Line Shape Function Research Articles

Measurement of temperature-dependent line parameters of ammonia transitions near 1103 cm−1

Accurate knowledge of the line parameters of ammonia (NH3) transitions is important for developing precise laser-based NH3 sensors. We report the measurement of line-strengths and temperature-dependent broadening coefficients of NH3 with N2, air, Ar, and CO2 for six transitions in the ν2 fundamental band near 1103 cm−1. The absorption feature contributed by the target transitions is of particular interest for combustion emission applications due to its strong absorbance and the minimal spectral interference from other species such as H2O, CO2, and NOX. In this work, we measured NH3 absorption spectra with different collisional partners at the temperature range of 296–573 K using a quantum cascade laser. Spectroscopic parameters were determined by conducting multi-line fitting of the measured spectra using the Galatry lineshape function due to the evident line narrowing effect. Our study will aid the development of mid-infrared NH3 sensors particularly for high-temperature applications.

Improved ozone monitoring by ground-based FTIR spectrometry

Abstract. Accurate observations of atmospheric ozone (O3) are essential to monitor in detail its key role in atmospheric chemistry. The present paper examines the performance of different O3 retrieval strategies from FTIR (Fourier transform infrared) spectrometry by using the 20-year time series of the high-resolution solar spectra acquired from 1999 to 2018 at the subtropical Izaña Observatory (IZO, Spain) within NDACC (Network for the Detection of Atmospheric Composition Change). In particular, the effects of two of the most influential factors have been investigated: the inclusion of a simultaneous atmospheric temperature profile fit and the spectral O3 absorption lines used for the retrievals (the broad spectral region of 1000–1005 cm−1 and single micro-windows between 991 and 1014 cm−1). Additionally, the water vapour (H2O) interference in O3 retrievals has been evaluated, with the aim of providing an improved O3 strategy that minimises its impact and, therefore, could be applied at any NDACC FTIR station under different humidity conditions. The theoretical and experimental quality assessments of the different FTIR O3 products (total column (TC) amounts and volume mixing ratio (VMR) profiles) provide consistent results. Combining a simultaneous temperature retrieval with the optimal selection of single O3 micro-windows results in superior FTIR O3 products, with a precision of better than 0.6 %–0.7 % for O3 TCs as compared to coincident NDACC Brewer observations taken as a reference. However, this improvement can only be achieved provided the FTIR spectrometer is properly characterised and stable over time. For unstable instruments, the temperature fit is found to exhibit a strong negative influence on O3 retrievals due to the increase in the cross-interference between the temperature retrieval and instrumental performance (given by the instrumental line shape function and measurement noise), which leads to a worsening of the precision of FTIR O3 TCs of up to 2 %. This cross-interference becomes especially noticeable beyond the upper troposphere/lower stratosphere, as documented theoretically as well as experimentally by comparing FTIR O3 profiles to those measured using electrochemical concentration cell (ECC) sondes within NDACC. Consequently, it should be taken into account for the reliable monitoring of the O3 vertical distribution, especially over long-term timescales.

Infrared-active phonon modes and static dielectric constants in α-(AlxGa1−x)2O3 (0.18 ≤ x ≤ 0.54) alloys

We determine the composition dependence of the transverse and longitudinal optical infrared-active phonon modes in rhombohedral α-(AlxGa1−x)2O3 alloys by far-infrared and infrared generalized spectroscopic ellipsometry. Single-crystalline high quality undoped thin-films grown on m-plane oriented α-Al2O3 substrates with x = 0.18, 0.37, and 0.54 were investigated. A single mode behavior is observed for all phonon modes, i.e., their frequencies shift gradually between the equivalent phonon modes of the isostructural binary parent compounds. We also provide physical model line shape functions for the anisotropic dielectric functions. We use the anisotropic high-frequency dielectric constants for polarizations parallel and perpendicular to the lattice c axis measured recently by Hilfiker et al. [Appl. Phys. Lett. 119, 092103 (2021)], and we determine the anisotropic static dielectric constants using the Lyddane–Sachs–Teller relation. The static dielectric constants can be approximated by linear relationships between those of α-Ga2O3 and α-Al2O3. The optical phonon modes and static dielectric constants will become useful for device design and free charge carrier characterization using optical techniques.

Terahertz electron paramagnetic resonance generalized spectroscopic ellipsometry: The magnetic response of the nitrogen defect in 4H-SiC

We report on terahertz (THz) electron paramagnetic resonance generalized spectroscopic ellipsometry (THz-EPR-GSE). Measurements of field and frequency dependencies of magnetic response due to spin transitions associated with nitrogen defects in 4H-SiC are shown as an example. THz-EPR-GSE dispenses with the need of a cavity, permits independently scanning field and frequency parameters, and does not require field or frequency modulation. We investigate spin transitions of hexagonal (h) and cubic (k) coordinated nitrogen including coupling with its nuclear spin (I = 1), and we propose a model approach for the magnetic susceptibility to account for the spin transitions. From the THz-EPR-GSE measurements, we can fully determine polarization properties of the spin transitions, and we can obtain the k coordinated nitrogen g and hyperfine splitting parameters using magnetic field and frequency dependent Lorentzian oscillator line shape functions. Magnetic-field line broadening presently obscures access to h parameters. We show that measurements of THz-EPR-GSE at positive and negative fields differ fundamentally and hence provide additional information. We propose frequency-scanning THz-EPR-GSE as a versatile method to study properties of spins in solid state materials.

Quantum vibration perturbation approach with polyatomic probe in simulating infrared spectra.

The quantitative prediction of vibrational spectra of chromophore molecules in solution is challenging and numerous methods have been developed. In this work, we present a quantum vibration perturbation (QVP) approach, which is a procedure that combines molecular quantum vibration and molecular dynamics with perturbation theory. In this framework, an initial Newtonian molecular dynamics simulation is performed, followed by a substitution process to embed molecular quantum vibrational wave functions into the trajectory. The instantaneous vibrational frequency shift at each time step is calculated using the Rayleigh-Schrödinger perturbation theory, where the perturbation operator is the difference in the vibrational potential between the reference chromophore and the perturbed chromophore in the environment. Semi-classical statistical mechanics is employed to obtain the spectral lineshape function. We validated our method using HCOOH·nH2O (n = 1-2) clusters and HCOOH aqueous solution as examples. The QVP method can be employed for rapid prediction of the vibrational spectrum of a specific mode in solution.

Error Analysis of Integrated Absorbance for TDLAS in a Nonuniform Flow Field

As an effective optical diagnosis method, tunable diode-laser absorption spectroscopy (TDLAS) has increasingly moved to examine nonuniform flows, such as two-dimensional combustion diagnosis. To investigate the effect of nonuniformity along the line of sight in a measurement using TDLAS, the integrated absorbance (IA, the key intermediate quantity in TDLAS) error was quantified. The error distribution is obtained from the line-shape parameters through the comprehensive analysis of the line-shape function and the fitting method. The effects of the fitting function and the absorption line overlap are also considered. A general method for estimating the error is given. The work illustrates the applicability of TDLAS technology in nonuniform flow fields and provides input parameters for the evaluation of tunable diode laser absorption tomography error.

Theory of molecular emission power spectra. II. Angle, frequency, and distance dependence of electromagnetic environment factor of a molecular emitter in plasmonic environments.

Our previous study [S. Wang et al., J. Chem. Phys. 153, 184102 (2020)] has shown that in a complex dielectric environment, molecular emission power spectra can be expressed as the product of the lineshape function and the electromagnetic environment factor (EEF). In this work, we focus on EEFs in a vacuum-NaCl-silver system and investigate molecular emission power spectra in the strong exciton-polariton coupling regime. A numerical method based on computational electrodynamics is presented to calculate the EEFs of single-molecule emitters in a dispersive and lossy dielectric environment with arbitrary shapes. The EEFs in the far-field region depend on the detector position, emission frequency, and molecular orientation. We quantitatively analyze the asymptotic behavior of the EFFs in the far-field region and qualitatively provide a physical picture. The concept of EEF should be transferable to other types of spectra in a complex dielectric environment. Finally, our study indicates that molecular emission power spectra cannot be simply interpreted by the lineshape function (quantum dynamics of a molecular emitter), and the effect of the EEFs (photon propagation in a dielectric environment) has to be carefully considered.

Calibration-free wavelength modulation spectroscopy based on even-order harmonics.

This paper proposes a novel and rapid calibration-free wavelength modulation spectroscopy algorithm based on even-order harmonics. The proposed algorithm, analytically deduced from Voigt line-shape function, only involves simple algebraic operations to describe the actual gas absorption spectra, thus eliminating the time-consuming simulations and line-shape fitting procedures adopted in traditional algorithms. Instead of acquiring the entirely scanned absorption line-shape, the proposed technique only requires extraction of the peak values of the harmonics. This characteristic significantly benefits gas diagnosis at elevated pressure and/or temperature, in which the entirely scanned absorption is very difficult to be obtained due to the broadened line-shapes. The proposed algorithm is validated by both numerical simulation and condition-controlled experiment, indicating millisecond-level calculation of gas parameters with the relative error less than 4% in the experiments.

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles.

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble's ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

Theoretical Modeling and Analysis of the Contribution of the Near-Field Absorption to the Dipole Radiation Power in Top-Emitting Organic Light-Emitting Diodes

We theoretically model the near-field (NF) absorption for a multilayer micro-cavity (MMC) structure and investigate the contribution of the NF absorption to the dipole radiation power in top-emitting organic light-emitting diodes (OLEDs). The NF absorption occurs due to the interaction between an evanescent wave with a large in-plane wave vector and a planar metal layer in the vicinity of the dipole radiation. The analytical expressions of the NF absorption in the MMC structure are derived from the plane wave expansions of the electric field amplitude, which includes the two-beam and multi-beam interference terms. The transverse magnetic polarization light emitted by both horizontally and vertically oriented dipole emitters is considered in the NF absorption while the contribution of the transverse electric polarization light is neglected. Based on the total spectral power density calculated in a top-emitting OLED, the respective spectral response functions of surface plasmon (SP) modes and NF absorption are compared, where the summation of the Lorentzian line shape functions is used to represent spectral responses of SP modes. At large values of in-plane wave vectors, the spectral response caused by the NF absorption becomes significant and approaches the total spectral power density. In addition, the relative optical powers from various dipole dissipation mechanisms are calculated with respect to the dipole emitter position in the emission layer (EML), which shows the optical power coupled to the NF absorption is predominant over other mechanisms when the distance between the dipole emitter and the EML/Ag interface is less than 10 nm in the top-emitting OLED.

Zinc gallate spinel dielectric function, band-to-band transitions, and Γ-point effective mass parameters

We determine the dielectric function of the emerging ultrawide bandgap semiconductor ZnGa2O4 from the near-infrared (0.75 eV) into the vacuum ultraviolet (8.5 eV) spectral regions using spectroscopic ellipsometry on high quality single crystal substrates. We perform density functional theory calculations and discuss the band structure and the Brillouin zone Γ-point band-to-band transition energies, their transition matrix elements, and effective band mass parameters. We find an isotropic effective mass parameter (0.24 me) at the bottom of the Γ-point conduction band, which equals the lowest valence band effective mass parameter at the top of the highly anisotropic and degenerate valence band (0.24 me). Our calculated band structure indicates the spinel ZnGa2O4 is indirect, with the lowest direct transition at the Γ-point. We analyze the measured dielectric function using critical-point line shape functions for a three-dimensional, M0-type van Hove singularity, and we determine the direct bandgap with an energy of 5.27(3) eV. In our model, we also consider contributions from Wannier–Mott type excitons with an effective Rydberg energy of 14.8 meV. We determine the near-infrared index of refraction from extrapolation (1.91) in very good agreement with results from recent infrared ellipsometry measurements (ε∞=1.94) [M. Stokey, Appl. Phys. Lett. 117, 052104 (2020)].

Fast Quantification of Air Pollutants by Mid-Infrared Hyperspectral Imaging and Principal Component Analysis.

An imaging Fourier-transform spectrometer in the mid-infrared (1850–6667 cm) has been used to acquire transmittance spectra at a resolution of 1 cm of three atmospheric pollutants with known column densities (Q): methane (258 ppm·m), nitrous oxide (107.5 ppm·m) and propane (215 ppm·m). Values of Q and T have been retrieved by fitting them with theoretical spectra generated with parameters from the HITRAN database, based on a radiometric model that takes into account gas absorption and emission, and the instrument lineshape function. A principal component analysis (PCA) of experimental data has found that two principal components are enough to reconstruct gas spectra with high fidelity. PCA-processed spectra have better signal-to-noise ratio without loss of spatial resolution, improving the uniformity of retrieval. PCA has been used also to speed up retrieval, by pre-calculating simulated spectra for a range of expected Q and T values, applying PCA to them and then comparing the principal components of experimental spectra with those of the simulated ones to find the gas Q and T values. A reduction in calculation time by a factor larger than one thousand is achieved with improved accuracy. Retrieval can be further simplified by obtaining T and Q as quadratic functions of the two first principal components.

Spin–phonon interaction and magnetoelastic coupling associated with unusual cluster-glass states in YFe0.9Cr0.1O3

The magnetic, optical phonon behavior of the polycrystalline YFe0.9Cr0.1O3 (YFC-10), prepared by solid-state reaction route, had been studied via static and ac magnetization measurements and Raman spectroscopic techniques respectively. The results indicated that YFe0.9Cr0.1O3 undergoes unusual cluster-glass transitions at low temperatures viz. Tf1 (SG1) = 108 K (Freez.1) and Tf2 (SG2) = 30 K (Freez.2) coexisting with the long-range weak ferromagnetic (WFM) state. Raman spectroscopic (RS) measurements revealed 12 distinct modes of vibrations at all temperatures with 83–433 K. Interestingly, the freezing transition at Tf1 is found to be accompanied by significant phonon renormalization. From the detailed analysis of the line-shape function of the Raman modes, the anomalous T-variation of the peak position and the linewidths suggests the existence of spin-phonon interaction in the present solid solution. Moreover the temperature dependent synchrotron X-ray diffraction studies between 10 and 300 K revealed the anomalous thermal variation of the lattice parameters and microscopic structural parameters such as super-exchange angles and (Fe/Cr)O6 octahedral bond lengths and bond angles at both the freezing transitions. Overall, the system exhibits the strong magnetoelastic and spin phonon coupling over a broad thermal regime viz. from Liquid. N2 to temperatures above room temperature (RT = 300 K) which makes YFe0.9Cr0.1O3 reliable for application purpose.

Line parameters for hot methane [formula omitted] band broadened by H[formula omitted] from 296 to 1100 K

Methane (CH4) spectra in the ν3 band near 3.3 m were measured for 0, 50, 150, 240, 320, and 400 Torr pressure of added hydrogen. The spectra were recorded using a high resolution Fourier transform spectrometer. The CH4 spectra were measured at 5 different temperatures from room temperature up to ∼ 1100 K. A multi-spectrum non-linear least squares fit method was used to determine the line parameters at each temperature. Voigt lineshape functions were used to determine the broadening and shifting of methane lines in the P and R branches. The temperature dependence of exponent parameters for the line width and the linear frequency shift coefficients were determined from a fit for temperatures ranging from 296 to 1098 K. The temperature dependence of the retrieved line broadening parameters was observed to follow the Double Power Law (DPL) proposed by Gamache and Vispoel. The temperature dependence of the pressure shift coefficients follows a linear trend for the first three temperatures. The pressure broadening parameters decrease with increasing temperature, and the pressure shift parameters increase with increasing temperature, especially for the first three temperatures. Finally, the dependence of pressure broadening (γ0) and shift (δ0) parameters on the rotational quantum number (J) was studied. The pressure broadening coefficients decrease about 20–30% for temperatures up to 894 K and about 40% for 1098 K, with increasing J quantum number. A complete set of fitted parameters including line position (σ), line intensity (S), pressure broadening (γ0), shifting (δ0), and their corresponding fitting errors are provided in supplementary tables.

Theoretical Study of Photo-Luminescence Emission Using the Line Shape Function for Semiconductor Quantum Dots

Theoretical Study of Photo-Luminescence Emission Using the Line Shape Function for Semiconductor Quantum Dots

Theory of molecular emission power spectra. I. Macroscopic quantum electrodynamics formalism.

We study the emission power spectrum of a molecular emitter with multiple vibrational modes in the framework of macroscopic quantum electrodynamics. The theory we present is general for a molecular spontaneous emission spectrum in the presence of arbitrary inhomogeneous, dispersive, and absorbing media. Moreover, the theory shows that the molecular emission power spectra can be decomposed into the electromagnetic environment factor and lineshape function. In order to demonstrate the validity of the theory, we investigate the lineshape function in two limits. In the incoherent limit (single molecules in a vacuum), the lineshape function exactly corresponds to the Franck-Condon principle. In the coherent limit (single molecules strongly coupled with single polaritons or photons) together with the condition of high vibrational frequency, the lineshape function exhibits a Rabi splitting, the spacing of which is exactly the same as the magnitude of exciton-photon coupling estimated by our previous theory [S. Wang et al., J. Chem. Phys. 151, 014105 (2019)]. Finally, we explore the influence of exciton-photon and electron-phonon interactions on the lineshape function of a single molecule in a cavity. The theory shows that the vibronic structure of the lineshape function does not always disappear as the exciton-photon coupling increases, and it is related to the loss of a dielectric environment.

Comparison between GaN and InN quantum‐dot semiconductor optical amplifiers

AbstractGaN/Al0.5Ga0.5N and InN/Al0.5Ga0.5N as a III‐nitride quantum dot semiconductor optical amplifiers (QD‐SOAs) are studied in detail in this paper. The optical gain, spontaneous emission rate, and lineshape function are calculated using non‐Markovian relaxation compared with Markovian one. Gain is then connected with the rate equations model to obtain a dB gain, output power, and shot noise in these SOAs. GaN peaked at 351 nm which is preferred in optical coherence tomography applications. InN is peaked at 1028 nm which can be used in gas detection and environmental pollution monitoring. Both structures studied have high gain and low noise and nearly equivalent TE and TM gain which makes them adequate for the use in both these two modes. These calculations show the importance of InN and GaN QD nanostructure in the applications.

Precision Spectroscopy of Nitrous Oxide Isotopocules with a Cross-Dispersed Spectrometer and a Mid-Infrared Frequency Comb.

As a potent greenhouse gas and an ozone-depleting agent, nitrous oxide (N2O) plays a critical role in the global climate. Effective mitigation relies on understanding global sources and sinks, which can be supported through isotopic analysis. We present a cross-dispersed spectrometer, coupled with a mid-infrared frequency comb, capable of simultaneously monitoring all singly substituted, stable isotopic variants of N2O. Rigorous evaluation of the instrument lineshape function and data treatment using a Doppler-broadened, low-pressure gas sample are discussed. Laboratory characterization of the spectrometer demonstrates sub-GHz spectral resolution and an average precision of 6.7 × 10-6 for fractional isotopic abundance retrievals in 1 s.

Determination of absorption coefficients and Urbach tail depth of ZnO below the bandgap with two-photon photoluminescence.

In this article, we demonstrate a novel approach to determine the absorption coefficient of ZnO below the bandgap via measuring the self-absorption (SA) effect on the two-photon luminescence (TPL) spectrum of the ZnO bulk crystal rod at cryogenic temperature. Under a geometric configuration of side-excitation and front-detection, the intensities of several major spectral components of TPL spectra of ZnO can be decisively tuned by precisely varying the transmitting distance of luminescence signal, so that the absorption coefficients at different wavelengths can be determined on the basis of Beer-Lambert law. Furthermore, the peak position of donor bound exciton luminescence exhibits a unique redshift tendency with increasing the transmitting distance. Starting from the product of Lorentzian lineshape function and exponential absorption edge of Urbach tail, an analytical formula is derived to quantitatively interpret the experimental redshift characteristic with the transmitting distance. The energy depth of Urbach tail of the studied ZnO crystal is deduced to be ∼13.3 meV. In principle, this new approach can be used to determine absorption coefficient of any luminescent solids as long as the SA effect happens.

Core level photoemission line shape selection: Atomic adsorbates on iron

Robust fitting of core level photoemission spectra is often central to reliable interpretation of X‐ray photoelectron spectroscopy (XPS) data. One key element is employment of the correct line shape function for each spectral component. In this study, we consider this topic, focusing on XPS data from atomic adsorbates, namely, O and S, on Fe(110). The potential of employing density functional theory (DFT) for generating adsorbate projected electronic density of states (PDOS) to support line shape selection is explored. O 1s core level XPS spectra, acquired from various ordered overlayers of chemisorbed O, all display an equivalent asymmetric line shape. Previous work suggests that this asymmetry is a result of finite O PDOS in the vicinity of the Fermi level, allowing O 1s photoexcitation to induce a weighted continuum of final states through electron‐hole pair excitation. This origin is corroborated by O DFT‐PDOS generated for an optimised five‐layer Fe(110)(2 × 2)‐O slab. Adsorbate DFT‐PDOS were also computed for Fe(110) ‐S. As, similar to adsorbed O, there is a significant continuous distribution of states about the Fermi level, it is proposed that the S 2p XPS core levels should also have asymmetric profiles. S 2p XPS data acquired from Fe(110) ‐S, and their subsequent fitting, verify this prediction, suggesting that DFT‐PDOS could aid line shape selection.