Search

The most common mid-infrared (MIR) attenuated total reflection (ATR) accessory has a nominal angle of incidence of 45° and does not have a polarizer. A spectrum recorded with such an accessory does not hold enough information for the sophisticated ATR correction of MIR spectra with strong peaks, which are often strongly affected by refractive index changes due to anomalous dispersion. Here we show that a 45° ATR spectrum recorded without a polarizer and the polarization angle for the same ATR Fourier transform infrared spectroscopy system provide enough information to determine the ATR s -polarized spectrum. Further analysis with an improved non-iterative Kramers–Kronig analysis immediately yields the complex refractive index function. The analysis is about two orders of magnitude faster than iterative formalism and runs within seconds on a typical office PC. The effectiveness of our advanced ATR correction formalism is showcased through its application to water, employing diamond, ZnSe, and Ge ATR crystals, along with two distinct ATR accessories. Additionally, the formalism is applied to octadecane spectra. Potential sources of errors such as incidence angle spread, dispersion of the polarization angle, and the influence of reflection at the air/ATR crystal interface are investigated by simulations. [ABSTRACT FROM AUTHOR]

Based on hybrid 2D correlation analysis, we recently derived and introduced a "smart error sum," a sophisticated loss function that can be used for solving nonlinear inverse problems like the determination of optical constants and oscillator parameters from a series of optical spectra in the infrared spectral region. The advantage of the smart error sum compared to the conventional sum of squared errors lies in its ability to marginalize multiplicative systematic errors such as, for example, reflectance values above unity in transflection spectra. This is enabled by a transformation, which allows fits to not exclusively focus on forcing fit spectra to agree with experimental spectra at every wavenumber point by all means, but also to take correlations such as spectral similarities and their changes with certain perturbations into account. In this work, we extend our approach to accommodate the treatment of individual spectra, instead of only series, based on hybrid two-trace two-dimensional (2T2D) correlation analysis. We evaluate and prove the value of our approach by individually analyzing experimental transflection spectra of polymethyl methacrylate (PMMA) layers on gold substrates. The comparison of the results with those obtained by the original smart error sum based on the whole set of spectra as well as those resulting from conventional fitting of series and individual spectra (using the conventional sum of squared errors) confirms the validity and soundness of the 2T2D smart error sum. Graphical Abstract This is a visual representation of the abstract. [ABSTRACT FROM AUTHOR]

Recently a new family of loss functions called smart error sums has been suggested. These loss functions account for correlations within experimental data and force modeled data to obey these correlations. As a result, multiplicative systematic errors of experimental data can be revealed and corrected. The smart error sums are based on 2D correlation analysis which is a comparably recent methodology for analyzing spectroscopic data that has found broad application. In this contribution we mathematically generalize and break down this methodology and the smart error sums to uncover the mathematic roots and simplify it to craft a general tool beyond spectroscopic modelling. This reduction also allows a simplified discussion about limits and prospects of this new method including one of its potential future uses as a sophisticated loss function in deep learning. To support its deployment, the work includes computer code to allow reproduction of the basic results. [ABSTRACT FROM AUTHOR]

Using linear dichroism theory, one would assume that a z-cut of a uniaxial crystal is equivalent to an x-cut to determine the perpendicular component of the dielectric tensor and the corresponding oscillator parameters. However, Fresnel's equations show that the effect of interfaces in the form of the continuity relations of the different components of the electric field must be considered. A consequence of the continuity relations is that perpendicular modes increase less significantly in strength with increasing angle of incidence than expected. This is a consequence of the fact that it is the inverse of the perpendicular component of the dielectric function that increasingly becomes important with a growing angle of incidence. An inverse dielectric function, however, has typically much smaller values than the dielectric function. An additional consequence is that perpendicular modes are blueshifted and coupled in such a way that oscillator strength is transferred to the higher wavenumber mode. Thus, the spectral signatures of perpendicular modes are often weak and masked by the parallel modes when two modes overlap. Accordingly, to enable dispersion analysis, it is suggested to use a hybrid of the conventional residual sum of squares and the two-trace two-dimensional (2T2D) smart error sum, which can correct systematic multiplicable errors in the experimental spectrum. As demonstrated for fresnoite (Ba2TiSi2O8), this is an important step toward determining the perpendicular component of the dielectric tensor and the corresponding oscillator parameters using dispersion analysis, since asynchronous 2T2D correlation spectra are, in particular, sensitive to perpendicular modes. [ABSTRACT FROM AUTHOR]

We have recorded attenuated total reflection infrared spectra of binary mixtures in the (quasi-)ideal systems benzene–toluene, benzene–carbon tetrachloride, and benzene–cyclohexane. We used two-dimensional correlation spectroscopy, principal component analysis, and multivariate curve resolution to analyze the data. The 2D correlation proves nonlinearities, also in spectral ranges with no obvious deviations from Beer's approximation. The number of principal components is much higher than two and multivariate curve resolution carried out under the assumption of the presence of a third component, results in spectra which only show bands of the original components. The results negate the presence of third components, since any complex should have lower symmetry than the individual molecules and thus more and/or different infrared-active bands in the spectra. Based on Lorentz–Lorenz theory and literature values of the optical constants, we show that the nonlinearities and additional principal components are consequences of local field effects and the polarization of matter by light. Lorentz–Lorenz theory is, however, not able to explain, for example, the different blueshifts of the strong A2u band of benzene in the three mixtures. Obviously, infrared spectroscopy is sensitive to the short-range order around the molecules, which changes with content, their shapes, and their anisotropy. Graphical Abstract [ABSTRACT FROM AUTHOR]

We suggest a new modality of infrared spectroscopy termed Infrared Refraction Spectroscopy, which is complimentary to absorption spectroscopy. The beauty of this new modality lies not only in its simplicity but also in the fact that it closes an important gap: It allows to quantitatively interpret reflectance spectra by simplest means. First, the refractive index spectrum is calculated from reflectance by neglecting absorption. The change of the refractive index is proportional to concentration, and the spectra with features similar to second derivative absorbance spectra can simply be computed by numerically deriving the refractive index spectra, something which can be easily carried out by standard spectra software packages. The peak values of the derived spectra indicate oscillator positions and are approximately proportional to the concentration in a similar way as absorbance is. In contrast to absorbance spectra, there are no baseline ambiguities for first derivative refractive index spectra, and in refractive index spectra, instead of integrating over a band area, a simple difference of two refractive index values before and after an absorption leads to a quantity that correlates perfectly linearly with concentration in the absence of local field effects. Graphical Abstract [ABSTRACT FROM AUTHOR]

[Display omitted] • Dispersion analysis was extended to include isotropic chiral materials. • We applied extended dispersion analysis to the VCD spectra of α-Pinene. • We applied extended dispersion analysis to the VCD spectra of Propylene oxide. • The area of a couplet divided by wavenumber is the same above and below zero. Classical electromagnetic theory applied to infrared (IR) and vibrational circular dichroism (VCD) spectra of chiral compounds can provide useful insights, such as the fact that the area of all bands of wavenumber-normalized absorbance above zero must be the same as the area below zero. Additionally, dispersion analysis based on wave optics and dispersion theory, which was extended by Born and Kuhn to include chiral substances, can be used to quantitatively describe the dielectric function and the chiral admittance functions that shape IR and VCD spectra. For dispersion analysis, pairs of coupled oscillators, with five different kinds of parameters, namely oscillator strength, damping, oscillator position, vertical distance between coupled oscillators, and the coupling constant are used to model the dielectric functions and chiral admittance functions. We report the results of such an analysis for α-Pinene and Propylene oxide. For most bands, the oscillator model using two coupled oscillators is sufficient to achieve a good correspondence between experimental and modelled data. [ABSTRACT FROM AUTHOR]

[Display omitted] • Wave optics is needed to explain the infrared 2D-COS spectra of oriented materials. • Wave optics allows to determine orientation to a much higher degree than LDT. • Two-trace 2D-COS can uniquely identify the orientation distribution of a sample. On the level of the Bouguer-Beer-Lambert approximation, the effects introduced by linear dichroism into absorbance spectra can be simulated by classic linear dichroism theory. If wave optics and dispersion theory are employed, linear dichroism can be modelled with a 4x4 matrix formalism. For linear dichroism theory, the angle between polarization direction and transition moment can be seen as a perturbation which allows to calculate corresponding infrared 2D correlation spectra. Similarly, with help of an orientation representation based on Euler's angles, varying the latter allows the same if electromagnetic theory is employed. Correspondingly, we compare the substantially different footprints of linear dichroism according to both theories in infrared 2D correlation spectra and show that only those based on wave optics and dispersion theory are in accordance with experimental results. Accordingly, in particular asynchronous 2D correlation spectra allow to detect orientation with a sensitivity that is unparalleled in case of conventional spectra, even if they are recorded with help of a polarizer and an analyzer. [ABSTRACT FROM AUTHOR]

[Display omitted] • A formalism to determine the chirality admittance functions was developed. • The corresponding functions were determined for α-Pinene and Propylene oxide. • For VCD spectra the Bouguer-Lambert approximation holds strictly. • The area of a VCD signal divided by wavenumber is the same above and below zero. Optical constants functions of analytes are indispensable for the effective design of plasmonic sensors. Such sensors are potentially able to enhance the sensitivity by several order of magnitudes which can greatly facilitate the determination of the generally weak spectral signals caused by vibrational circular dichroism. Accordingly, to demonstrate how to obtain these functions, we have determined the dielectric and chirality admittance functions of α-Pinene and Propylene oxide in the mid-infrared spectral range using attenuated total reflection and vibrational circular dichroism spectroscopy. Our iterative formalism starts with an estimation of the absorption index function, followed by the calculation of the refractive index function using the Kramers-Kronig relation and a modelled spectrum based on Fresnel's equations. By comparing the experimental and modelled spectra, we improve the absorption index function. To determine the chirality admittance function, we use the same iterative formalism, but with a modified 4x4 matrix formalism formulated by Berreman. Our results show that the experimental absorbance difference is independent of the dielectric function of the chiral substance and depends linearly on the cuvette thickness. Additionally, we provide a sum rule that can be used to assess the quality of VCD spectra and determine the position of the baseline. Our findings provide crucial insights into the optical properties of chiral substances in the mid-infrared spectral range, which have important implications for a range of applications in fields such as analytical chemistry and materials science. [ABSTRACT FROM AUTHOR]

Based on Beer's law, it is assumed that the absorbance of a mixture is that of the neat materials weighted by their relative amounts (linear mixing rule). In this contribution, we show that this is an assumption that holds only under various approximations for which no change of the chemical interactions is just one among several. To understand these approximations, which lead incrementally to different well known mixing rules, we finally derive the linear mixing rule from the Lorentz–Lorenz relation, with the first approximation that the local electric field is correctly described in this relation. Further levels of approximation are that the local field equals the applied field (Newton–Laplace mixing rule) and that the change of the index of refraction and, equivalently, absorption is weak (Gladstone–Dale/Arago–Biot mixing rule). Even then the linear mixing rule is only strictly valid if the indices of refraction in the transparency region at higher frequency than the absorption have the same value and the mixing is homogeneous relative to the resolving power of the light ("micro-homogeneous"). Under these preconditions, linear mixing of the individual absorbances is established. We illustrate the spectral differences between the different mixing rules, all of which are based on volume and not on mass fractions, with examples. For micro-heterogeneous samples, a different linear mixing rule governs the optical properties, which refers to the experimental quantities, reflectance, and transmittance. As a result, for such samples, mixtures of already comparably high content give only weak signals due to band flattening, which are hard to distinguish from baseline effects. [ABSTRACT FROM AUTHOR]

Substantial refractive index mismatches between substrate and layers lead to undulating baselines, which are known as interference fringes. These fringes can be attributed to multiple reflections inside the layers. For thin and plane parallel layers, these multiple reflections result in wave interference and electric field intensities which strongly depend on the location within the layer and wavenumber. In particular, the average electric field intensity is increased in spectral regions where the reflectance is reduced. Therefore, the most important precondition for the Beer–Lambert law to hold, absorption as the single reason for electric field intensity changes, is no longer valid and, since absorption is proportional to the electric field intensity, considerable deviations from the Beer–Lambert law result. Fringe removal is consequently synonymous with correcting deviations from the Beer–Lambert law in the spectra. Within this contribution, we introduce an appropriate formalism based on wave optics, which allows a particularly fast and simple correction of any interference based effects. We applied our approach for correcting transmittance spectra of Poly(methyl methacrylate) layers on silicon substrates. The interference effects were successfully removed and correct baselines, in good agreement with the calculated spectra, were obtained. Due to its sound theoretical foundation, our formalism can be used as benchmark to test the performance of other methods for interference fringe removal. [ABSTRACT FROM AUTHOR]

In contrast to the extensive molecular and crystal structure investigations on oxalic acid dihydrate (C 2 H 2 O 4 ·2H 2 O, α-POX) and its deuterated analogues (α-DOX), stands the absence of a complete vibrational spectra analysis. Such analysis is desirable in view of the proton dynamics in α-POX crystals. In this communication we report the room temperature polarized IR reflectance spectra of a single crystal of α-POX recorded from the ac crystal plane, and from the plane containing the b -crystallographic axis, with polarization along the axis. Dispersion analysis of the reflectance spectra of both B u and A u symmetry type modes, using model dielectric and reflectance function valid for the monoclinic case, have been performed and the results are discussed. Some aspects of the obtained fit results for some of the spectral regions and the peculiar change of the reflectance function with polarization angle are also discussed in this work. A correlation between the crystal structure and measured spectra, together with the results of the performed dispersion analysis, gave answers to some of the problems concerned with the orientation of the transition dipole moments of the IR active modes. The assignment of modes is assisted by DFT calculations. Another aspect covered in this work is the model reflectance functions using different averaging theories that have been applied in obtaining the reflectance spectrum of a polycrystalline sample. The results of the comparison between these spectra and the recorded reflectance spectra from a polycrystalline sample were further discussed. Unlabelled Image • The RT polarized reflectance spectra of a single crystal of α-POX recorded from the ac crystal plane are presented. • Dispersion analysis of the reflectance spectra, have been performed and the results are discussed. • The assignment of modes was assisted by DFT calculations. [ABSTRACT FROM AUTHOR]

Abstract We report a considerable improvement of Poor Man's Kramers-Kronig analysis and Kramers-Kronig constrained variational analysis. Whereas the first method is an alternative to the well-established conventional Kramers-Kronig analysis, but fully analytical, the second method allows to capture subtle spectral features that might get lost by conventional dispersion analysis using oscillator models. Since both methods share the same physical foundation, an improvement in the Kramers-Kronig conformity will be a benefit for either. The corresponding improvement that we report decreases the average errors and increases conformity by about three orders of magnitude. This puts Poor Man's Kramers-Kronig analysis in the range of Maclaurin's method, which is still one of the numerical benchmarks. Kramers-Kronig constrained variational analysis on the other hand can now unleash its full potential and is able to correctly model even spectra of inorganic materials with their strong absorption bands without being supported by conventional oscillators. Graphical abstract Unlabelled Image Highlights • Increase of the accuracy of Poor Man's Kramers-Kronig analysis and Kramers-Kronig constrained variational analysis by three orders of magnitude. • Kramers-Kronig constrained variational analysis can now be employed without support from damped harmonic oscillators, also for materials with very strong absorption. • Kramers-Kronig conformity of Poor Man's Kramers-Kronig analysis is henceforth in the range of Maclaurin's method. [ABSTRACT FROM AUTHOR]

A hybrid formalism combining elements from Kramers–Kronig based analyses and dispersion analysis was developed, which allows removing interference-based effects in the infrared spectra of layers on highly reflecting substrates. In order to enable a highly convenient application, the correction procedure is fully automatized and usually requires less than a minute with non-optimized software on a typical office PC. The formalism was tested with both synthetic and experimental spectra of poly(methyl methacrylate) on gold. The results confirmed the usefulness of the formalism: apparent peak ratios as well as the interference fringes in the original spectra were successfully corrected. Accordingly, the introduced formalism makes it possible to use inexpensive and robust highly reflecting substrates for routine infrared spectroscopic investigations of layers or films the thickness of which is limited by the imperative that reflectance absorbance must be smaller than about 1. For thicker films the formalism is still useful, but requires estimates for the optical constants. [ABSTRACT FROM AUTHOR]

We show that an electric field standing wave effect is responsible for the oscillations and the non-linear dependence of the absorbance on the layer thickness in thin layers on a reflective surface. This effect is connected to the occurrence of interference inside these layers. Consequently, the absorptance undergoes a maximum electric field intensity enhancement at spectral positions close to those where corresponding non-absorbing layers on a metal show minima in the reflectance. The effect leads to changes of peak maxima ratios with layer thickness and shows the same periodicity as oscillations in the peak positions. These peculiarities are fully based on and described by Maxwell's equations but cannot be understood and described if the strongly simplifying model centered on reflectance absorbance is employed. [ABSTRACT FROM AUTHOR]

We investigate electric field standing wave effects in the system semiinfinite incidence medium with high index of refraction/layer/vacuum, the latter being the semiinfinite exit medium. If the layer has a lower index of refraction than the incidence medium, then very strong resonances occur between the two critical angles of the system defined by the systems incidence medium/layer and incidence medium/vacuum, as the layer is then a cavity. In particular close to the lower critical angles, the evanescent fields extend strongly into the exit medium. Based on this effect we suggest two new spectroscopic modalities, namely interference-enhanced internal reflection Raman spectroscopy and interference-enhanced attenuated total reflection infrared spectroscopy. [ABSTRACT FROM AUTHOR]

[Display omitted] • That the refractive index function squared equals the dielectric function, is one cause of coupling effects in IR spectra. • Another cause are local field effects like those represented by the Lorentz-Lorenz or Clausius-Mossotti-relation. • Coupling effects are important for band fitting and for understanding the results of quantum mechanical calculations. We discuss coupling effects in infrared spectra which are caused by dispersion and local field effects. The first effect is instigated by changes of the refractive index due to absorption which have an impact on the strength of adjacent absorptions. The second effect is a consequence of the light-induced polarization of one molecule affecting neighboring ones. These coupling effects do not only effect band positions, but also influence relative intensities. They are particularly strong in case of overlapping bands and complicate their deconvolution by band fitting. We investigated the corresponding challenges for the HO-stretching vibrations in water and the Amide I band in proteins. Our findings show that the effects are significant and of high interest for protein and water structure determination. Especially, for the water stretching vibrations we conclude that it is of utmost importance to consider such coupling effects in quantum mechanical calculations of water spectra. Otherwise, progress in understanding band positions and profiles is likely to be hampered. Also, in case of the Amide I band we found a distinct impact of such coupling effects. Accordingly, we strongly recommend consideration of dispersion and local field effects to ensure the possibility of an accurate, quantitative determination of α-helix and β-sheet structures. [ABSTRACT FROM AUTHOR]

Several samples of flat soda-lime silicate glass were investigated by the Infrared Attenuated Total Reflection (IR-ATR) spectroscopy technique. The specular reflectance spectra together with the results of the performed dispersion analysis and the generated reflectance spectra, using Fresnel equations, suggest that the samples are isotropic. In contrast, spectra recorded by the ATR technique suggest an anisotropic structure on the surface of the specimen different from that in the bulk. This is established through differences in the s- and p-polarized IR-ATR spectra, which cannot be simply transformed into one another employing Fresnel formula for an isotropic case. It appears that this thin film having a structure different from the bulk is larger than the ATR effective penetration depth of the evanescent ray for each incidence angle above the critical one. The investigation suggests C 2 symmetry of the SiO 4 unit. [ABSTRACT FROM AUTHOR]

We investigate how dispersion analysis can profit from the use of a Lorentz-type description of the inverse dielectric function. In particular at higher angles of incidence, reflectance spectra using p -polarized light are dominated by bands from modes that have their transition moments perpendicular to the surface. Accordingly, the spectra increasingly resemble inverse dielectric functions. A corresponding description can therefore eliminate the complex dependencies of the dispersion parameters, allow their determination and facilitate a more accurate description of the optical properties of single crystals. [ABSTRACT FROM AUTHOR]

[Display omitted] • Classical chemometric methods are based on Beer's approximation, which does not hold for ideal liquid mixtures. • Multivariate Classical Least Squares (CLS) regression is found to be inferior to Univariate CLS if peak values of a band with a comparably weak oscillator is selected. • Inverse Least Squares (ILS) Regression should therefore also be based on bands of comparably weak oscillators. • Principle Component Regression is superior to CLS and ILS if all available components are used. A considerable reduction of components is not advisable. We have recorded ATR-IR spectra of binary mixtures in the (quasi-)ideal systems Benzene-Toluene, Benzene-Carbon tetrachloride and Benzene-Cyclohexane and performed classical least squares, inverse least squares and principal component regression on the resulting spectra. In contrast to the general expectation, the spectra of ideal mixtures follow only roughly Beer's approximation, in particular stronger bands show shifts and increased intensities for intermediary compositions since the polarization of matter by light cannot be neglected. As a consequence, these conventional regression techniques lead to principle and unavoidable errors, even though some of the classical regression techniques are assumed to be able to cope with nonlinearities. In particular in the system Benzene-Carbon tetrachloride large errors result and the relative average error of the volume fraction determination is about 10 % for all three methods. Especially remarkable is that the multivariate regression methods do not perform better than the classical univariate calibration if for the latter a peak due to an oscillator with comparably low oscillator strength is selected, since for such bands polarization effects are weak and Beer's approximation holds comparably well. [ABSTRACT FROM AUTHOR]

Abstract We present a rigorous derivation of Beer's law from electromagnetic theory which allows to establish the connection of wave optics and Maxwell's equations with quantitative UV/VIS and infrared spectroscopy. As a result of this derivation, the attenuation constant is shown to be a function of the index of refraction. For small concentrations and an index of refraction not very different from unity, however, the empirical law is retrieved. Only for very strong absorptions with attenuation constants beyond 103 l/(mol·cm) and high concentrations, noticeable deviations from the empirical law and its linear concentration dependence are predicted to occur. The derivation is presented in a form, which is not only similar to that leading to the Clausius-Mossotti equation, but also shares the same starting point. Accordingly, it can easily be included in the curricula of physical chemistry. Graphical abstract Unlabelled Image Highlights • Derivation of Beer's law from simple electromagnetic Theory • Result of the derivation shows that the molar attenuation constant depends on the index of refraction. • This dependency can be neglected except for high molar attenuation constants and concentrations. [ABSTRACT FROM AUTHOR]

[Display omitted] • The upper limit of the Kramers-Kronig integrals can generally be adapted to the upper measurement range by the use of the (square root of the) dielectric background. • For the calculation of the absorption index or the phase function of reflectance, setting all values below the measured region to the value at the limit of the measurement range marginalizes the errors of the KKA. • A further error reduction can be achieved if a two stage Kramers-Kronig analysis is employed or if a slope is introduced by a fit procedure. • All suggested methods are reliable, fast and, in particular, simple. Therefore, existing KKR programs can be easily adapted and even conventional spreadsheet software can be used. Since about 60 years, it is possible to determine the set of optical constants from reflectance measurements by the Kramers-Kronig relations. Unfortunately, the potential of the method seems to be limited in practice by the need to extend measured data into unknown regions by extrapolation, which is prone to error and leads to deviations from the true values in the known region depending on the method of extension. With the advent of infrared refraction spectroscopy, which uses reflectance measurements at normal or near normal incidence, the development of a fast method to determine the complex index of refraction function reliably for these cases has become an even more interesting goal. In this work, we introduce a way to perform a Kramers-Kronig analysis of such reflectance spectra without the need to extrapolate the measured data for higher wavenumbers beyond the measurement range. Furthermore, we introduce and compare very simple and reliable material-independent ways to extrapolate the measured data for lower wavenumbers. As a result, we devise fast and sufficiently accurate methods, which are easily implementable into existing spectrometer software, to extract quantitative spectral information from reflectance measurements at near normal incidence. [ABSTRACT FROM AUTHOR]

Highlights: [•] Complete dispersion analysis of polarized IR reflectance spectra was performed. [•] A technique for discriminating between anion vibrations and water librations was proposed. [•] The HOH stretching transition dipole directions were discussed. [•] The reason for the isolated ion stretching vibration red shift was discussed. [ABSTRACT FROM AUTHOR]

We reply to a comment made in [E. Rousseau, N. Izard, J.-L. Bantignies, D. Felbacq, Comment on the paper "Improving Poor Man's Kramers-Kronig analysis and Kramers-Kronig constrained variational analysis", Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, (2021) 119849]. [ABSTRACT FROM AUTHOR]

Abstract: Results of the first dispersion analyses of polarized reflection spectra from a monoclinic a–c crystal plane taking properly into account the monoclinic symmetry and non-normal incidence on the crystal surface are reported. Spectra were recorded for the incidence angles α =8°, 16°, 40° and 60°, and for each at four different polarization angles. For the first two incidence angles the spectra were additionally analyzed under the assumption of normal incidence and the results were compared to those which resulted from the exact treatment. The comparison focused on two different aspects. The first aspect concerns the validity of the oscillator parameters. Accordingly, oscillator parameters of IR active modes obtained by dispersion analysis under the assumption of normal incidence do not show systematic errors despite the simplified treatment. This is a consequence of the fact that errors due to the incorrect assumption of normal incidence are compensated mainly by increases of the diagonal terms of the high frequency dielectric tensor. The corresponding values obtained under the assumption of normal incidence show averaged standard deviations of about 2% at 8° and about 9% at 16°. The second aspect investigated focuses on the employment of the oscillator parameters to generate the dielectric function tensor for optical calculations. Here we found that, as a direct consequence of the increased high frequency dielectric tensor, errors substantially increase if the resulting dielectric tensor functions are employed to calculate the reflectance at higher angles of incidence. Therefore, and since the increase of computational effort due to the exact treatment is small, we strongly suggest and encourage its use instead of the simplified treatment. [Copyright &y& Elsevier]

Abstract: Based on Berreman''s 4×4 matrix formalism [W. Berreman, J. Opt. Soc. Am. 62, 502 (1972)] we derive simplified expressions for the reflection formulas from the a–c crystal surface for non-normal incidence. The computational effort to apply the formulas was found to be only insignificantly higher than those for normal incidence, but considerably lower than for the general expressions. Consequently, the simplified formulas can be readily applied for dispersion analysis of spectra gained by spectroscopic ellipsometry or attenuated total reflection. [Copyright &y& Elsevier]

Abstract: The 390cm−1 spectral feature of polycrystalline hematite is shown to be caused by a crystallite size effect which is caused by the anisotropic nature of single crystalline hematite. This effect occurs if the probing light is able to resolve the heterogeneous nature of a polycrystalline material and if the corresponding single crystalline material is optically anisotropic. Therefore it does not depend on whether the material of interest is a powder or consolidated. As a consequence, the resulting macroscopic reflectance and transmittance of the polycrystalline material is an average of the microscopic reflectance and transmittance of the individual crystallites. Therefore, randomly oriented polycrystalline materials with large crystallites show characteristic changes in their spectral profile compared to the spectral profiles of polycrystalline materials consisting of crystallites that are small in comparison with the wavelength. The extent of the spectral changes depends on the degree of optical anisotropy of the corresponding single crystalline material. The spectral changes also comprise non-zero cross-polarization terms despite of random orientation. Therefore a characterization of a polycrystalline material with a scalar dielectric function is possible in general only if the material consists of randomly oriented crystallites small compared to the wavelength. [Copyright &y& Elsevier]

Abstract: Using a single crystal of fresnoite (Ba2TiSiO8), we demonstrate that polyethylene (PE) can be used as a contacting agent to enable the recording of ATR-spectra of materials with hard surfaces. The performance of our method is compared with the standard according to literature where CS2 is used as an immersion liquid. A Harrick Seagull cell, equipped with a ZnSe semi-sphere ATR-crystal has been used in measuring s- and p-polarized spectra at different incidence angles. The experimental results were compared with model calculations based on the dielectric function tensor of fresnoite. The comparison reveals advantages of our method compared to the use of CS2 like: closer resemblance between experimental and modeled spectra, repeatability and persistent optical contact. Moreover, our technique is easier to use. [Copyright &y& Elsevier]

Abstract: A dense silica glass was prepared by consolidating a highly dispersed silicic acid powder (particle size <10nm) with the Spark Plasma Sintering (SPS) technique. The glass was characterized by ellipsometry, transmission electron microscopy (TEM), infrared reflectance and transmittance spectroscopy, as well as by Raman, UV–Vis–NIR and solid-state nuclear magnetic resonance (NMR) spectroscopy. The prototypic sample showed a transmittance of about 63% compared to silica glass in the UV–Vis spectral range. Based on the results of infrared transmittance spectroscopy this lower transparency is due to the comparably high water content, which is about 40 times higher than that in silica glass. 1H magic-angle spinning (MAS) NMR confirmed an increase in hydroxyl groups in the sample prepared by SPS relative to that of the conventional SiO2 reference glass. Aside from the comparably high water content, we conclude from the similarity of the IR-reflectance and the 29Si MAS NMR spectra of the SPS sample and the corresponding spectra of the conventionally prepared silica glass, that the short- and medium-range order is virtually the same in both materials. Raman spectroscopy, however, suggests that the number of three- and four-membered rings is significantly smaller in the SPS sample compared to the conventionally prepared sample. Based on these results we conclude that it is possible to prepare glasses by compacting amorphous powders by the SPS process. The SPS process may therefore enable the preparation of glasses with compositions inaccessible by conventional methods. [Copyright &y& Elsevier]

Abstract: Polarized IR reflectance spectra of eight Tutton salts single crystals: M′2M″(SO4)2·6H2O; M′: K+ or NH4 +; M″: Ni2+, Co2+, Zn2+ or Mg2+) were recorded at near-normal incidence. Dispersion analysis was performed for the whole mid-IR region. The results on ν 3(SO4 2−) frequency region are reported in this paper. Reflectance spectra were recorded using radiation with polarization along the b crystallographic axis and in the ac crystal plane. Results of the fit for the transversal frequency, oscillator strength, attenuation constant and the orientation of the transition moments in the ac crystal plane for the ν 3(SO4 2−) frequency region are presented. The longitudinal frequencies for the A u vibrations were obtained from the energy-loss function spectra, while for the B u vibrations a particular approximation was used. In addition to frequency values, the directions of the longitudinal transition dipole moments in the ac crystal plane were also found. The dependence of the principal axes of the real and the imaginary parts of the dielectric tensor, on the radiation frequency, was established. An attempt was made to estimate the transition moment directions of the ν 3(SO4 2−) mode components by correlation of the spectroscopic and structural findings. [Copyright &y& Elsevier]

Abstract: Polarized IR reflectance spectra of K2Ni(SO4)2·6H2O single crystal (belonging to the group of Tutton salts) were recorded at near-normal incidence. From the dispersion analysis performed on the spectra recorded from the ac crystal plane, mode parameters: transversal frequency, oscillator strength, attenuation constant and the orientation of the transition moment were determined. The polarized spectrum along the b crystallographic axis was also recorded and a dispersion analysis performed. Comparison between the spectroscopically obtained transition moment directions with those obtained from the structure data for various modes is discussed. All dielectric tensor component values were obtained for the whole mid-IR frequency range. Also, the real and the imaginary parts of the complex indexes of refraction for the waves with wave vector in the direction of the b crystallographic axis and in the ac plane (when the direction of the electric vector is oriented along the b axis) were found as functions of frequency. [Copyright &y& Elsevier]

Abstract: If two overlapping bands originate from transition moments that are perpendicular and lie along the principal axes of the infinity frequency dielectric tensor, an isosbestic-like point (ILP) appears in the overlaid polarized IR reflectance spectra of single crystals. These conditions can also be met in principle in case of the reflectance from the ac-plane of a monoclinic crystal despite of the crystal''s low symmetry. In order to determine the transition moment directions, diagonalization of the infinity frequency dielectric tensor should be performed. It is shown that a critical magnitude for the appearance of ILP is the angle of incidence. An increase of this angle leads to a transformation of the ILP to an isosbestic-like region, which eventually vanishes at higher incidence angles. Polarized reflectance spectra of gypsum (CaSO4·2H2O), recorded from the ac crystal face, were used to verify the theoretical results. [Copyright &y& Elsevier]

Abstract: Dispersion analysis in the ν3(SO4 2−) frequency region of two Tutton salt monoclinic single crystals, K2Ni(SO4)2·6H2O and (NH4)2Ni(SO4)2·6H2O, was performed. Employing analytical expressions for the dielectric tensor and the reflectance function valid for monoclinic crystals, oscillator parameters like, transversal mode frequencies and the corresponding attenuation constants, transition moments orientation and oscillator strengths as well as longitudinal mode frequencies and the corresponding transition moment orientations were obtained. These oscillator parameters were used in simulations in order to explain certain peculiarities in the reflectance spectra occurring with directional changes of the polarization vector. From the simulations it follows that the appearance of spectra with two totally overlapped bands (having quite different oscillator strengths) depends particularly on the orientation of the longitudinal transition moment of the mode with the smaller LO–TO splitting. [Copyright &y& Elsevier]

Abstract: How effective optical constants of randomly oriented polydomain media are determined by the dielectric tensor functions of the domains is still an open question. On this matter, we show that the basis of the often-applied effective medium approximation (EMA) is not compatible with the linear dichroism theory. Despite the similarity of the approaches there exists a striking discrepancy, which is obvious especially in the large anisotropy limit, while only small differences in the vicinity of resonances emerge if the anisotropy is negligible. The application of several different effective optical constants approaches taking into account either local field corrections or non-principal orientations lead to rather similar results except for very strong anisotropies. Since all of the approaches have a seemingly valid theoretical basis and due to the lack of experimental data it is difficult to decide which approach should be favoured. [Copyright &y& Elsevier]

Abstract: A new kind of orientation representation called symmetric Euler orientation representation (SEOR) is presented. It is based on a combination of the conventional Euler orientation representations (Euler angles) and Hamilton''s quaternions. The properties of the SEORs concerning orientational averaging are explored and compared to those of averaging schemes that are based on conventional Euler orientation representations. To that aim, the reflectance of a hypothetical polycrystalline material with orthorhombic crystal symmetry was calculated. The calculation was carried out according to the average refractive index theory (ARIT [T.G. Mayerhöfer, Appl. Spectrosc. 56 (2002) 1194]). It is shown that the use of averaging schemes based on conventional Euler orientation representations leads to a dependence of the result from the specific Euler orientation representation that was utilized and from the initial position of the crystal. The latter problem can be overcome partly by the introduction of a weighing factor, but only for two-axes-type Euler orientation representations. In case of a numerical evaluation of the average, a residual difference remains also if a two-axes type Euler orientation representation is used despite of the utilization of a weighing factor. In contrast, this problem does not occur if a symmetric Euler orientation representation is used as a matter of principle, while the result of the averaging for both types of orientation representations converges with increasing number of orientations considered in the numerical evaluation. Additionally, the use of a weighing factor and/or non-equally spaced steps in the numerical evaluation of the average is not necessary. The symmetrical Euler orientation representations are therefore ideally suited for the use in orientational averaging procedures. [Copyright &y& Elsevier]

Two recently developed formalism, one for the modelling of spectra of randomly oriented polycrystalline bulk materials consisting exclusively of crystallites being small compared to the resolution limit [Appl. Spectrosc. 56 (2002) 1194] and one for polycrystalline bulk materials in the large crystalline limit [J. Opt. A: Pure Appl. Opt. 4 (2002) 540] are combined in a unified approach in order to enable the modelling of spectra of materials consisting of both optically small and large regions of order. Based on this generalized formalism, several model calculations are carried out to demonstrate the influence of different crystallite size distribution on IR-reflectance spectra. The model calculations for a sample consisting of a 3:1 mass mixture of small and large crystallites are compared with the experimental results; the good correspondence between measured and modeled spectra confirms the value of the unified approach. [Copyright &y& Elsevier]

Conventional qualitative and quantitative IR-reflectance spectrum interpretation of glasses is discussed in light of new findings on the optics of polycrystalline materials and the close relation of the structure of crystallites and regions of medium range order in related glasses. According to these findings, a glass spectrum must not be compared in general with the spectrum of a related polycrystalline material, if the crystallite size exceeds the resolution limit of light. As a consequence of the similarities between the spectra of glassy and related polycrystalline compounds (optically small crystallites) and based on medium range order, the macroscopic optical properties of glasses result not only from disorder and fluctuations, but also from an orientational average of the optical properties of the medium range regions similar to the macroscopic optical properties of polycrystalline materials. Consequently, the assumption of cubic symmetry, which underlies all conventional types of dispersion analysis used for glasses, is inadequate. Based on ARIT (average refractive index theory), [Appl. Spectrosc. 56 (2002) 1194], which permits modeling the optical properties of polycrystalline materials with optically small crystallites, a method is proposed to generate artificial glass spectra from single crystal data. This method is particularly useful if polycrystalline bulk samples with optically small crystallites are not available, since it enables us to determine glass structure on a semi-quantitative level by comparing measured and artificial spectra. The value of the approach is demonstrated for fresnoite glass (Ba2TiSi2O8), Sr-fresnoite glass (Sr2TiSi2O8) and Ge-fresnoite glass (Ba2TiGe2O8). An important consequence of the assumption of an orientational average of the microscopic optical properties of medium range order regions is the prediction of the occurrence of mixed TO–LO modes in glasses. This is confirmed by the resemblance between peak shapes of model oscillators with large oscillator strengths and small damping constants and the prominent high wave number feature of vitreous silica. [Copyright &y& Elsevier]

The DHBD quantity represents the hydroxyl group density of alcoholic solvents or water. DHBD is purely physically defined by the product of molar concentration of the solvent (N) and the factor Σn=n×f which reflects the number n and position (f‐factor) of the alcoholic OH groups per molecule. Whether the hydroxyl group is either primary, secondary or tertiary is taken into account by f. Σn is clearly linearly correlated with the physical density or the refractive index of the alcohol derivative. Relationships of solvent‐dependent UV/Vis absorption energies as ET(30) values, 129Xe NMR shifts and kinetic data of 2‐chloro‐2‐methylpropane solvolysis with DHBD are demonstrated. It can be shown that the ET(30) solvent parameter reflects the global polarity of the hydrogen bond network rather than specific H‐bond acidity. Significant correlations of the log k1 rate constants of the solvolysis reaction of 2‐chloro‐2‐methylpropane with DHBD show the physical reasoning of the approach. [ABSTRACT FROM AUTHOR]

• Overview of the use of infrared spectroscopy for point-of-care applications. • Recent technological and scientific developments. • Easy to read and tailored for readers less familiar with infrared spectroscopy. In this contribution we review selected point-of-care applications of infrared spectroscopy and the technological innovations they are based on. After a short introduction summarizing the general idea behind point-of-care applications we introduce the reader to important infrared spectroscopy sensing principles on a very basic level. We discuss the role of optical components like quantum cascade lasers, supercontinuum sources, waveguides and how they are potentially going to revolutionize point-of-care applications. First, we focus on the technological solutions of some principal problems like increasing the pathlength in a transmission cell to enhance the sensitivity for solutes in aqueous solutions and discuss indirect methods which circumvent the problem of low transmittance. In the second part we show how the technological progress of the last decades enabled scientific progress leading to selected concrete and outstanding point-of-care solutions and applications based on infrared spectroscopy. These include the detection and quantification of malaria parasitemia, early recognition of Alzheimer's disease long before the onset of clinical symptoms and a non-invasive method for testing the blood glucose content. The selected examples demonstrate and showcase that infrared spectroscopy is on the way to become an indispensable technique for point-of-care applications. [ABSTRACT FROM AUTHOR]

A classical way of describing dielectric functions employs sums of contributions from damped harmonic oscillators. We derive the corresponding dispersion relations for the dielectric function and the inverse dielectric function to investigate and establish the relationship between the transversal and longitudinal optical oscillator strengths, which can differ, according to experimental results, by up to three orders of magnitude. We demonstrate that transversal and longitudinal oscillator strengths should be identical for a single oscillator and that the experimental differences are in this case due to the introduction of a dielectric background in the dispersion formula. For this effect we derive an exact correction. Based on this correction we further derive a modified Kramers-Kronig sum rule for the isotropic case as well as for the components of the inverse dielectric function tensor. For systems with more than one oscillator, our model provides oscillator strengths and LO resonance wavenumbers for uncoupled LO modes. Image 1 [ABSTRACT FROM AUTHOR]

We investigate exemplary the longitudinal optical (LO) mode order in compounds with a plasmon or plasmon-like phonon mode and additional phonon modes. When the oscillator strength of the plasmon or plasmon-like mode is gradually increased, a reordering of the modes takes place. Since it is not possible in crystals with orthorhombic or higher symmetry that a LO mode crosses a transverse optical (TO) mode's position, this reordering takes place via mode hybridization. During this mode hybridization, the plasmon or plasmon-like LO mode gradually becomes the originally higher situated LO mode while the latter morphs into the former. As a consequence, inner (LO-TO) and an outer (TO-LO) mode pairs are formed. These insights can be readily transferred to other semiconductors or many mode materials with reststrahlen bands, as long as their dielectric tensor can be (partly) diagonalized, and allow easily correct mode assignments. Image 1 • Provision/testing of a formalism to determine the longitudinal mode order in materials with plasmon or plasmon-like modes. • Determination of the longitudinal optical mode order in SrTiO 3. • Determination of the longitudinal optical mode order along the b-axis of monoclinic Ga 2 O 3. [ABSTRACT FROM AUTHOR]

We present a generalizable fabrication method for a new class of analytical devices that merges virtually any microfluidic design with high-sensitivity on-chip attenuated total reflection (ATR) sampling using any standard Fourier transform infrared (FTIR) spectrometer. Termed "spectIR-fluidics", a major design feature is the integration of a multi-groove silicon ATR crystal into a microfluidic device, compared with previous approaches in which the ATR surface served as a structural support for the entire device. This was accomplished by the design, fabrication, and aligned bonding of a highly engineered ATR sensing layer, which con'''tains a seamlessly embedded ATR crystal on the channel side and an optical access port that matched the spectrometer light path characteristics at the device exterior. The refocused role of the ATR crystal as a dedicated analytical element, combined with optimized light coupling to the spectrometer, results in limits of detection as low as 540 nM for a D -glucose solution, arbitrarily complex channel features that are fully enclosed, and up to 18 world-to-chip connections. Three purpose-built spectIR-fluidic cartridges are used in a series of validation experiments followed by several point-of-application studies on biofilms from the gut microbiota of plastic-consuming insects using a small portable spectrometer. [ABSTRACT FROM AUTHOR]

Abstract With generalized dispersion analysis it is possible to gain the dispersion parameters and dielectric tensor function of crystals with not only unknown orientation of the symmetry elements in within the sample but with also unknown crystal symmetry. The developed procedure is applied to two spectra sets of each crystal symmetry type to cover various levels of difficulty in the evaluation with generalized dispersion analysis. Graphical Abstract Unlabelled Image Highlights • Dielectric tensor function of a crystal is gained by dispersion analysis. • A priori knowledge of crystal symmetry and orientation not necessary any more • New evaluation scheme of a set of reflection spectra gives dielectric tensor function. • Crystal symmetry, orientation and oscillator parameters gained as by-product during evaluation [ABSTRACT FROM AUTHOR]

Abstract A single crystal of monoclinic sodium dichromate dihydrate was investigated by FTIR-spectroscopy in the spectral region of 4000–80 cm−1. On the measured reflection spectra dispersion analysis was performed to gain the oscillator parameters of the transition dipole moments of Na 2 Cr 2 O 7 ·2H 2 O and by that the dielectric tensor function. The gained oscillator parameters were verified by forward-calculation of spectra using different crystal faces. Graphical Abstract Unlabelled Image Highlights • Full dispersion analysis of Na 2 Cr 2 O 7 ·2H 2 O for the MIR and FIR spectral region • Complement information to the dichromate ion in addition to K 2 Cr 2 O 7 , Cs 2 Cr 2 O 7 and Rb 2 Cr 2 O 7 • Dispersion parameters confirmed by forward-calculation of spectra of different faces [ABSTRACT FROM AUTHOR]

• The photonic nanojet (PNJ) properties and parameters showed complex dependency. • The incident beam position can be tuned to achieve two different types of PNJs. • Type 1 has lower intensity and larger size, type 2 has high intensity and smaller size. • The PNJ intensity generally is higher when microsphere and beam sizes are comparable. • As microsphere size increases, the width and length of the PNJ increase. • As the beam size increases, the width and length decrease for type 1, and increase for type 2. • When the wavelength is decreased, the PNJ intensity and confinement increase. A photonic nanojet (PNJ) is a narrow beam of concentrated light emerging from the illuminated micro-scattering objects, which has attracted a lot of attention lately. However, so far the variation and the properties of the PNJ of a microsphere have been computationally investigated in a limited scope and mostly for plane wave as a source. Within the framework of the Generalized Lorenz-Mie theory (GLMT), a large-scale investigation of the PNJ properties (intensity, position, length and width) and their dependence on the parameters which influence the PNJ (beam wavelength, beam size, beam position and microsphere size) is presented. The calculations are carried out for more than 400 000 configurations of parameters, with Gaussian beam source. Computations show that each parameter plays an important role in the PNJ formation. The influence of each of the parameters and their complex interplay is studied in detail. Depending on the beam position, PNJs are classified into two types, with different characteristics and possible applications. We believe this systematic and comprehensive presentation of the widest range of PNJs so far will advance the knowledge of this phenomenon, and serve as a reference for tailoring any PNJ according to one's needs and applications. Table of content [Display omitted] [ABSTRACT FROM AUTHOR]

Polarized infrared and Raman spectra of triclinic LiAl(PO 4 )(OH) [montebrasite] single crystal were recorded for appropriate optical configurations. Dispersion analysis was applied on the infrared reflectivity spectra taken at low incidence angle (11°) to determine the oscillator parameters and the dipole directions of the polar phonons. In particular, all the 27 polar phonons, predicted by group theory for triclinic P 1 ¯ structure, were determined. The obtained dielectric tensor parameters have been checked by comparison between predicted and measured infrared spectra at higher incidence angle (34°). The azimuth and co-elevation angles obtained from the dispersion analysis showed that the response of several polar phonons is close to that of an orthorhombic system. Polarized Raman spectra obtained in several scattering geometries allowed us to obtain well-defined 24 non-polar modes, also in perfect agreement with group theory. The selection rule between Raman and infrared phonons was respected, confirming the centrosymmetric structure and ruling out any relevant influence of defects. The relatively narrow phonon bands are compatible with a highly ordered structure with fully occupied atomic sites. [ABSTRACT FROM AUTHOR]

Abstract: Polarized IR-reflection spectra of a single crystal of K2Cr2O7 were recorded at near normal incidence. Dispersion analysis was applied, taking fully into account the triclinic symmetry of the crystal and the measuring conditions, to determine the oscillator parameters. The oscillator parameters and the dielectric background tensor were proven valid by comparison between measured and based on these parameters modeled spectra of a randomly oriented polycrystalline sample. [Copyright &y& Elsevier]

Abstract: We present the first successful dispersion analysis of a triclinic crystal in the infrared spectral region. The corresponding scheme involves the parallel evaluation of 12 polarized reflection spectra recorded from three mutual perpendicular faces of a cube-shaped crystal. The dispersion analysis was carried out on a CuSO4·5H2O single crystal. The determined oscillator parameters and the corresponding dielectric function tensor were used to model the spectra of polycrystalline CuSO4·5H2O. The good correspondence between modeled and experimental spectra of the polycrystalline species proves the correctness of the approach. [Copyright &y& Elsevier]