Complex Refractive Index Spectra Research Articles

(Invited) High Temperature Exciton Properties in Aggregated Single-Walled Carbon Nanotubes

Individual single-walled carbon nanotubes (SWCNTs) at high temperatures have been reported to generate narrow-band thermal radiation in the near-infrared region due to thermally robust excitonic effects [1,2]. This phenomenon potentially offers a new opportunity for utilizing exciton properties in thermal engineering such as thermophotovoltaic energy harvesting requiring excellent wavelength selective near-infrared thermal emitter. However, for its realistic applications in macroscale, it is necessary to make the distinct exciton effect available under high temperature conditions in macroscopic assemblies of SWCNTs. As a first step toward this goal, we have recently determined broadband complex refractive index spectra of single-chirality SWCNT membranes in which SWCNTs are aligned two-dimensionally in a plane [3] and reported their birefringent properties [4]. In the presentation, we will discuss the change in the optical spectra of SWCNT assemblies with increasing temperature, as well as how the aggregation states affect the exciton properties. [1] T. Nishihara, A. Takakura, Y. Miyauchi, and K. Itami, Nat. Commun. 9, 3144 (2018). [2] S. Konabe, T. Nishihara, and Y. Miyauchi, Opt. Lett. 46, 3021 (2021). [3] T. Nishihara, A. Takakura, M. Shimasaki, K. Matsuda, T. Tanaka, H. Kataura, and Y. Miyauchi, Nanophotonics 11, 1011 (2022). [4] H. Wu, T. Nishihara, A. Takakura, K. Matsuda, T. Tanaka, H. Kataura, and Y. Miyauchi, Carbon, in press.

A first-principles investigation on the structural, electronic and optical characteristics of tetragonal compounds XAgO (X = Li, Na, K, Rb)

First-principles calculations employing the density functional theory full-potential (linearized) augmented plane-wave plus local orbitals (FP-(L)/APW + lo) method were conducted to investigate the structural, electronic and optical characteristics of silver-based ternary oxides XAgO (X = Li, Na, K, and Rb). The GGA-PBEsol and TB-mBJ functionals were employed to describe the exchange-correlation potential. The optimized lattice parameters and atomic positions obtained from the calculations exhibit good agreement with both theoretical predictions and experimental measurements. Various exchange-correlation functionals were employed to evaluate the electronic properties, revealing that the newly developed Tran–Blaha modified Becke–Johnson functional yields a significant improvement in the band gap value. All XAgO compounds under consideration are categorized as semiconductor materials where the band gap value decreases as the atomic size of the X element increases. The study also explored the total and site-projected l-decomposed densities of states. Additionally, the complex dielectric function, refractive index, extinction coefficient, reflectivity, and loss function spectra were calculated for the incident radiation polarized parallel to both the [100] and [001] crystalline directions. The interband transitions that contribute effectively to the observed peaks in the imaginary part of the dielectric function were identified.

Birefringent optical responses of single-chirality carbon nanotube membranes

Membranes composed of single-walled carbon nanotubes (SWCNTs) with a specific chiral structure (chirality) possess unique optical properties dominated by thermally robust quasi-one-dimensional excitons. Therefore they have emerged as promising materials for photonic and/or thermo-optic applications. As SWCNTs in the membranes are usually aligned two-dimensionally in a plane, and the optical responses of individual SWCNTs are highly anisotropic, the macroscopic responses of membranes are expected to depend on the light-propagation direction. However, the complex refractive-index spectra of some membrane axes are unknown, hindering the optical design of SWCNT-based devices that respond to arbitrarily propagating light. Here, we report the anisotropic complex refractive index spectra of a single-chirality SWCNT membrane fabricated via vacuum filtration. The polarization- and angle-resolved reflection spectra were obtained in the near-infrared-to-visible region. All spectral features in different polarizations and incident angle configurations were consistent with a uniaxial birefringent membrane, reflecting the random in-plane orientations of the SWCNTs. The ordinary (in-plane) refractive index spectra presented a series of sharp resonances of parallel-polarized excitons. The extraordinary (out-of-plane) refractive index in the 0.8–2.4 eV range was determined as ∼1.9. The extraordinary spectra included small but indispensable contributions from the cross-polarized exciton resonance, which are necessary for properly predicting the angle-dependent optical responses of the membrane. By completely unveiling the birefringent optical responses of single-chirality SWCNT membranes, this work paves the way for integrating SWNCT membranes into precise and diverse photonic and/or thermo-optic devices.

Pressure-induced metallization in the absence of a structural transition in the layered transition-metal dichalcogenide ZrSe2.

First-principles calculations were carried out on the ZrSe2 compound, which has been of interest owing to its technologically important physical properties. The structural, electronic and optical properties of this compound were investigated under pressure through the plane wave pseudopotential approach within the framework of density functional theory. A comparison between the computed crystal structure parameters and the corresponding experimental counterparts shows a very good agreement between them. Fitting the pressure-volume data using the third-order Birch-Murnaghan equation of state yielded a bulk modulus B0 = 38.17 GPa and a pressure derivative of bulk modulus B'0 = 8.2 for hexagonal ZrSe2. The relationship between the band structure and pressure is revealed. We calculated the total density of state (TDOS) under different pressures and partial density of state (PDOS) from 0 to 10 GPa. According to our calculations, metallization of hexagonal ZrSe2 is predicted to occur at around 10 GPa and pressure-induced band-gap engineering reveals the transformation of the indirect to direct band gap with increasing pressure. Furthermore, optical properties, such as the complex dielectric function, refractive index and reflectivity spectra of this compound, were studied for incident electromagnetic waves in an energy range up to 45 eV. The contributions to various transition peaks in the optical spectra are analyzed and discussed with the help of the energy-dependent imaginary part of the dielectric function.

(Invited) Anisotropy in Complex Refractive Index Spectra of Single-Chirality-Enriched Carbon Nanotube Films

Toward macroscopic applications of exceptional optical properties of single-walled carbon nanotubes (SWCNTs), we reported in-plane complex refractive index spectra [1] of various single-chirality-enriched [2] SWCNTs films in which the SWCNTs are mostly oriented in two dimensions parallel to the film surface. However, in order to describe the anisotropic optical responses of such SWCNT films for incident light from all the directions, out-of-plane refractive index spectra are also required, in addition to the in-plane ones. We will report complete broadband complex refractive index spectra of single-chirality-enriched SWCNTs films for in-plane and out-of-plane optical responses. [1] T. Nishihara, A. Takakura, M. Shimasaki, K. Matsuda, T. Tanaka, H. Kataura, and Y. Miyauchi, Nanophotonics 11, 1011 (2022). [2] Y. Yomogida, T. Tanaka, M. Zhang, M. Yudasaka, X. Wei, and H. Kataura, Nat. Commun. 7, 12056 (2016).

Violet phosphorus with high-index and low-loss: A promising candidate for nanophotonics applications

The recent synthesis and characterization of violet phosphorus (VP) demonstrate that it is the most stable allotrope of phosphorus, which could become a promising 2D layered semiconductor with potential applications in optoelectronic and electronic devices. However, experiments exploring the complex refractive index or permittivity have yet to be performed, hindering further application access. Due to the small size of the VP crystal sample available by the current growth method, the measurement for the complex refractive index is challenging. In this work, coherent acoustic phonon spectroscopy was performed first in the a–b plane using polarization-resolved pump-probe spectroscopy, revealing negligible anisotropy in the refractive index in the VIS–NIR regime (400–1000 nm). Then, the non-polarized reflectance spectra of VP films with different thicknesses on Si in the VIS–NIR regime were collected. The complex refractive index spectra were obtained by fitting the reflectance spectra with Fresnel's law considering multiple reflections in thin films. It was found that VP has high refractive indices and low extinction coefficients in the spectral range of 560–1000 nm, based on which a metasurface with VP nanodisks could achieve a high reflection band in the VIS–NIR regime by simulation. These results unveil the striking potential of VP for nanophotonics applications.

Optical properties of pulsed dc magnetron sputtered thin film tantalum nitride by spectroscopic ellipsometry

Ellipsometric spectra of polycrystalline thin film tantalum nitride (TaN) have been collected and analyzed to obtain the complex dielectric function (ɛ = ɛ1 + iɛ2) and complex refractive index (N = n + ik) spectra over the photon energy range of 0.059–8.500 eV. Complex optical properties are obtained for TaN in the as-deposited state and rapid thermal annealed at 750 °C for 30 s post deposition. A parametric expression including the contribution from intraband and interband transitions along with a structural model is used and fitted to experimental ellipsometric spectra using iterative least-square regression, which minimizes the unweighted error function or mean square error to extract complex optical properties. The parametric expression developed in this work is successful in describing and differentiating the optical response of measured as-deposited and annealed TaN films and can potentially be used to analyze the optical properties of similar TaN films regardless of their deposition techniques.

Optical determination of layered-materials InSe thickness via RGB contrast method and regression analysis

Indium selenide (InSe) features intriguing thickness-dependent optoelectronic properties, and a simple, and precise way to identify the thickness is essential for the rapid development of InSe research. Here, a red, green, and blue (RGB) color contrast method with regression analysis for quantitative correlation of three optical contrasts from RGB channels with the InSe thickness (1–35 nm), is demonstrated. The lower accuracy of the thickness identification obtained from the individual channels was discussed. Moreover, the effective refractive indices in the three RGB regions can be extracted from the Fresnel equation and numerical analysis by finding the best fit to the experimental optical contrast. After further consideration of the wavelength-dependent refractive indices, the slope of the regression line between the estimated thickness and that obtained from the atomic force microscope was improved from 1.59 ± 0.05 to 0.97 ± 0.02. The complex refractive index spectra of InSe (1–10 layers) generated from ab initio numerical calculation results were also adopted to identify the InSe thickness. Compared to dispersion, the evolution of the band structure had less effect on thickness identification. This work could be extended to other layered materials, facilitate the thickness-dependent study of layered materials, and expedite the realization of their practical applications.

Empirical formulation of broadband complex refractive index spectra of single-chirality carbon nanotube assembly

Abstract Assemblies of single-walled carbon nanotubes with a specific chiral structure are promising future optofunctional materials because of their strong light–matter coupling arising from sharp optical resonances of quasi-one-dimensional excitons. Their strong optical resonances, which lie in the infrared-to-visible wavelength region, can be selected by their chiralities, and this selectivity promises a wide range of applications including photonic and thermo-optic devices. However, the broadband complex optical spectra of single-chirality carbon nanotube assemblies are scarce in the literature, which has prevented researchers and engineers from designing devices using them. Here, we experimentally determine broadband complex refractive index spectra of single-chirality carbon nanotube assemblies. Free-standing carbon nanotube membranes and those placed on sapphire substrates were fabricated via filtration of the nanotube solution prepared by the separation method using gel chromatography. Transmission and reflection spectra were measured in the mid-infrared to visible wavelength region, and the complex refractive indices of nanotube assemblies were determined as a function of photon energy. The real and imaginary parts of the refractive indices of the nanotube membrane with a bulk density of 1 g cm−3 at the first subband exciton resonance were determined to be approximately 2.7–3.6 and 1.3i–2.4i, respectively. We propose an empirical formula that phenomenologically describes the complex refractive index spectra of various single-chirality nanotube membranes, which can facilitate the design of photonic devices using carbon nanotubes as the material.

A comparative study of structural, thermal, and optoelectronic properties between zircon and scheelite type structures in SrMoO4 compound: An ab-initio study

First principles calculations were carried out on the SrMoO4 compound which has been of interest owing to its technologically important physical properties. The structural, electronic, optical and thermal properties of this compound have been investigated under low pressure (LP) through the full potential linearized augmented plane wave method (FP-LAPW) within the framework of density functional theory. It is found that the phase transition from zircon to scheelite type structure occurs at negative pressure. The calculated ground state properties in scheelite structure are found to be in good accord with previously published data. Using the recently developed Tran Blaha-modified Becke Johnson approach, we have also studied the electronic band structure of this compound which shows the semiconducting behavior with a direct band gap of 4.30 eV in the scheelite phase, whereas the band gap is found to be 2.18 eV in the zircon phase. Various thermodynamic properties including the thermal volume expansion coefficient and heat capacities at constant volumes and pressures were calculated via the quasi-harmonic Debye model at different temperatures (0–1000 K). Furthermore, optical properties such as complex dielectric function, refractive index, and reflectivity spectra of the titled compound were studied for incident electromagnetic waves in an energy range up to 16 eV. The contributions to various transitions peaks in the optical spectra are analyzed and discussed with the help from the energy dependent imaginary part of the dielectric function.

Comparison of equations used to estimate soot agglomerate absorption efficiency with the Rayleigh-Debye-Gans approximation

The contribution of soot aerosols to radiative forcing and climate change depends on their optical properties. Since these aerosols are agglomerates composed of quasi-spherical primary particles (usually small with respect to the radiation wavelength), their properties can be calculated following the Rayleigh-Debye-Gans approximation, which considers primary particles as independent absorbers and scatterers, with corrections made to account for multiple scattering and absorption within the agglomerate. A variety of equations can be used for particles small compared to the wavelength. In this study, results of the Rayleigh, Bohren and Huffman, simplified Bohren and Huffman, and Dobbins and Megaridis equations have been compared to the results from the exact Mie equations for the absorption efficiency. This comparison has been made for individual particles with different diameters and for an ensemble of primary particles composing an agglomerate. It has been shown that some of the largest primary particles of a typical agglomerate may not behave as Rayleigh absorbers at short wavelengths, contributing to errors in the estimation of the absorption efficiency. Both Bohren and Huffman and Dobbins and Megaridis equations are useful to extend the application range of the Rayleigh equation, thus reducing the accumulated error in the estimation of the agglomerate absorption efficiency. This analysis has been performed for several complex refractive index spectra. To choose the best equation for a particular application, the wavelength spectrum of the radiation and the range of primary particle sizes should be considered, aiming for a compromise between simplicity and accuracy.

Light extinction spectroscopy applied to polystyrene colloids: Sensitivity to complex refractive index uncertainties and to noise

The measurement of particle size distribution (PSD) in colloids and nanofluids presents many challenges, especially when it requires to be conducted in-situ and real-time. Our work aims to assess the capabilities of Light Extinction Spectroscopy (LES) technique to determine concentration and volumetric PSD (vPSD) of colloids and nanofluids. Numerical simulations are performed to verify robustness of LES data inversion algorithm and to identify the most relevant uncertainty sources. Experiments are carried out on well-dispersed water based colloids containing Polystyrene particles with median diameters at 120 nm and 300 nm. LES results are compared with supplier’s data, 3D-DLS measurements, and SEM images. Via sensitivity analyses, LES sensitivity to particle complex refractive index spectrum and to system noise level are examined. To improve accuracy, we limit LES data inversion at shorter wavelengths where high SNR is acquired. The noise is experimentally characterized and embedded into numerical simulations to better mimic the real conditions. We show that while noise level affects mostly vPSDs’ peak height, small inaccuracies in complex refractive index spectrum deteriorate the stability of the inversion, especially for smaller vPSDs. To overcome the latter, we carry out a preliminary in-situ calibration on particle complex refractive index spectrum. Accordingly, results are substantially improved with maximal discrepancies smaller than 3% for median and volume mean diameters, and lower than 13% for number concentrations. Besides, the retrieval of bi-modal distribution is promising. In conclusion, our methodology can be considered as a guideline to evaluate the applicability and accuracy of the LES technique in colloids.

Optical constants and critical point energies of (AgInSe2)0.75–(In2Se3)0.25 single crystals

AgInSe2 and In2Se3 are two attractive semiconducting materials for various technological applications especially for photovoltaic applications. In the present study, structural and optical properties of (AgInSe2)x–(In2Se3)1−x crystals for composition of x = 0.75 corresponding to chemical formula of Ag3In5Se9 were characterized by X-ray diffraction, energy-dispersive spectroscopy, room temperature transmission, and ellipsometry experiments. The transmittance spectrum was analyzed to reveal energy band gap. The derivative spectrophotometry analysis resulted in band gap energy of 1.22 eV. The spectra of complex dielectric function, refractive index and extinction coefficient were presented between 1.6 and 6.2 eV from the outcomes of ellipsometry analyses. Critical point energies have been determined using the derivative analyses of dielectric function. Five critical points at 2.70, 3.30, 4.05, 4.73, and 5.42 eV were revealed from the analyses. Crystal structure and atomic composition in semiconducting compound were also reported in the present work. The obtained results were compared with those reported for constituent compounds.

Effect of Fe doping on the structural, optical and electronic properties of BaTiO3: DFT based calculation

In this paper, the effect of high concentrated Iron (Fe) doping on the structural, electronic and optical properties of Barium Titanate (BaTiO3) based on density functional theory (DFT) are reported. The calculated lattice parameters show that the phase of BaTiO3 transformed into tetragonal from cubic phase after Fe doping. The electronic structure shows that Fe creates some defect states in the energy band which create weak coordinate covalent bond because of metal-metal interaction. The complex dielectric function, absorption, reflectivity, refractive index, optical conductivity and energy-loss spectrum for BaTiO3 and Fe doped BaTiO3 are calculated, and the results show a dramatic behavior near Fermi level after Fe doping.

Metrology of complex refractive index for solids in the terahertz regime using frequency domain spectroscopy

Frequency domain spectroscopy allows an experimenter to establish optical properties of solids in a wide frequency band including the technically challenging 10 THz region, and in other bands enabling metrological comparison between competing techniques. We advance a method for extracting the optical properties of high-index solids using only transmission-mode frequency domain spectroscopy of plane-parallel Fabry–Perot optical flats. We show that different data processing techniques yield different kinds of systematic error, and that some commonly used techniques have inherent systematic errors which are underappreciated. We use model datasets to cross-compare algorithms in isolation from experimental errors, and propose a new algorithm which has qualitatively different systematic errors to its competitors. We show that our proposal is more robust to experimental non-idealities such as noise or apodization, and extract the complex refractive index spectrum of crystalline silicon as a practical example. Finally, we advance the idea that algorithms are complementary rather than competitive, and should be used together as part of a toolbox for better metrology.

Complex refractive index spectra of whole blood and aqueous solutions of anticoagulants, analgesics and buffers in the mid-infrared

Mid-infrared (MIR) spectroscopy is a powerful tool for characterising the vibrations of molecular bonds and is therefore ideal for label-free detection of chemical species. Recent research into thin-film deposition and etching techniques for mid-infrared materials shows potential for realising miniaturised bedside biosensors for clinical diagnostics exploiting MIR spectroscopy, to replace laboratory based-techniques. However, lack of refractive index information for commonly encountered biological media and analytes hampers optimisation of biosensor performance for maximum sensitivity, especially for devices exploiting evanescent spectroscopy. Here we present refractive index data for human whole blood and several aqueous solutions of general interest to the clinical community: anticoagulants, analgesics and buffers. The refractive indices are generally dominated by the water content of each sample and the whole blood spectra exhibit additional strong features due to protein content. Furthermore, we present a generalised method for extracting complex refractive indices of aqueous solutions in the mid-infrared region using conventional attenuated total reflection Fourier transform spectroscopy (ATR-FTIR) without the need for collimated or polarised incident light, as is required for existing methods.

Spectral line-shape study by cavity-enhanced complex refractive index spectroscopy

We present a unique experimental setup that enables measurement of high-resolution complex refractive index spectra of gas sample using several cavity-enhanced methods: frequency-stabilized cavity ring-down spectroscopy, cavity mode-width spectroscopy and one-dimensional cavity mode-dispersion spectroscopy. Presented examples of applications cover molecular spectral line-shape investigations, line intensities and unperturbed line center frequency measurements and high-precision detection of systematic instrumental errors of various spectroscopic methods.

Computational and quantum chemical study on high-frequency dielectric function of tert-butylmethyl ether in mid-infrared and near-infrared regions

Complex dielectric function of tert-butylmethyl ether (TBME) was determined and analyzed in a broad spectral region covering mid-infrared (MIR) and near-infrared (NIR) regions (6500–560cm−1). Spectra of the complex electric permittivity and complex molecular polarizability have been derived from complex refractive index spectra. The molar vibrational polarization (Pvib) corresponding to individual modes has been estimated based on the data derived from fitting damped harmonic oscillator model to the experimental complex permittivity spectrum. Factors determining the dielectric functions due to vibrational resonance absorptions corresponding to fundamental and non-fundamental (overtones and combination modes) modes were taken into account. Direct comparison of contributions to total Pvib value stemming from corresponding fundamental and non-fundamental modes has been carried out and discussed for the first time. In order to identify overtones and binary combination modes, quantum chemical calculation of the vibrational spectrum of tert-butylmethyl ether was performed for MIR and NIR regions. Fully anharmonic approach by means of generalized second-order vibrational perturbation theory (GVPT2) was applied on DFT-B2PLYP/SNST level. An accurate reproduction of experimental data was achieved with subsequent assignment of fundamental and non-fundamental bands, which enabled detailed discussion of relations between dielectric contributions of fundamental and non-fundamental modes of tert-butylmethyl ether.

Brain tumor imaging of rat fresh tissue using terahertz spectroscopy.

Tumor imaging by terahertz spectroscopy of fresh tissue without dye is demonstrated using samples from a rat glioma model. The complex refractive index spectrum obtained by a reflection terahertz time-domain spectroscopy system can discriminate between normal and tumor tissues. Both the refractive index and absorption coefficient of tumor tissues are higher than those of normal tissues and can be attributed to the higher cell density and water content of the tumor region. The results of this study indicate that terahertz technology is useful for detecting brain tumor tissue.

Structural, elastic, electronic and optical properties of the quaternary nitridogallate LiCaGaN2: First-principles study

First-principles density functional theory calculations were performed to predict some of the not yet explored physical properties of the monoclinic quaternary nitridogallate LiCaGaN2. The calculated lattice parameters, including the lattice constants, angle β and internal atomic coordinates, are in excellent agreement with the corresponding measured ones, proving the reliability of the chosen theoretical approach. The equation of state, pressure dependence of the lattice constants, unit cell volume, angle β and bond-lengths were explored in detail. The single-crystal and polycrystalline elastic constants and their pressure dependence were numerically estimated. The mechanical stability, ductility/brittleness, average elastic wave velocity, Debye temperature and elastic anisotropy were also assessed. The electronic structure and its evolution with external applied hydrostatic pressure were explored. The bonding character was demonstrated by calculating the site-projected density of states, charge density and effective Mulliken charges of all ions. The effective masses of the charge-carriers were numerically estimated. The complex dielectric function, refractive index, extinction coefficient, absorption coefficient, reflectivity and electron energy-loss function spectra were calculated for different polarizations of the incident light. Pressure dependence of the static dielectric constant, static refractive index and static reflectivity are also reported. To the best of our knowledge, this is the first attempt to explore the aforementioned physical properties for the title material.