Frequency-dependent Refractive Index Research Articles

Deep neural network ensembles for THz-TDS refractive index extraction exhibiting resilience to experimental and analytical errors.

Terahertz time-domain spectroscopy (THz-TDS) achieves excellent signal-to-noise ratios by measuring the amplitude of the electric field in the time-domain, resulting in the full, complex, frequency-domain information of materials' optical parameters, such as the refractive index. However the data extraction process is non-trivial and standardization of practices are still yet to be cemented in the field leading to significant variation in sample measurements. One such contribution is low frequency noise offsetting the phase reconstruction of the Fourier transformed signal. Additionally, experimental errors such as fluctuations in the power of the laser driving the spectrometer (laser drift) can heavily contribute to erroneous measurements if not accounted for. We show that ensembles of deep neural networks trained with synthetic data extract the frequency-dependent complex refractive index, whereby required fitting steps are automated and show resilience to phase unwrapping variations and laser drift. We show that training with synthetic data allows for flexibility in the functionality of networks yet the produced ensemble supersedes current extraction techniques.

In-depth analysis of ternary NaCuX (X = Se and Te) chalcogenides: Bridging structural elastic, electronic, and optical properties

This study employs density functional theory (DFT) using the full potential linearized augmented plane wave plus local orbital (FP-LAPW+1o) approach to investigate the structural, elastic, electronic, and optical properties of NaCuX (X = Se and Te) compounds. Additionally, the modified Becke-Johanson (TB-mBJ) potential is applied to ensure accurate band gap results. Both compounds exhibit semiconducting behavior with a direct band gap at the Γ point. The computed elastic constants confirm mechanical stability for NaCuSe and NaCuTe, as evidenced by their respective bulk modulus, Young modulus, shear modulus, Poisson's ratio, B/G ratio, and elastic anisotropy. The materials display ductile characteristics, indicated by their B/G ratio and Poisson's ratio. The Debye temperature (θD) reveals that NaCuSe possesses the highest thermal conductivity. A decrease in θD is observed from NaCuSe to NaCuTe due to declining elastic constants. Additionally, anisotropy in acoustic velocities is assessed and discussed. The study's equilibrium structural properties align well with experimental data. Optical properties, including frequency-dependent dielectric function, refractive index, extinction coefficient, absorption coefficient, reflectivity, and energy loss function, are calculated and comprehensively analyzed.

Frequency-dependent nonlinear optical response and refractive index investigation of lactone-derived thermochromic compounds

Nonlinear optical (NLO) switchable materials play a crucial role in the fields of electronics and optoelectronics. The selection of an appropriate switching approach is vital in designing such materials to enhance their NLO response. Among various approaches, thermos-switching materials have shown a 4-fold increase in NLO response compared to other photo-switching materials. In this study, we computationally investigated the geometric, electronic, and nonlinear optical properties of reversible lactone-based thermochromic compounds using the ωB97XD/6-311+G (d,p) level of theory. Molecular orbital studies are employed to analyze the electronic properties of the close and open isomers of these compounds, while time-dependent density functional theory (TD-DFT) analysis is utilized to evaluate their molecular absorption. Our findings reveal that the π-electronic conjugation-induced delocalization significantly influences the ON-OFF switchable nonlinear optical response of the lactone-based thermochromic compounds. Notably, among all compounds, the open isomer of lactone 2 exhibits the highest hyperpolarizability value (6596.69 au). Furthermore, we extended our analysis to investigate the frequency-dependent second and third-order hyperpolarizabilities. The most pronounced frequency-dependent NLO response is observed at 532 nm. Additionally, we calculated the refractive index of these thermochromic compounds to further assess their nonlinear optical response. The open isomer of lactone 1 demonstrates the highest refractive index value (3.99 × 10−14 cm2/W). Overall, our study highlights the excellent potential of reversible thermochromic compounds as NLO molecular thermos-switches for future applications.

Role of Delocalization, Asymmetric Distribution of π-Electrons and Elongated Conjugation System for Enhancement of NLO Response of Open Form of Spiropyran-Based Thermochromes.

Switchable nonlinear optical (NLO) materials have widespread applications in electronics and optoelectronics. Thermo-switches generate many times higher NLO responses as compared to photo-switches. Herein, we have investigated the geometric, electronic, and nonlinear optical properties of spiropyranes thermochromes via DFT methods. The stabilities of close and open isomers of selected spiropyranes are investigated through relative energies. Electronic properties are studied through frontier molecular orbitals (FMOs) analysis. The lower HOMO-LUMO energy gap and lower excitation energy are observed for open isomers of spiropyranes, which imparts the large first hyperpolarizability value. The delocalization of π-electrons, asymmetric distribution and elongated conjugation system are dominant factors for high hyperpolarizability values of open isomers. For deep understanding, we also analyzed the frequency-dependent hyperpolarizability and refractive index of considered thermochromes. The NLO response increased significantly with increasing frequency. Among all those compounds, the highest refractive index value is observed for the open isomer of the spiropyran 1 (1.99 × 10-17 cm2/W). Molecular absorption analysis confirmed the electronic excitation in the open isomers compared to closed isomers. The results show that reversible thermochromic compounds act as excellent NLO molecular switches and can be used to design advanced electronics.

Terahertz Vibrational Modes of Sodium Magnesium Chlorophyllin and Chlorophyll in Plant Leaves

The low-frequency (terahertz) vibrational spectroscopy has been investigated experimentally for two chlorophyll species, Chl-a and one of its magnesium derivatives (Chl-Mg-Na). The combination of terahertz time-domain spectroscopy and Fourier transform infrared spectroscopy has enabled a broad frequency range to be covered (0.2 to 18 THz). For Chl-Mg-Na, the terahertz spectra show clear and well-marked features at 1.44, 1.64, and 1.83 THz dominated by intermolecular interactions. The frequency dependent refractive index and absorption coefficient of Chl-Mg-Na were both determined using the Fit@TDS software. Below 1.0 THz, a refractive index of 2.09 was measured. In order to acquire further understanding of the observed vibrational modes, a detailed study of the temperature dependence of the line positions of the lowest modes in Chl-Mg-Na was performed. As the temperature was increased from 88 K to 298 K, the feature at 1.83 THz experienced a notable red shift of frequency and line shape broadening, whereas the feature at 1.44 THz showed little change. These results suggest that the 1.83 THz feature is dominated by intermolecular motions occurring over the crystalline unit cell of the Chl-Mg-Na molecular crystal. Finally, terahertz time-domain spectroscopy was used to acquire the spectra of an ornamental plant bearing yellow-green variegated leaves (ivy, Aureomarginata variety), the yellow sectors having lower chlorophyll content compared to the green sectors. In dehydrated green tissue, the chlorophyll molecules showed well-marked intermolecular vibrational modes at 1.86 THz, indicating that chlorophyll molecules are prone to packing with an ordered molecular arrangement. These results demonstrate the potential application of THz spectroscopy in the field of agronomy.

Study of birefringence inside nanocrystalline Zinc Oxide thin films using terahertz spectroscopy

We present experimental characterizations of nanocrystalline Zinc Oxide (ZnO) thin films in far-infrared (terahertz) frequency region using terahertz time-domain spectroscopy. A time dependent profile, frequency dependent transmission coefficient, refractive index, absorption coefficient and optical density of ZnO thin films are measured in the terahertz regime. A birefringence is observed as a result of TO–LO phonon splitting took place in the ZnO deposited at 400 °C substrate temperature, while at low substrate temperature of 200 °C there is no sign of birefringence. Thus, it can be clearly evidenced that the presence of birefringence in ZnO is correlated with crystallinity exists inside of the thin films. Absorption behaviour of ZnO nano-crystalline thin films shows the potential use of it for future THz photonics devices. RF magnetron sputtering is the key for the deposition of nanocrystalline ZnO thin films on Si (100) substrate at different temperatures. The X-ray diffraction pattern of ZnO thin films were confirmed the formation of wurtzite hexagonal structure and nanocrystalline nature of the deposited ZnO thin films.

High energy Compton scattering, electronic structure and optical response of zirconium substituted lead titanate

The electron momentum densities of PbTi1-xZrxO3 (x = 0, 0.4 and 1) measured using high energy 137Cs Compton spectrometer are reported. To validate the measurements, theoretical Compton profiles (CPs) and electronic structure of PbTi1-xZrxO3 (x = 0, 0.4 and 1) are computed using the linear combination of atomic orbitals (LCAO) method. Differences between experimental and theoretical CPs unveil that the hybrid scheme (WC1LYP) is more applicable to account exchange and correlation energies in such materials than the other frequently used generalized gradient approximation (GGA) potentials. Experimental CPs based on scaling of equal-valence-electron-density show a more covalent character of PbTiO3 than that of PbTi0.6Zr0.4O3 and PbZrO3, which is in consonance with the present LCAO based Mulliken's population charge reorganization data. The density of states, dielectric constants, frequency-dependent absorption spectra and refractive indices are computed using the modified Becke-Johnson potential as incarnated in the full-potential augmented plane wave method. The present optical response suggests the possibility of using PbTi1-xZrxO3 in the device for ultra-violet detection.

THz Time-Domain Ellipsometer for Material Characterization and Paint Quality Control with More Than 5 THz Bandwidth

Quality control of car body paint in the automotive industry is a promising industrial application of terahertz technology. Terahertz time-domain spectroscopy in reflection geometry enables accurate, fast, and nondestructive measurement of individual layer thicknesses of multi-layer coatings. For high precision thickness measurements, the frequency dependent complex refractive index of all layers must be calibrated very accurately. THz time-domain ellipsometry is self-referencing and provides reliable, frequency resolved material properties with high signal-to-noise ratio. The method is characterized by a high sensitivity to optical material properties and layer thicknesses. We present characterization results in the frequency range 0.1–6 THz for typical automotive paints and different substrates such as polypropylene (PP), which features a high material anisotropy. We demonstrate that the broadband material properties derived from ellipsometry allow for inline thickness measurements of multi-layer car body paints with high accuracy.

New lead‐free double perovskites X 2 GeI 6 (X = K, Rb, Cs) for solar cells, and renewable energy as an alternate of hybrid perovskites

Recently, the unique double perovskites are continuously being used for solar cells and thermoelectric applications because of stable structures and high energy conversion efficiency. We addressed the optical and transport characteristics of X2GeI6 (X = K, Rb, Cs) by first-principle calculations. The tolerance factor confirms the structural stability. The computed band gaps 1.27 eV (K2GeI6), 1.24 eV (Rb2GeI6), and 1.13 eV (Cs2GeI6) plunge the maximum absorption in visible light zone. The first absorption bands 459 to 826 nm for K2GeI6, 477 to 885 nm for Rb2GeI6, and 653 to 992 nm for Cs2GeI6 are outstanding for visible light solar cells. While the second absorption bands are for other optoelectronic devices like surgical equipment. The optical characteristics are debated by frequency-dependent dielectric constants (ε1, ε2), refractive index, and absorption coefficient. Thermoelectric performance is evaluated by large values of power factor and ultralow values of thermal conductivity for both n- and p-type of charge carriers. Highlights An alternative of organic-inorganic and Pb based perovskites Ideal band gaps 1.27 eV, 1.24 eV, and 1.13 eV of K2GeI6, Rb2GeI6, and Cs2GeI6 for solar cells Absorption in the visible region increases their potential for solar cells. Observation of ultralow lattice thermal conductivity.

Frequency-dependent focal length of a plano-spherical convex subsonic index lens

This study aims to investigate the frequency-dependent characteristics of the focal length of an acoustic lens made of a material with a frequency-dependent acoustic refractive index (ARI). For this purpose, an exchangeable plano-spherical convex subsonic index lens (PSCSIL) was fabricated using a polydimethylsiloxane (PDMS) material. The ARI of the lens material was evaluated via the tone-burst through-transmission method over the frequency range of 1–10 MHz. The frequency dependence of the focal length of the fabricated PSCSIL was evaluated through graphical analysis of the acoustic field scanned by a hydrophone as well as of that simulated using the finite element method. The measured ARI and focal length were observed to be dependent on frequency. The simulated and measured focal lengths of the PSCSIL exhibited a great discrepancy with their respective values predicted using the conventional focal length equation. This discrepancy was further studied using the ray-tracing method and is described in the discussion section. In conclusion, the spherical curvature of PSCSIL does not induce the convergence of rays to meet in a point. The ray tracing method does not take into account the phase complexity of the near-field region inside the lens. This causes the actual focal length to be shorter than the predicted one.

Simulated infrared and Raman spectroscopy, complex dielectric function and refractive index dataset of monoclinic C2/m stoichiometric clinochlore Mg6Si4O10(OH)8 as obtained from Density Functional Theory.

This article reports a simulated dataset of the vibrational (infrared and Raman) and optical properties (complex dielectric function and refractive index) of clinochlore, an important mineral belonging to the phyllosilicate family [1]. The data here reported were calculated from ab initio Density Functional Theory (DFT) simulations at B3LYP level, including a correction for the dispersive forces (B3LYP-D* approach) and all-electron Gaussian-type orbitals basis sets. This dataset was calculated between 0 cm–1 and 4000 cm–1 and comprises infrared, reflectance and Raman spectra, frequency-dependent complex dielectric function and complex refractive index of clinochlore. The data was validated against available experimental spectroscopic results reported in literature and can be of help in several application fields, for instance fundamental georesource exploration and exploitation, in applied mineralogy, geology, material science, and as a reference to assess the quality of other theoretical approaches.

High-precision THz-TDS via self-referenced transmission echo method.

Terahertz time-domain spectroscopy (TDS) is a powerful characterization technique which allows for the frequency-dependent complex refractive index of a sample to be determined. This is achieved by comparing the time-domain of a pulse transmitted through air to a pulse transmitted through a material sample; however, the requirement for an independent reference scan can introduce errors due to laser fluctuations, mechanical drift, and atmospheric absorption. In this paper, we present a method for determining complex refractive index without an air reference, in which the first pulse transmitted through the sample is compared against the "echo", where the internal reflections delay the transmission of the echo pulse. We present a benchmarking experiment in which the echo reference method is compared to the traditional air method, and show that the echo method is able to reduce variation in real refractive index.

Design of a one-way multichannel and wide-angle absorber based on the one-dimensional superconductor photonic crystals with the cascaded quasi-period structure

In this paper, a one-way multichannel and wide-angle absorber based on the one-dimensional superconductor photonic crystals (SPCs) in the terahertz regime is realized via splicing the classical quasi-period sequences and manipulating the ambient temperature properly, whose characteristics and mechanisms are theoretically investigated by the transfer matrix method. The preeminent absorbing features of the proposed SPCs are ascribed to the temperature and frequency-dependent refractive index of the superconductor components, whose imaginary part plays a role in giving rise to the high dissipation. Additionally, when the thickness of the whole structure is of the order of the incident electromagnetic wavelength, the one-way absorption and the reflection in the opposite direction can be perfectly obtained. The calculated results demonstrate that the relative bandwidths of the one-way effective absorption regions in our proposed SPCs can reach to 51.94%, 30.18%, and 19.12%, respectively, and the maximum angle where the wide-angle absorption region can sustain is up to 84° for TM wave by controlling the related parameters. Moreover, the impacts of the external factors such as temperature and incident angle and the interior elements including the thicknesses of diverse layers and the recursive numbers of the cascading sequences on the absorbing performance are also taken into account. To explicitly verify the reliability of our model, the impedance matching and the average refractive index are introduced for explaining the splendid multichannel absorption. As a whole, our research offers effective guidance for the theoretical excogitation of the multichannel and wide-angle absorber in the optical field.

Optical properties in the infrared range of the birefringent α-GeO2 single crystal

The components of the frequency-dependent complex refractive index were determined indirectly for the new non-centrosymmetric α-GeO2 crystal using polarized Fourier transform infrared reflectivity spectra measured in the far- and mid-infrared spectral region at room temperature. All the longitudinal- and transverse-optical infrared active modes with E and A2 symmetry, according to the D3 point group, were identified and localized within the 100−1000 cm−1 range in very good agreement with a previous first-principles based calculation. For the A2- and E-type modes, both the longitudinal- and transverse-optical splitting were detected. The refractive indices no (E→ ⊥c) and ne (E→ //c) in the infrared domain present considerably higher values than the ones observed in the visible light range, and the high birefringence would find application in many optical devices.

Characterization of volatile organic compounds (VOCs) in their liquid-phase by terahertz time-domain spectroscopy.

In this work the terahertz spectra of benzene, toluene, p-xylene and styrene-four volatile organic compounds (VOCs) of interest in environmental pollution studies-have been measured in their liquid phase at room temperature using terahertz time-domain spectroscopy (THz-TDS). Their frequency-dependent refractive index and absorption coefficient have been extracted and analyzed in the spectral range from 0.2 to 2.5 THz. The optical properties of bi-component VOCs mixtures have also been investigated and described in terms of a linear combination of pure VOCs optical components.

BaTeMo2O9 crystals: optical properties and applications in the terahertz range

The optical properties of the α/β-BaTeMo2O9 (α/β-BTM) crystal in the terahertz range were characterized by the terahertz time domain spectroscopy (TDS) system. Frequency-dependent refractive indices and absorption coefficients of two crystals were measured from 0.2 to 2 THz, and discussions and comparisons were made on birefringence, absorption and phonon modes by referring to their structures. The Sellmeier equations for both crystals were also fitted in their transparent ranges. Based on the mode properties and parameters, a feasible scheme for terahertz generation via stimulated polariton scattering (SPS) with β-BTM was proposed and the angle tuning characteristics were calculated. Simulations show that β-BTM has great potential and should be more advantageous than LiNbO3 in generating high-frequency terahertz waves.

Internal exchange interaction of Tb+3 ions and influence of Si substitution on structural, electronic, magnetic and optical properties of YNi4Si -type TbNi5−xSix (x = 0, 1, 2) compounds

We report the FPLAPW + lo study on new YNi4Si-type TbNi5−xSix (x = 0, 1, 2) compounds. The YNi4Si structure is a new structure type, which is an orthorhombic derivative of CaCu5 structure. The optimized lattice constants and internal cell parameters are in agreement with the available data. The calculated band structures show the valence band (VB) is mainly dominated by Ni–3d states in the energy range 0–4 eV below the EF, whereas conduction band (CB) by Tb–4f states about 2 eV above the EF. With the substitution of Si atoms for Ni, total magnetic moments decreases from 8.308 μB/f.u. (x = 0) to 6.052 μB/f.u. (x = 1), whereas magnetic moments on Tb+3ions increase from 5.92 μB/atom (x = 0) to 6 μB/atom (x = 1, 2) and the induced moments on Ni+2(x = 1, 2) ions decrease rapidly to a negligibly small value. Charge density estimates show that Tb-5d, Ni-3d and Si-3porbitals are mainly involved in bondings and there is a weak hybridization between Ni-3d and Si-3porbitals which varies with Si substitution. Furthermore, the complex role played by the Tb-5d1 electrons is also investigated, and found to be partly involved in metallic bondings as well as in intra-atomic charge transfer from 5d1 to 4f8 states. The calculated interband optical conductivity spectra reproduce the main features of the experimental spectra well and also reveal their metallic nature. Frequency-dependent refractive index, η(ω), the reflectivity, R(ω) and the extinction coefficient, κ(ω) for (x = 0, 1, 2) are also calculated for the incident radiation up to 12 eV.

The density functional study of electronic structure and optical properties of gadolinium monophosphate

The lattice constants, electronic structure, and optical properties of Gadolinium monophosphate GdPO4 are investigated using the first principles calculations. Our calculated lattice constants are in excellent agreement with the available theoretical and experimental data. Band structure calculations of GdPO4 depict insulator nature with a direct band gap. Density of states, Mulliken atomic charges and bond overlap populations have been obtained and discussed. The linear optical properties, namely the frequency-dependent dielectric function, refractive index, extinction coefficient, absorption coefficient, reflectivity and energy-loss function, have been calculated and analyzed in a wide energy range up to 20 eV. The calculated frequency-dependent optical function spectra show an optical anisotropy. The estimated results of dielectric constant and refractive indexes fall in the range of the phosphate experimental data.

Simultaneous acquisition of complex transmittance and birefringence with two counter-rotating, circularly polarized THz pulses.

Here we demonstrate simultaneous measurements of the complex transmittance and birefringence using left- and right-handed circularly polarized terahertz (THz) pulses. We change the polarization of the THz pulses periodically by modulating the polarization of the pump pulses directed onto a ZnTe (111) crystal, and we convert linear to circular polarization using a broadband THz quarter-wave retarder. By integrating the alternating-emission system with the polarization-sensitive terahertz time-domain spectrometer, we are able to obtain the electric-field vector of the transmitted terahertz pulses for both the left- and right-handed circular polarizations. Utilizing this technique, we are able to measure simultaneously the frequency-dependent complex refractive indices (real and imaginary parts) and the orientations of the slow and fast axes of birefringent materials, a quartz disc and a barium borate crystal, in a single temporal sweep.

Maximum reflectance and transmittance of films coated with gapped graphene in the context of the Dirac model

The analytic expressions for the maximum and minimum reflectance of optical films coated with gapped graphene are derived in the application region of the Dirac model with account of multiple reflections. The respective film thicknesses are also found. In so doing the film material is described by the frequency-dependent index of refraction and graphene by the polarization tensor defined along the real frequency axis. The developed formalism is illustrated by an example of the graphene-coated film made of amorphous silica. Numerical computations of the maximum and minimum reflectances and respective film thicknesses are performed at room temperature in two frequency regions belonging to the near-infrared and far-infrared domains. It is shown that in the far-infrared domain the graphene coating makes a profound effect on the values of maximum reflectance and respective film thickness leading to a relative increase of their values by up to 65% and 50%, respectively. The maximum transmittance of a graphene-coated film of appropriately chosen thickness is shown to exceed 90%. Possible applications of the obtained results are discussed.