Lorentzian Width Research Articles

Pressure broadening and narrowing due to oxygen and nitrogen gas mixtures at 1270 nm band: part III

Collisional effects on the absorption spectrum of oxygen and nitrogen gas mixtures at 1270 nm band appear as a broadening or narrowing at the component of Lorentzian width in the Voigt profile. The deconvolution method of spectral lines reveals two kinds of bands, the first centered at 1264 nm, and the second centered at 1268 nm. At high pressures, the Gaussian full width may be fixed, and Voigt's full width at half maximum (FWHM) nearly equals to Lorentzian full width. Partial pressures of each gas were between 1-10 bar at 298 K. New results highlight the effect of nitrogen as a collisional partner on the oxygen spectrum. PACS: 32.30. Bv; 33.20. Ea; 33.20.-t; 34.50.-s; 34.50. Ez; 51.30. +I; 87.64. km.

Development and application of a three-dimensional pseudo-Voigt function for muon spin relaxation analysis of weakly magnetic materials.

We present a three-dimensional pseudo-Voigt function to analyze muon spin relaxation (μSR) in weakly magnetic materials. Our approach approximates the Voigt function by superimposing Gaussian and Lorentzian functions using a one-dimensional method proposed by Di Rocco and Cruzado [Acta Phys. Pol., A 122, 666 (2012)]. We derive the peak of the Voigt function analytically and express the Half Width at Half Maximum (HWHM) of the Voigt function as a function of the HWHMs of the Gaussian and Lorentzian functions. We compare the pseudo-Voigt function to the exact Voigt function and find a maximum normalized discrepancy of ∼20% at the tail of the distribution function, depending on the ratio of Lorentzian to Gaussian HWHMs and internal magnetic field. We apply the derived three-dimensional pseudo-Voigt function to calculate μSR functions for zero- and longitudinal-field experiments and use them to fit μSR time spectra of La2-xSrxCuO4 with 2.4% Sr, employing a strong collision model with the static-based pseudo-Voigt muon spin relaxation function as the initial condition. Our results show that the Gaussian- and Lorentzian-fitted parameters and fluctuation rate are in good agreement with results from the exact Voigt function for a temperature range of 30-200K, with the deviation of Gaussian and Lorentzian width parameters reaching ∼0.15G below 30K.

Broadening of He 1083nm, 388.8 nm, 501.6 nm, 587.5 nm, 667.8 nm, 706.5 nm, 728.1 nm lines and of H(α), H(β) and O 777 nm lines in atmospheric pressure helium

Helium atoms in electronically excited states are produced in atmospheric pressure parallel plate DBD helium plasma. Pressure broadening coefficients of several helium lines and of O(777 nm), H(β) and H(α) lines are deduced from the analysis of the spectral profiles of those lines. Absorption spectroscopy on He(3S) metastable atoms with a diode laser is used for 1083 nm He line. The influence of the laser power density on recorded absorption spectral profile is analyzed. For the other lines, emission from the plasma is analyzed with a very high resolution 2 m focal length spectrometer, working in the 2nd, 3rd or 4th diffraction order of the 1200 g/mm grating. Instrumental width ΔI ranges between 2.2 and 9.8 pm, depending on the spectral line. Knowing with high precision ΔI and the Doppler widths of the lines and the fact that the resulting Gaussian width of each line remains, at least, 4 times smaller than its Lorentzian width, permits to deduce the pressure broadening coefficients of helium 388.8, 501.6, 587.5, 667.8, 706.5, 728.1 and 1083 nm lines and of 777 O line with less than 3 % uncertainty for most of them. Observation of the forbidden 2p 1P1 –4f 1F3 component in the blue wing of the allowed 492.19 nm He(2p 1P1 –4d 1D2) line, indicates the presence of a static electric field E ≈ 5 ± 1 kV/cm during the 0.4 µs light collection time from the DBD. It is concluded that in pulsed plasmas, like DBD and plasma-jet, before deducing the plasma density from the homogeneous widths of H(β) or H(α) lines, one should ascertain that the static E-field in the gas is small enough during the light collection period for not inducing significant splitting of these lines. This would induce an extra broadening of the line, leading to an overestimated electron density.

Information hidden behind a single peak in the C 1s spectrum of graphene on Ir(111)

The energy resolution that can be achieved in x-ray photoelectron spectroscopy experiments allows to disentangle the contribution arising from the presence of a large variety of surface atoms in non-equivalent configurations which manifests itself not only with the appearance of different spectral components, but also as unusual lineshape.In the present work, we show that the fit of the C 1s core level spectrum of graphene grown on Ir(111) realized using 200 peaks based on ab initio calculations, accounting for the non-equivalent C atoms in the 10×10 moiré cell, does not improve the fit quality with respect to the use of a single component. On the contrary, the quantitative fit quality can be drastically increased by introducing a dependency of the Lorentzian width on the distance between C and Ir first-layer atoms. This result is associated to the different electronic properties, and in particular to the different density of states of the σ and π bands, of C atoms sitting on TOP (hills) or FCC (valleys) regions of graphene which affect the lifetimes of the core-holes generated during the photoemission process.

Stark broadening of the cesium 52D5/2 → 102F line shape

Pump modulated laser absorption spectroscopy was used to measure the cesium 52D5/2→102F5/2,7/2 line shape. Alkali density in an optically pumped low pressure cell was increased from 0.5 to 85×1012cm−3, resulting in a factor of 200 increase in Lorentzian width due to Stark broadening (2.76GHz/1012cm−3). The observed red shift is consistent with literature, and the shift-to-width ratio δ/γ=−0.356±0.015 informs an electron temperature of 1820±100K. A linear trend between alkali density and electron density is seen, suggesting that electron impact is the primary plasma production mechanism. A maximum ionized concentration of 28% was observed.

Impact of Faddeeva–Voigt broadening on line-shape analysis at critical points of dielectric functions

Faddeeva–Voigt broadening (FVB) couples the physical characteristics of both Lorentzian and Gaussian profiles as a combined analytic function shaping the dielectric response. Accurate extraction of the Gaussian and Lorentzian broadening contents in line-shape analysis is essential for reliable optical characterization of semiconductors and dielectrics. By adding the Gaussian-broadening width to each Lorentzian width, we investigate how FVB affects critical-point (CP) analysis. We revisit a selection of earlier work based on classical Lorentz broadening in modulation spectroscopy and spectral ellipsometry. To generalize CP analysis, we derive the FVB’s analytical representation in terms of fractional derivatives of the Faddeeva function and apply the twenty-pole Martin–Donoso–Zamudio approximation for its precise and efficient computation of the FVB of model dielectric functions and derivatives. We investigate the FVB of the electroreflectance line shape of HgCdTe for three-dimensional M0 transitions and of the photoreflectance line shape of InP excitonic E0 transitions. Furthermore, we explore how FVB affects the dielectric functions of three-dimensional excitonic and two-dimensional M0 transitions vs Tanguy’s analytical two-dimensional exciton E1 and E1+Δ1 fits of GaAs to the second-order derivatives. We use the Akaike information criterion to quantitatively estimate the goodness of fit that statistically penalizes overfitting due to extraneous parameters. By consolidating both Gaussian and Lorentzian broadenings, the FVB significantly affects the CP analysis of modulation-spectroscopy line shapes and second-order derivatives of the dielectric function.

Application of the Martin-Donoso-Zamudio multipole approximation for generalized Faddeeva/Voigt broadening of model dielectric functions

Faddeeva/Voigt broadening of dielectric functions (DFs) couples the physical properties of mutual Lorentzian and Gaussian broadening as a combined unit. This work investigates accurate computations for the general Faddeeva/Voigt broadening of complex analytic DFs and their derivatives. The paper builds on the multipole approximation for broadening profiles and exploits the reduction of the approximation into a finite sum of Lorentzian profiles. Using a two-point Padé approximant for the Faddeeva function, we computed this study's twenty-pole Martin-Donoso-Zamudio (MDZ20) approximation. First, we evaluated the accuracies of the MDZ20 approximation relative to high-precision evaluation of the Faddeeva function and its first three derivatives. Second, we applied the MDZ20 approximation to derive the general approximation formula for the Faddeeva/Voigt broadening of Kramer-Kronig-consistent complex analytic DFs. Third, we assessed the accuracy of Voigt broadening in two theoretical applications: the universal-dispersion model through piecewise polynomial elements and the three-dimensional (3D) M0 critical point and derivatives by using the MDZ20 approximation. Finally, we developed formulas for the Faddeeva/Voigt broadening of Tanguy's 3D excitons and the Tauc-Lorentz models. The Faddeeva/Voigt-broadened Tanguy model is investigated within Gilliot's dielectric model of sol-gel ZnO. The Faddeeva/Voigt-broadened Tauc-Lorentz model is applied to amorphous silicon (a-Si). Specifically, we evaluated the impact of adding a Gaussian component to each Lorentzian width on the agreement of the Voigt-broadened DF to experimental data.

Physical properties of rhodium retrieved from modeling its dielectric function by a simulated annealing approach

Optical, charge carriers transport, quantum mechanics, magnetic, thermal, and plasmonic properties of the transition metal rhodium are considered. An extended Drude-Lorentz (DL) model is applied to describe the dielectric function (DF) of rhodium in a spectral range going from the mid-infrared (12.4 μm) to the vacuum ultraviolet (32 nm). The Drude term of the DF includes, as optimization parameters, the inverse of the high frequency dielectric constant, the volume plasma frequency and scattering frequency of the electrons, the scattering frequency of holes relative to that of electrons, the ratio between the effective masses of electrons and holes, the number of holes per atom relative to that of electrons, and the renormalized times between grain boundary scattering events for electrons and holes. The Lorentz contribution to the DF includes the number of conduction electrons per atom, the oscillator strengths, the resonance energies, and the Lorentzian widths. Values of the parameters involved in the DF are optimized by an acceptance-probability-controlled simulated annealing method that minimizes spectral differences between the real and imaginary parts of the DF values obtained from the literature and those evaluated from the DL parametric formulation, accounting for the presence of electrons and holes as charge carriers. Once an optimized spectral description of the DF of rhodium is obtained, a large set of charge-transport, magnetic, thermal, plasmonic, and quantum mechanics derived quantities are evaluated: mobilities, relaxation times, Fermi velocities, effective masses, electrical and thermal conductivities, heat capacity coefficients, Hall coefficient, diamagnetic and paramagnetic susceptibilities, effective number of Bohr magnetons, Fermi energies and corresponding densities of states, energy loss functions, effective number of charge carriers participating in conduction, and effective number of electrons involved in inter-band transitions.

Predissociation and pressure dependence in the low frequency far wing of the Wulf absorption band of ozone near 1.2 µm

The weak low frequency tail of the ozone Wulf band is newly studied by high sensitivity cavity ring down spectroscopy (CRDS) in the 7920–8700 cm−1 range. Although strongly obscured by impurity lines, the ozone absorption signature shows up in the recorded spectra as two mostly unresolved absorption bands. These two bands with maximum near 8154 and 8450 cm−1 are hot bands from the (020) and (100) ground state vibrational levels reaching the same predissociated 3A2(000) upper state of 16O3. The observed bands include a mostly structureless continuum and lines exhibiting a clear broadening due to the predissociation of the 3A2(000) upper state. On the basis of assignments of the rotational structure available in the literature for the 3A2(000)-X1A1(000) cold band centered near 9553 cm−1, seventy-four relatively narrow lines could be rotationally assigned to the 3A2(000)-X1A1(020) and 3A2(000)-X1A1(100) hot bands. A line shape analysis, performed using a Voigt profile, provided the width of the Lorentzian component. Additional recordings performed at various pressures for 18 lines allowed to disentangle the pressure and predissociation contributions to the fitted Lorentzian widths. As a result, the newly derived pressure broadening coefficients of the considered rovibronic transitions are found to be similar to those of the rovibrational infrared bands. All the lines studied are affected by significant predissociation due the spin-orbit coupling between the 3A2(000) level and high lying dissociative vibrational levels of the X1A1 electronic ground state. The resulting set of predissociation widths for sixty lines ranges between 9 × 10−3 and 0.2 cm−1 corresponding to upper state lifetime of 560 and 25 ps, respectively. The reported results are discussed in relation with previous experimental and theoretical studies.

Air-broadened N2O line-shape parameters and their temperature dependences by requantized classical molecular dynamics simulations

In this paper, we used requantized Classical Molecular Dynamics Simulations (rCMDS), corrected by the room temperature air-broadening coefficients measured in the ν3 band of N2O, to predict line-shape parameters including the broadening coefficient, its speed dependence component, the Dicke narrowing and the line-mixing coefficients, associated with various line-shape models for air-broadened N2O absorption lines. For that, we first computed the auto-correlation functions of the N2O dipole moment, responsible for the absorption transitions. The Fourier-Laplace transform of these functions directly yields the absorption spectra. Calculations were made for three temperatures 200, 250 and 296 K and 1 atm of N2O/air mixtures and for a large range of values of the ratio between the Doppler and Lorentzian widths. The obtained spectra were then fitted with the quadratic speed-dependent Voigt profile including the first-order line mixing using a multi-spectrum fitting procedure. Comparisons with values determined from room temperature high-precision measurements in the ν3 band of N2O by using the same profile [Loos et al, J. Quant. Spectrosc. Rad. Transf., 151, 2015, 300-309] show that our retrieved line broadening coefficients are overestimated by about 4%. The difference between the measured and predicted line broadening coefficients was used to empirically correct the rCMDS auto-correlation functions and thus the corresponding absorption spectra. These latter were then fitted with the Voigt, the speed-dependent Voigt, and the speed-dependent Nelkin-Ghatak profiles, all of them being associated with the first-order line-mixing approximation, providing the corresponding line-shape parameters for lines up to J′′ ≤ 59. The temperature dependences of various line-shape parameters were also deduced. The results show a very good agreement with available experimental data for all the considered parameters.

A discrete integral transform for rapid spectral synthesis

Accurate synthetic spectra that rely on large Line-By-Line (LBL)-databases are used in a wide range of applications such as high temperature combustion, atmospheric re-entry, planetary surveillance and laboratory plasmas. Conventionally synthetic spectra are calculated by computing a lineshape for every spectral line in the database and adding those together, which may take multiple hours for large databases. In this paper we propose a new approach for spectral synthesis based on an integral transform: the synthetic spectrum is calculated as the integral over the product of a Voigt profile and a newly proposed three-dimensional “lineshape distribution function”, which is a function of spectral position and Gaussian- & Lorentzian width coordinates. A fast discrete version of this transform based on the Fast Fourier Transform (FFT) is proposed, which improves performance compared to the conventional approach by several orders of magnitude while maintaining accuracy. Strategies that minimize the discretization error are discussed. A Python implementation of the method is compared against state-of-the-art spectral code RADIS, and is since adopted as RADIS's default synthesis method. The synthesis of a benchmark CO2 spectrum consisting of 1.8 M spectral lines and 200k spectral points took only 3.1 s using the proposed method (1011 lines × spectral points/s), a factor ∼300 improvement over the state-of-the-art, with the relative improvement generally increasing for higher number of lines and/or number of spectral points. An experimental GPU-implementation of the method was also benchmarked, which demonstrated another 2~3 orders performance increase, achieving up to 5 ⋅ 1014 lines × spectral points/s.

Accurate Chebyshev Approximations for the Width of the Voigt Profile, Differential Peaks, and Deconvolution of the Lorentzian Width

Accurate formulas have been developed using rational Chebyshev approximations for the spectral features/quantities of the Voigt profile and its first two derivatives. The rational polynomial expression for the half width at half maximum (HWHM) of the Voigt profile in terms of the Lorentzian and Gaussian widths is presented in Eq. (7) and provides 12-digit accuracy. The correction expression for the deconvolution of the Gaussian broadening from the Lorentzian broadening in the Voigt profile is presented in Eq. (11) and provides 13-digit accuracy. The expression for the position of the peak in the first derivative of the Voigt profile in terms of the Lorentzian and Gaussian widths is presented in Eq. (15) and provides 14-digit accuracy. The expression for the position of the side peak in the second derivative of the Voigt profile in terms of the Lorentzian and Gaussian widths is presented in Eq. (17) and provides 12-digit accuracy. The expressions for the peak amplitude ratios for the first and second derivatives of the Voigt profile in terms of the Lorentzian and Gaussian widths are presented in Eq. (19) and Eq. (21), respectively, and provide 13-digit accuracy. The reported accuracies are higher than those of earlier work, and the presented expressions provide a reference for the direct calculation of spectral quantities for Voigt profiles. The accuracy of the presented formulas establishes a general foundation for the deconvolution of instrument-based broadening and other broadening mechanisms in the HWHW and the positions of the first- and second-derivative peaks.

Line width at half maximum of the Voigt profile in terms of Gaussian and Lorentzian widths: Normalization, asymptotic expansion, and chebyshev approximation

Normalization by the Voigt width was applied to both the Lorentz and Gaussian widths in the half width at half maximum (HWHM) equation. The normalization simplified the HWHM equation into a univariate relation for the normalized Lorentz width ηL=ΛηG as a function of the normalized Gaussian width with a finite domain ηG∈0,1. The asymptotic expansion of the last function provided local analytical approximations with limited accuracy at both ends of the Lorentz and Gaussian limits. Chebyshev approximations resulted in far better accuracies with a greatly improved range span. The rational Chebyshev approximation provided the highest accuracies and was implemented for deriving polynomial equations for the Voigt width γV in terms of both the Lorentz width γL and the Gaussian width γG. Seventh-order and ninth-order polynomial approximations provided up to a ten-digit accuracy. Quartic and segmented closed-form analytical approximations provided a five-digit accuracy. All of these approximations were more accurate than the four-digit maximum accuracy approximations reported in earlier studies.

Non-paraxial propagation of a circular Lorentz-Gauss vortex beam.

The optical field of a circular Lorentz-Gauss vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integrals. The expression of the longitudinal component of the angular momentum density of a circular Lorentz-Gauss vortex beam is also presented. The normalized intensity, the three components of intensity, and the longitudinal angular momentum density of a circular Lorentz-Gauss vortex beam are demonstrated in the reference plane, respectively. The effects of linearly polarized angle, topological charge, and Lorentzian width parameter on the intensity, the three components of intensity, and the longitudinal angular momentum density are analyzed, respectively. The normalized intensity and the longitudinal angular momentum density of a paraxial circular Lorentz-Gauss vortex beam are also shown in the same reference plane. The missing longitudinal component of the optical field will result in deficient patterns of the intensity and the longitudinal angular momentum density. In terms of the longitudinal angular momentum density, the longitudinal component of a circular Lorentz-Gauss vortex beam cannot be neglected under the condition that the Lorentzian width parameter and the Gaussian waist are of the order of the optical wavelength.

Spectral Distribution of Oscillator Strength for Core-to-Valence Transitions probed by using X-ray Absorption and Total Electron Yield Modes

Abstract Changes in spectral distribution of oscillator strength for core-to-valence transitions probed by X-ray absorption and total electron yield (TEY) modes are studied in more detail. The quantitative analysis of their redistribution in TEY due to the saturation effect is performed by applying the model M ˜ $\tilde M$ -function method suggested by Flesch et al. J. Chem. Phys. 138 (2013) 144302. The model M ˜ $\tilde M$ -function method is generalized to account for the saturation-induced distortion of the line shape of the transitions embedded into the core ionization continua and located below them. It is shown that TEY measurements produce essential changes not only in the relative intensity of the transitions but also shift upward the transition energy, broaden the Lorentzian and Gaussian widths and enhance the line asymmetry. The Gaussian width of the TEY signal undergoes the most substantial broadening though the Lorentzian width increases significantly too. The saturation-induced distortion of the line shapes is not negligible even if the well-known escape-to-penetration condition is valid.

High resolution study of the autoionizing states of He in their exchange interference energy region

The electron impact excitation (and their decay into the same final ionic state) of the autoionizing states of helium (2s2(S1), 2s2p(P3), 2p2(D1) and 2s2p(P1)) have been studied. The interference of these states can occur when the energies of the autoionizing electrons match that of the scattered electrons. The observation of this exchange interference is disturbed by the Fano interference, which occurs at all primary energies. We intend to study it separately in the neighborhood of the critical energy, and then to estimate its measure for the critical energy. The present measurements were made at 88 eV and 97 eV primary energies (where the groups of the ejected and the scattered electron peaks are well separated), at 130°, 90° and 50° scattering angles. The measured spectra were evaluated by a computer code, using the Shore parametrization. We give the obtained peak parameter values in tabulated form. We found an anomaly of the fitted values of Lorentz width of 2s2(S1) peak.

Optical, magnetic, and charge-carriers transport properties of a transition metal: bulk palladium.

Three parametric models of Drude-Lorentz (DL) are used to describe the spectral variation of the dielectric function of bulk palladium. An improved version of the acceptance-probability-controlled simulated annealing method is applied to optimize the values of the parameters involved in the models: high-frequency dielectric constant, free-electron collision frequency and corresponding relaxation time, oscillation strengths, nominal resonance frequencies, and Lorentzian widths. Normalization of the oscillation strengths allows the introduction of a new parameter in the context of the original DL model: the number density ratio, which is the ratio between the number density of conduction electrons and the number density of metal atoms. Inclusion of this parameter in the optimization procedure allows us to evaluate additional parameters related to the charge-carriers transport: the number density of conduction electrons, average effective mass of conduction electrons and holes, Fermi energy and electronic density of states at the Fermi energy, electrical resistivity, intrinsic mean-free path of conduction electrons, electronic heat capacity, Hall coefficient, as well as the mobilities of conduction electrons and holes. The paramagnetic and diamagnetic susceptibilities are also included as derived parameters. A parametric form of the bulk Pd dielectric function, with incorporation of the average local electric field effect in the Lorentz contribution, is reported.

Further understanding of doorway states in elastic systems.

In a previous work an elastic bar with a groove or notch that presents a doorway state was studied when the system was excited with 20 cycles of harmonic signals. The strength function had a Lorentzian width Γd = 1/πτd, where τd is the decay time of the prompt response. In the present paper, the doorway-state phenomenon is analyzed again for the same harmonic signals but for a very large number of cycles. The strength-function phenomenon is once more obtained, but now with a Lorentzian width Γ' which is larger than Γd. A qualitative and numerical explanation of this fact is given, leading therefore to further understanding of doorway states in elastic systems. The numerical results show a very good agreement with the values measured in the laboratory.

A Comparative Study of the Crystallite Size and the Dislocation Density of Bent Steel Plates using Bragg-edge Transmission Imaging, TOF Neutron Diffraction and EBSD

Line broadening analysis was performed on the time-of-flight neutron diffraction data for the plastically bent plates of a ferritic steel and a duplex stainless steel. A Rietveld analysis program, Z-Rietveld ver. 1.0 was used to fit the anisotropically broadened patterns where the increase in Lorentzian full width at half maximum (FWHM) and the Gaussian FWHM involves information of the crystallite size and the dislocation density, respectively. The derived results were compared with those obtained by using Bragg-edge transmission spectrum analysis and electron backscatter diffraction (EBSD) observations.

Trapping of coherence and entanglement in photonic band-gaps

We investigate the coherence trapping of a two-level atom transversally interacting with a reservoir with a photonic band-gap structure function. We then focus on the multipartite entanglement dynamics via genuinely multipartite concurrence among N independent atoms each locally coupled with its own reservoir. By considering the Lorentzian width and the system size, we find that for the resonant and near-resonant conditions, the increase of Lorentzian width and the decrease of system size can lead to the occurrence of coherence trapping and entanglement trapping. By choosing the multipartite GHZ state as atomic initial state, we show that the multipartite entanglement may exhibit entanglement sudden death depending on the initial condition and the system size. In addition, we also analyze how the crossover behaviors of two dynamical regimes are influenced by the Lorentzian width and the weight ratio, in terms of the non-Markovianity.