Kramers-Kronig Method Research Articles

Optical properties and band-gap engineering of group (I) element-doped ZnO nanoparticles as P-type semiconductors

This study investigated the optical properties and band-gap engineering of zinc oxide (ZnO) nanoparticles doped with Group I elements, focusing on their potential as p-type semiconductors.Zn0.95M0.05O (M = Li, Na, and K) nanoparticles were synthesized by a gelatin-based sol-gel method.Through a combination of experimental characterization techniques including field emission scanning electron microscopy (FESEM), X-ray diffraction (XRD), and UV–vis spectroscopy, the crystal morphology, structure, and optical properties of the doped ZnO nanoparticles were analyzed. The Kramers-Kronig (K–K) method was employed to evaluate the behavior of the refractive index and optical dielectric function, which are complex quantities. The incorporation of Group I dopants into the ZnO lattice is explored for its impact on the band-gap structure and the realization of p-type conductivity.

Study of Urbach energy and Kramers–Kronig on Mn and Zn doped NiFe2O4 ferrite nanopowder for the determination of structural and optical characteristics

MxNi1-xFe2O4 spinel ferrite (M = Mn, Zn, and x = 0, 0.05) has been successfully synthesized by co-precipitation technique with hydrazine hydrate reduction agent (instead of NaOH) and Ethylene glycol surfactant. The XRD spectra of the samples illustrated high crystallinity. The structural characterization of pure and doped fcc NiFe2O4 were calculated by Scherrer, Modified Scherrer, Williamson–Hall, and SSP methods. In comparison of several methods, the Scherrer method is unreasonable method and W–H method has an acceptable range and can calculate both < L > and strain without restriction. The specific surface area in Zn-doped increased, demonstrate increment of adsorption properties in Ni ferrite structure. TEM images revealed the shape of grains is spherical, cubic, and irregular, with a grain size in the range of 35–65 nm. Hysteresis loops illustrated the magnetic behavior of samples. From the reflectance data, the band gap energies were estimated at 1.984, 1.954, and 1.973 eV for un-doped, Mn, and Zn-doped NiFe2O4 respectively (red shift). The almost low value of Urbach energy for pure, Mn, and Zn -doped NiFe2O4 indicates low structural disorder, which can approve the high crystallinity of samples. Direct band gap energy (Eg), refractive index, and extinction coefficient were estimated by the Kramers–Kronig method with linear optical evaluations. The Eg by K-K method is in good agreement with the Eg by Kubelka–Munk function.

Effects of Iron Doped LiTaO3 Films on Transverse Optic (TO) and Longitudinal Optic (LO) Values Using Kramers-Kronig Method

Film fabrication of LiTaO3 has been successfully prepared with 0%, 2%, 4%, and 6% Iron containing variations using the Chemical Solution Deposition (CSD) method. Each sample was characterized using FTIR and the wavenumber and transmittance values were obtained. This value was analyzed using the Kramers-Kronig (KK) method and obtained the Transverse Optic (TO) and Longitudinal Optic (LO) values. The results show that TO value is in wave numbers 462.25 cm-1 – 556.00 cm-1. While the value of LO is in the range of wave numbers 478.50 cm-1 – 571,00 cm-1. The results show an increase in both TO and LO values as the Iron Oxide percentage increases. Based on the analyses of TO, LO, ε₁ and ε₂, film fabrication of LiTaO3 has the potential as light, pressure and temperature sensors.&#x0D;

Strain-magneto-optics: Magnetoreflectivity in MnFe2O4 ferrite-spinel crystal

The single crystal of ferromagnetic magnetostrictive spinel MnFe2O4 was grown by the zone-floating method. The magnetic, magneto-elastic, optical, and magneto-optical properties of the MnFe2O4 ferrite-spinel were investigated in the infrared spectral range. A strain-magneto-optical phenomenon, which demonstrate the connection between magnetoreflection of non-polarized light and magnetostriction of MnFe2O4, was revealed. A maximum magnetoreflection of up to 1 % was observed at room temperature in a magnetic field of 2 kOe. Using the Kramers-Kronig method, the magnetorefractive effect and magnetooptical conductivity of MnFe2O4 were also calculated. The observed correlation between magnetoelastic and magneto-optical properties of MnFe2O4 was attributed to the significant contribution of linear magnetostriction to the magnetic anisotropy constant (ΔK/K1 ∼ 8 %) in the MnFe2O4 crystal. Additionally, a criterion of ΔK/K1 ∼ 1 % was proposed to evaluate the potential use of magnetostrictive materials in strain-magneto-optics.

Synthesis, characterization, and nonlinear optical properties of copper (II) ligand Schiff base complexes derived from 3-Nitrobenzohydrazide and benzyl

A new series of Cu (II) complexes were prepared using Schiff base ligand of N–N′-(1,2-diphenyl ethane-1,2-diylidene)bis(3-Nitrobenzohydrazide). The prepared ligand and Cu (II) complex were characterized using various physicochemical investigations such as X-ray diffraction (XRD), Field emission scanning electron microscopy (FESEM), and Energy dispersive X-ray analysis (EDX), Fourier Transform Infrared (FT-IR), {}^{13}C Nuclear Magnetic Resonance (NMR), {}^{1}H NMR, Diffuse Reflectance Spectroscopy (DRS), Vibrating Sample Magnetometer (VSM), and Z-Scan technique (Nonlinear optical (NLO) properties). In addition, the prepared samples have been examined for their NLO characteristics with the help of the Density Functional Theory calculations which proved that the Cu (II) Complex is more polarized than Ligand. According to XRD and FESEM results, the nanocrystalline nature of the samples is confirmed. The metal-oxide bond assigned in the functional studies by FTIR. Magnetic studies demonstrate weak ferromagnetic and paramagnetic nature for Cu (II) complex and diamagnetic nature for the ligand, respectively. DRS spectrum exhibited higher reflectance for Cu (II) than the ligand. The band gap energies of the synthesized samples were estimated by employing the Tauc relation and Kubelka–Munk theory on reflectance data and found to be 2.89 eV and 2.67 eV for Cu (II) complex and ligand, respectively. Extinction coefficient and refractive index values were calculated using the Kramers–Kronig method. The z-scan technique was applied to estimate the NLO properties by a 532 nm Nd:YAG laser.

Single-shot Kramers–Kronig complex orbital angular momentum spectrum retrieval

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrieval remains elusive, due to the signal–signal beat interference inherent in the measurement. Here, we introduce the concept of Kramers–Kronig (KK) receiver in coherent communications to the OAM domain, enabling rigorous, single-shot OAM spectrum measurement. We explain in detail the working principle and the requirement of the KK method and then apply the technique to precisely measure various characteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and the number of sampling points essential for rigorous retrieval and evaluate the performance on a large set of random OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormous potential for characterizing complex OAM states in real time.

Comparison study of the structure, dielectric function, and two-photon absorption cross-section of BiOI and Ag/BiOI nanomaterials

In this research, the interesting methods including X-ray diffraction (XRD) pattern, Field Emission Scanning Electron Microscopy (FESEM) images, energy dispersive X-ray (EDX), UV–Vis spectroscopy, Diffuse reflectance (DRS) spectrum, KK method, and Z-scan measurements were employed for characterizations of prepared BiOI and Ag/BiOI nanomaterials. The optical indices such as n, k, and ε1 and ε2 were assessed based on reflectance spectra data and the Kramers-Kronig (KK) method. Furthermore, the nonlinear optical (NLO) properties of prepared BiOI and Ag/BiOI nanomaterials in different Ag precents were examined through the Z-scan method using the laser beam at 532 nm wavelength. The two-photon absorption (TPA) and self-focusing performance are revealed by the prepared nanomaterials. Adding Ag into BiOI structures, significantly increases the TPA cross-section, σ2 which reaches up to 1.14578 × 10−21 cm4/W for the sample of S3. One of the significant factors that affected the improvement of the optical nonlinearity properties of Ag/BiOI and over BiOI was ascribed to the combined consequence of Ag's localized surface plasmon resonance (LSPR) phenomena, resulting in improved light absorption intensity coupling interaction, significant photo-produced electron-hole separability, and prolonged carrier lifetime.

Effects of Fe, Co, or Ni substitution for Mn on [formula omitted] perovskite: Structural, morphological, and optical analyses

In this work, lanthanum strontium-based perovskites La0.7Sr0.3BO3 (B = Mn, Fe, Co, or Ni) samples are successfully synthesized. Hexagonal and Rhombohedral phases in the LSMO sample are observed using the XRD results. From reflectance data, the band gap energies are found to be 2.95 eV, 3.19 eV, 3.03 eV, and 3.14 eV for LSMO, LSFO, LSCO, and LSNO, respectively leading to a blue shift after the replacement. Linear optical evaluations exhibit increased band gap energy and decreased Urbach energy with the replacement of the Fe, Co, or Ni at the Mn site indicating presence of the localized defect states. The calculated extinction coefficient and refractive index parameters, using the Kramers-Kronig method, represent maximum values at the same wavelength for the LSFO. The nonlinear optical parameters are calculated using the obtained data from Diffuse reflectance spectroscopy. The connection of nonlinear optical absorption (β) with localized defect states has been discussed.

A comparison of the crystal structure and optical properties of reduced graphene oxide and aminated graphene nanosheets for optoelectronic device applications

Optical properties of graphene transform in presence of amine or amide groups. So, the comparison of the linear and nonlinear optical (NLO) properties of reduced graphene oxide (RGO) nanosheets and aminated graphene (AMG) nanosheets will significantly accelerate the development of a flexible optoelectronic device based on this material in the future. In this paper, the structural and optical properties of RGO and AMG are investigated by TEM, XRD, Raman, and UV-Vis analysis. TEM images show the formation of the very thin layer of RGO and AMG nanosheets. The peak of XRD spectra (26.6◦) for both indicate the good quality of crystallization of RGO and AMG. Raman spectra result in ID/IG of about 0.9 and 1.1 for RGO and AMG, respectively. Also, different functional groups for RGO and AMG nanosheets are shown in FTIR spectra. Then, Kramers-Kronig (KK) method was employed to determine the dielectric function, ε̃(λ), extinction coefficient, k(λ) and refractive index, n(λ). Third-order optical nonlinearities of nanosheets dispersed in DMF are investigated with the Z-scan method. The nanosheets achieve an appropriate figure of merit (FOM) due to their high nonlinear refractive (NLR) index, n2 (10−8cm2/W) and low nonlinear absorption (NLA) coefficient, β (10−4cm/W).

Effect of reactive gas flow on structural and optical properties of sputtered silver oxide thin films; Kramers-Kronig method

Effect of reactive gas flow on structural and optical properties of sputtered silver oxide thin films; Kramers-Kronig method

Investigation of dielectric, linear, and nonlinear optical properties of synthesized 2D Ruddlesden-Popper-type halide perovskite

Ruddlesden-Popper-type halide perovskites (RPPs) have been widely investigated because of their tunable optical properties. The BA2MAPb2I7 (BA = CH3(CH2)3NH3 and MA = CH3NH3) powder is synthesized by a chemical solution-based method at low temperature and deposited on a glass substrate by spin coating technique. The optical transmission, reflection, and absorption investigations are conducted to determine the optical constants of the nano-powder and thin film of BA2MAPb2I7. The obtained results reveal that the optical band gap energy of BA2MAPb2I7 thin film and BA2MAPb2I7 nanoparticles are ∼ 1.95 and ∼ 2.02 eV, which is close to the photoluminescence (PL) peak at around 2.15 eV (576 nm). The optical indexes such as n, k, ε1, and ε2 are assessed based on reflectance spectra data and the Kramers-Kronig (KK) method. Moreover, the third-order nonlinear optical (NLO) characteristics, including nonlinear absorption coefficient (β), nonlinear refractive index (n2), third-order susceptibility (χ(3)) and second-order hyperpolarizability (γ) are investigated at different laser power. The positive signs of the n2 and β reveal that the BA2MAPb2I7 thin film exhibits self-focusing and saturable absorption (SA) properties due to thermal nonlinearity under the continuous wave (CW) laser regime. The magnitude of χ3 is from 20.275 ×10-2 to 29.908 ×10-2esu and the value of γ is from 19.633 ×10-27 to 28.961 ×10-27esu. The superior NLO responses of BA2MAPb2I7 thin-film open the path for the future design and synthesis of desirable and distinct materials for optoelectronic devices.

Investigation of the structural, dielectric, and optical properties of MoSe2 nanosheets

In this research, solvothermal synthesized MoSe2 nanosheets were analyzed to determine their structure and optical properties. Measurements through atomic force microscopy, scanning electron microscopy, and transmission electron microscopy confirmed the formation of MoSe2 nanosheets. The energy-dispersive x-ray results revealed the presence of high-purity MoSe2 and an atomic percentage ratio of Mo:Se ∼ 1:1.93. Additionally, x-ray diffraction and Raman showed the crystal structure of MoSe2 and the existence of a two-dimensional (2D) layer, respectively. The linear optical properties of the MoSe2 nanosheets were analyzed by Fourier transform infrared (FTIR) spectroscopy and the Kramers–Kronig method. The FTIR research indicated the vibrational modes of several chemical groups, thus proving the presence of MoSe2 ions. For the varying concentrations of MoSe2 nanosheets in dimethylformamide, the third-order nonlinear optical properties of MoSe2 nanosheets were determined in detail using the Z-scan approach and a continuous-wave Nd:YAG laser. As the transmittance measurements in an open aperture Z-scan setup indicated, all the synthetized samples had saturable absorption. Similar investigations using a close-aperture Z-scan technique proved that all samples had nonlinear refractive indices in the range of 10−7 cm2/W with a positive sign and self-focusing behavior. Moreover, the third-order susceptibility and the figure of merit were found to be in the order of 10−5 esu and 10−4 esu cm, respectively. The findings of this study provide insight about modified 2D materials and expand the use of MoSe2 nanosheets in photonic devices.

Investigation of structural and optical properties of deposited mercury sulphide thin layers as a function of growth time

ABSTRACT Mercury sulphide (HgS) films were deposited on glass substrates by the chemical bath deposition method (CBD) at different deposition times and then post-annealed at 300°C for about 1 h. The structure of the produced films was studied by X-ray diffraction (XRD). Elemental analyses of the prepared films were characterised by the energy-dispersive X-ray analysis (EDX). The film’s optical properties were measured by spectrophotometry. The optical constants of films were derived from reflectivity curves by the Kramers–Kronig method. The absorption coefficient, extinction coefficient, refractive index, real and imaginary parts of the dielectric constant, and the optical band gaps were calculated. X-ray diffraction details showed a crystalline phase for all deposited HgS thin films with trigonal structures. Optical results exhibited photoluminescence property for HgS thin films. By increasing deposition time, the dielectric property, refractive index and band gap values are increased. The values obtained for electronic and optical properties of HgS are essentially crucial for applications in optoelectronics.

VECTOR: Very deep convolutional autoencoders for non‐resonant background removal in broadband coherent anti‐Stokes Raman scattering

AbstractRapid label‐free spectroscopy of biological and chemical specimen via molecular vibration through means of broadband coherent anti‐Stokes Raman scattering (B‐CARS) could serve as a basis for a robust diagnostic platform for a wide range of applications. A limiting factor of CARS is the presence of a non‐resonant background (NRB) signal, endemic to the technique. This background is multiplicative with the chemically resonant signal, meaning the perturbation it generates cannot be accounted for simply. Although several numerical approaches exist to account for and remove the NRB, they generally require some estimate of the NRB in the form of a separate measurement. In this paper, we propose a deep neural network architecture called Very dEep Convolutional auTOencodeRs (VECTOR), which retrieves the analytical Raman‐like spectrum from CARS spectra through training of simulated noisy CARS spectra, without the need for an NRB reference measurement. VECTOR is composed of an encoder and a decoder. The encoder aims to compress the input to a lower dimensional latent representation without losing critical information. The decoder learns to reconstruct the input from the compressed representation. We also introduce skip connection that bypass from the encoder to the decoder, which benefits the reconstruction performance for deeper networks. We conduct abundant experiments to compare our proposed VECTOR to previous approaches in the literature, including the widely applied Kramers–Kronig method, as well as two another recently proposed methods that also use neural networks.

Dependence of Growth Time on Optical Properties of Mercury Sulfide Thin Layers Synthesis by Chemical Bath Deposition Method; Based on KramersKronig Relations

Mercury sulfide films were deposited on amorphous glass substrates from aqueous solutions by chemical bath deposition method (CBD) at same temperature and different deposition times. Produced layers were post annealed at 250°C about one hour. X-ray diffraction (XRD) was used to study of film’s crystalline structural. Their optical properties were measured by spectrophotometry in the spectra range of 400-850 nm, Kramers-Kronig method was used for the analysis of reflectivity curves of HgS films to obtain the optical constants of films in order to investigation of relation between deposition time and optical properties. According to X-ray diffraction details, all thin films showed crystalline phase with a preferential growth along the (220) planes. Optical results have been shown photolminisance property for HgS produced thin films. By increasing deposition time, the dielectric property, refractive index and band gap values are increased.

A Low-wavelength host absorption edge of LiB-=SUB=-3-=/SUB=-O-=SUB=-5-=/SUB=- and Li-=SUB=-2-=/SUB=-B-=SUB=-4-=/SUB=-O-=SUB=-7-=/SUB=- crystals

We have carried out an experimental study of the VUF- edge of the optical host absorption of lithium borate crystals LiB3O5 (LBO) and Li2B4O7 (LTB). The transmission (T=293 K) and absorption (T=80, 293 K) spectra were studied, the short-wavelength edge of the transparency band (cutoff wavelength) and the energy position of the edge fundamental absorption at which the absorption coefficient k=50 cm-1 were determined. The absorption edge temperature shift coefficient -(3-4.7)·10-4 eV/K was determined. The dependence of the absorption edge parameters of oriented LBO normal Y and LBO normal X crystals has been studied. Based on low-temperature reflection spectra (T=10 K, theta=17o, E=4-32 eV) the Kramers-Kronig method was used to calculate the spectra of optical constants: refractive index (n) and absorption index (k), real (ε1) and imaginary (ε2) parts of the complex permittivity, as well as the absorption coefficient μ. The lowest energy peak, due to electronic transitions from the top of the valence band to the states of the bottom of the conduction band, was studied in the ε_2(E) spectrum, the thresholds for interband transitions were determined (Eg at T=10 K): 8.5-8.6 eV(LBO normal Y), 8.6-8.7 eV (LBO normal X) and 8.8-8.9 eV (LTB). The origin of the fundamental absorption edge of lithium borates is discussed. Keywords: Lithium triborate LiB3O5, lithium tetraborate Li2B4O7, host absorption edge, optical properties.

A Low-Wavelength Host Absorption Edge of Cesium-Lithium Borate CsLiB-=SUB=-6-=/SUB=-O-=SUB=-10-=/SUB=-

We have carried out an experimental study of the VUV edge of the optical host absorption of cesium-lithium borate crystals CsLiB6O10 (CLBO). The transmission (T=293 K) and absorption (T = 80, 293 K) spectra were studied, the short-wavelength edge of the transparency band (cutoff wavelength) and the energy position of the edge fundamental absorption at which the absorption coefficient k=50 cm-1 were determined. The absorption edge temperature shift coefficient -5.5·10-4 eV/K was determined. Based on low-temperature reflection spectra (T=10 K, theta=17o, E=7-30 eV) the Kramers-Kronig method was used to calculate the spectra of optical constants: refractive index (n) and absorption index (k), real (ε1) and imaginary (ε2) parts of the complex permittivity , as well as the absorption coefficient μ. The lowest energy peak, due to electronic transitions from the top of the valence band to the states of the bottom of the conduction band, was studied in the ε2(E) spectrum, the thresholds for interband transitions were determined Eg=7.95 eV. The origin of the fundamental absorption edge of cesium-lithium borate is discussed. Keywords:: Cesium-lithium borate CsLiB6O10 (CLBO), host absorption edge, optical properties.

First principles DFT calculations of the optical properties of A4BX6 group crystals

The results of investigating of the electron band energy structure and optical properties of A4BX6 (Tl4HgI6 and Tl4CdI6) group crystals are presented. The energy band structures of Tl4HgI6 and Tl4CdI6 crystals are calculated from the first principles within generalized gradient approximation (GGA). The band structure and reflection index were calculated using a pseudopotential method in the framework of density functional theory. Optical absorption edge in Tl4HgI6 and Tl4CdI6 is formed by direct optical transitions. The spectral dependence of the reflection index was calculated on the basis of the energy band results with using the Kramers–Kronig method. The spectra show pronounced anisotropy in E||a(b) and E||c polarizations. It was found the anomalous by large values of the birefringence (Δn &gt; 0.18 for Tl4HgI6 and Δn &gt; 0.03 for Tl4CdI6) in the visible and near infrared region.

Characterization of silver doped In2S3 films

Silver doped Indium sulphide thin films with different [Ag/In] molar ratio concentrations (0, 0.9, 1.0, 1.1) were deposited on glass substrates using chemical bath deposition method. The structural, morphological, optical and electrical properties are characterized using XRD, EDAX, SEM, AFM, spectrophotometer and Hall measurement system, respectively. Kramers-Kronig method was used to obtain optical constants of the films. It is found that Ag can change physical properties of Indium sulfide thin films, depending on the Ag concentration. XRD results show the incorporation of Ag concentration did not change the structure of In2S3. Doped films had rough surfaces. As the [Ag/In] molar ratio increased, conductivity increases and optical direct band gap energy decreases from 2.75 to 2.38 eV.

Consequence of Mn and Ni doping on structural, optical and magnetic characteristics of ZnO nanopowders: the Williamson–Hall method, the Kramers–Kronig approach and magnetic interactions

The crucial role of Ni and Mn dopants on the structural, optical, and magnetic characteristics of the zinc oxide (ZnO) nanopowders have been investigated in detail using XRD, diffuse reflectance spectroscopy (DRS), Kramers–Kronig (KK), and vibrating sample magnetometer (VSM). The structural analysis indicates that all patterns are mostly assigned to the hexagonal wurtzite structure. Also, XRD analysis shows that the Ni2+ and Mn2+ ions replace Zn2+ ions which causes lattice strain. Other than the Debye–Scherrer method, the Williamson–Hall method has also been applied to study the influence of strain in the calculation of the crystallite size. Based on DRS data, the band gap of the nanoparticles (NPs) is calculated by Tauc relation in two different ways. The band gap of the synthesized undoped ZnO NPs decreases from 3.25 to 3.23 and 3.15 eV through Ni and Mn doping, respectively. The band gap investigation shows a red-shift with Ni and Mn doping. The width of the localized states or sub-band gap absorption edge (often termed Urbach energy) of the samples was determined by the curves of Ln α versus photon energy hυ. The optical parameters such as complex refractive index, complex dielectric function, and absorption coefficient of the samples were evaluated by applying KK method. Investigating on magnetic properties showed a room temperature ferromagnetic (RTFM) behavior. Also, the interactions and reasons of the observed RTFM mechanisms are examined in detail.