates may be misinterpreted. Indeed, adsorption processes can result in either capacitive or inductive time-constants, usually observed in the low frequency domain. Such a behavior has been reported in the literature for corrosion processes. In this presentation, we will show how non-stationarity can modify an impedance diagram. Particular attention will then be paid to the case of the response of an adsorbed intermediate, such as the corrosion of Mg, for which inductive feature can be observed. The importance of the Kramers-Kronig relationships will then be discussed.

Optical constants of magnetron sputtered aluminum in the range 17–1300 eV with improved accuracy and ultrahigh resolution in the L absorption edge region

This work determines a new set of EUV/x-ray optical constants for aluminum (Al), one of the most important materials in science and technology. Absolute photoabsorption (transmittance) measurements in the 17–1300 eV spectral range were performed on freestanding Al films protected by carbon (C) layers, to prevent oxidation. The dispersive portion of the refractive index was obtained via the Kramers–Kronig transformation. Our data provide significant improvements in accuracy compared to previously tabulated values and reveal fine structure in the Al L1 and L2,3 regions, with photon energy step sizes as small as 0.02 eV. The implications of this work in the successful realization of EUV/x-ray instruments and in the validation of atomic and molecular physics models are also discussed.

Investigation of structural, morphological and optical characteristics of (Ni,Co)S/Fe3O4 nanocomposites and (Ni,Co)-doped Fe3O4 nanoparticles

Abstract The present search seeks to customize the optical, magnetic, and structural characteristics of NiS/Fe3O4 and CoS/Fe3O4 nanocomposites in contrast to Ni-doped Fe3O4 and Co-doped Fe3O4 nanoparticles to investigate linear, nonlinear, and optoelectronic applications. In this regard, the preparation of magnetite nanoparticles (Fe3O4) doped by Ni and Co and also NiS/Fe3O4 and CoS/Fe3O4 nanocomposites was successfully carried out through the co-precipitation method. The XRD obtained results revealed the presence of a face-centered cubic structure in all samples. Moreover, the estimation of the crystalline size for the Fe3O4, Ni-doped Fe3O4, Co-doped Fe3O4 NiS/Fe3O4, and CoS/Fe3O4 nanopowders was carried out using the Debye–Scherrer formula, yielding values ranging from 8.45 nm to 10.13 nm. Furthermore, nanopowder microstructure images were taken through a field emission scanning electron microscope (FESEM), which represented that the shape of the grains was spherical and irregular. Furthermore, the samples validate the purity of the samples which revealed the presence of vibrational modes in the metal oxide bonds. An optical investigation was conducted on all samples utilizing a diffuse reflectance spectroscopy. Band gap values ​​were estimated based on diffuse reflectance spectroscopy data through Tauc plot analysis, which yielded a range from 2.88 eV to 3.01 eV, indicating that the red shift in the band gap of Fe3O4 with all impurities except CoS/Fe3O4, provides catalytic applications of synthesized materials. Additionally, numerical calculations utilizing the Kramers-Kronig relation and Wemple-DiDomenico (WDD) model, were performed to assess the extinction coefficient (k), refractive index (n), linear susceptibility ( χ 1 ), and third-order nonlinear susceptibility ( χ 3 ) parameters on the reflectance data. Compared to other studied samples, the maximum evaluated values of χ 3 and the density of polarizable constituents (N) were related to the Ni-doped Fe3O4 NPs. This observation suggests that the prepared nanopowders possess significant potential for utilization in both fields of linear and nonlinear optical devices.

Fully-relativistic electron Bernstein wave current drive simulations in the STEP spherical tokamak

Abstract Electron Bernstein waves (EBWs) are theorised to efficiently drive current in spherical tokamak power plants, e.g. Spherical Tokamak for Energy Production (STEP). At high temperatures ( T e ≳ 4 keV), relativistic effects can significantly impact wave propagation. This work presents relativistic calculations of EBW wave propagation, damping, and current drive (CD) in a conceptual STEP plasma. Kramers–Kronig relations are exploited to efficiently evaluate the fully-relativistic dispersion relation for arbitrary wave-vectors, leading to a > 50 × speed-up compared to previous efforts. CD efficiency is calculated using both linear and quasilinear codes. Thus, for the first time, large parametric scans of fully-relativistic EBW CD simulations are performed through ray-tracing. In STEP, three main classes of rays are identified. The first class propagate deep into the core (ρ < 0.5), but exist only if relativistic effects are accounted for. They damp strongly at the fundamental harmonic on nearly-thermal electrons and thus drive little current. A second class of rays propagate to intermediate depths ( ρ ≈ 0.3 − 0.7 ) before damping at the 2nd harmonic. Their CD efficiencies are significantly altered due to relativistic changes to trajectory and polarisation. The third class of rays damp strongly far off-axis (ρ > 0.7), predominantly at the second harmonic. These ray trajectories are sufficiently short and ‘cold’ that relativistic effects are unimportant. In linear CD simulations, the optimal launch point corresponds to this third class of rays, suggesting that non-relativistic simulations are adequate. However, quasilinear calculations indicate that, at reactor relevant powers, CD is maximised at ρ ≈ 0.6. This quasilinear optimal point corresponds to the second class of rays, for which relativistic propagation does matter.

The influence of bandgap tunability on the physical features of Rb2LiSbX6 (X=Cl, Br) double perovskites in the context of green technologies

Rubidium-based perovskites have the potential to significantly transform renewable energies by making devices more affordable and environmentally friendly. The DFT is employed to conduct an inclusive analysis of the elastic, structural, electronic structure, transport and optoelectronic properties of Rb2LiSbCl6 and Rb2LiSbBr6. The analysis of tolerance factor, optimization curves and octahedral tilting serves to validate the structural stability. The brittle character of Rb2LiSbCl6 and ductile nature of Rb2LiSbBr6 are substantiated by their mechanical properties. The (W-L) symmetry points for Rb2LiSbCl6 and Rb2LiSbBr6 demonstrate the indirect bandgap of 3.72 eV and 2.9 eV, respectively. A decline in the bandgap is observed upon substitution of the Cl with Br atom. The Kramer-Kronig relations are employed for the assessment of the optical properties, revealing substantial absorption within the UV spectrum for both structures, hence enabling their application in optoelectronics. A wide range of thermoelectric properties are computed utilizing the Boltzmann semi-classical theory. Perovskites possess considerable promise for the implementation of renewable energy applications due to their notable ZT values (i.e., 0.73 for Rb2LiSbCl6 and 0.74 for Rb2LiSbBr6), as well as their enhanced Seebeck coefficients. These characteristics enhance their appropriateness for usage in green technologies.

Driving deep-learning-based metasurface design with Kramers-Kronig relations

Driving deep-learning-based metasurface design with Kramers-Kronig relations

Nonminimal coupling holographic superconductors

We explore a holographic superconductor model in which a real scalar field is nonminimally coupled to a gauge field. We consider several types of the nonminimal coupling function h(ψ) including exponential, hyperbolic (cosh), power-law, and fractional forms. We investigate the influences of the nonminimal coupling parameter α on condensation, critical temperature, and conductivity. We can categorize our results in two groups. In the first group, conductor/superconductor phase transition is easier to occur for larger values of α, while in the second group stronger effects of the nonminimal coupling makes the formation of scalar hair harder. Although the real and imaginary parts of conductivity are impressed by different forms of h(ψ), they follow some universal behaviors such as connecting with each other through Kramers–Kronig relation in ω → 0 limit or the appearance of gap frequency at low temperatures around ωg ∼ 8 Tc, which shifts to larger values by increasing the strength of α. Among all forms of h(ψ) we observe that h(ψ) = 1 + αψ2 gives us better information in wide range of nonminimal coupling constant and temperature. Choosing the best form of h(ψ), we construct a family of solutions for holographic conductor/superconductor phase transitions to discover the effect of the hyperscaling violation when the gauge and scalar fields are nonminimally coupled. we find that the critical temperature increases for higher effects of hyperscaling violation θ and nonminimal coupling constant α. By increasing these two parameters, we obtain lower values of condensation which means that conductor/superconductor phase transition will acquire easier. Furthermore, we understand that the hyperscaling violation affects the conductivity σ of the holographic superconductors and changes the expected relation in the gap frequency. Some universal behaviors like infinite DC conductivity are observed. In addition, we consider a five-dimensional Gauss–Bonnet (GB) black hole with a flat horizon. We find out that the critical temperature decreases for larger values of GB coupling constant, λ, or smaller values of nonminimal coupling constant, α, which means that the condensation is harder to form. Moreover, we study the electrical conductivity in the holographic setup. We observe that the gap frequency shifts to larger values for stronger λ, and becomes flat by increasing α.

Novel method to analyse and reconstruct optical constants of biological substances with application of Kramers–Kronig relations

Spectroscopic measurements of dielectric characteristics of biomolecules and tissues are a basis of many modern methods of medical diagnostics, research, and engineering. This requires accurate knowledge about the refraction index, n, and the extinction coefficient, k, at various frequencies, which are usually not available from the literature. Moreover, spectral data often need to be analysed, compared, or verified, especially if obtained for different samples and experimental conditions. The above problems can be tackled with the help of Kramers–Kronig relations, which are based on fundamental physical principles and can be generally used for arbitrary substances, including complex biological molecules and tissues. However, their direct application for analysis and reconstruction of the optical constants from experiment is hindered by the restricted frequency range of data, the presence of experimental errors, and the prevalence of qualitative rather than quantitative spectra. Our work focuses on the calibration of measured data and the reconstruction of missing spectra. We developed robust reconstruction techniques designed for cases, when disjoint intervals of absorbance data are available, commonly given in IR or/and UV ranges. The techniques hinge on a reference refractive index, given within a certain frequency window and preferably situated in proximity to the absorbance data. The proposed methods are applied to reconstruct the dielectric functions of the protein bovine serum albumine (BSA) and glucose across the entire frequency range. The acquired data are further employed to assess the feasibility of constructing a protein-based coating for implanted antennas. By incorporating spectral characteristics from different frequency ranges into one consistent picture, our methods supply the full information about dielectric response, which is associated with concentration, structure and environment of biomolecules. This provides a mathematical background for combined applications of spectroscopic instruments operating in different frequency ranges that will support fundamental research and stimulate the development of medical technologies.