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We present the derivation of a new kind of loss function from the symmetry rules of synchronous and asynchronous two-dimensional correlation maps. This loss function, which takes into account correlations that are based on causal relations among the members of a series of spectra, can be employed to solve non-linear inverse problems that are plagued by systematic multiplicative errors. This possibility results from the correlation-based loss function being practically insensitive to such systematic errors, which often arise in spectroscopy because sample spectra are usually ratioed against reference spectra. Using dispersion analysis, a sophisticated method of band fitting, of the spectra of poly(methyl methacrylate) films deposited on gold, we demonstrate the applicability and validity of the new loss function. If gold is used as a substrate, experimental spectra are often unphysical, that is, they display reflectance values larger than unity. In such cases, our correlation-based loss function not only helps to achieve accurate fits but also provides corrections to obtain physically meaningful spectra, which leads to results that are superior to conventional correction methods. The validity of the results is checked and proved with help of the results of dispersion analysis of spectra of films of poly(methyl methacrylate) on calcium fluoride (CaF

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The UV/Vis spectra of a hypothetical negative solvatochromic dye in a solvent are theoretically calculated assuming the classical damped harmonic oscillator model and the Lorentz-Lorenz relation. For the simulations, the oscillator strength of the solvent was varied, while for the solute all oscillator parameters were kept constant. As a result, a simple change of the oscillator strength of the solute can explain the redshift and intensity increase of the UV/Vis band of the solute. Simulated results are compared with measured UV/Vis spectroscopic data of 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate B30 (Reichardt's dye) Significant correlations of the absorption energy (1/λ

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.

The thermal infrared (TIR, or vibrational) emission spectra of a suite of synthetic Mg-Fe olivines exhibit notable differences from their natural igneous counterparts in terms of their band shapes, relative depths, and reduced shifts in some band positions with Mg-Fe solid solution. Comparable reflectance spectra acquired from olivine-dominated matrices and fusion crusts of some carbonaceous chondrite meteorites exhibit similar deviations. Here we show that these unusual spectral characteristics are consistent with crystallite sizes much smaller than the resolution limit of infrared light. We hypothesize that these small crystallites denote abbreviated crystal growth and also may be linked to the size of nucleation sites. Other silicates and non-silicates, such as carbonates, exhibit similar spectral behaviors. Because the spectra of mineral separates are commonly used in the modeling and analysis of comparable bulk rock, meteorite, and remote sensing data, understanding these spectral variations is important to correctly identifying the minerals and interpreting the origin and/or secondary processing histories of natural materials.

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.

A non-resonant, concentrated, narrow beam of light emerging from an illuminated microlens is called a photonic nanojet (PNJ). According to currently prevailing opinion, microspheres and microcylinders are only able to generate a PNJ in their exterior when their refractive index ns (or refractive index contrast) is less than 2. In this Letter we demonstrate that a PNJ can emerge from a microsphere even when ns > 2: first by employing the laws of geometrical optics for a divergent light source; then, by using ray transfer matrix analysis, a mathematical condition for the Gaussian beam (GB) outside the high ns microsphere is derived. The PNJ outside the microsphere with ns = 2.5 is simulated using Generalized Lorenz–Mie theory (GLMT), by using a front focused GB source. The simulated difference between front and back focusing on the dependence of ns is confirmed experimentally by Raman imaging. By opening the PNJ field for high refractive index materials, we believe this work will be a nucleus for new ideas in the field and enable new PNJ applications.

The Beer‐Lambert law is unquestionably the most important law in optical spectroscopy and indispensable for the qualitative and quantitative interpretation of spectroscopic data. As such, every spectroscopist should know its limits and potential pitfalls, arising from its application, by heart. It is the goal of this work to review these limits and pitfalls, as well as to provide solutions and explanations to guide the reader. This guidance will allow a deeper understanding of spectral features, which cannot be explained by the Beer‐Lambert law, because they arise from electromagnetic effects/the wave nature of light. Those features include band shifts and intensity changes based exclusively upon optical conditions, i. e. the method chosen to record the spectra, the substrate and the form of the sample. As such, the review will be an essential tool towards a full understanding of optical spectra and their quantitative interpretation based not only on oscillator positions, but also on their strengths and damping constants., If August Beer would have had a chance to combine Pierre Bouguer's findings and Johann Heinrich Lambert's law with his own results under consideration of James Clerk Maxwell's relations, he would have ensured the Bouguer‐Beer‐Lambert law to be well‐funded on electromagnetic theory. At least, he would have made users well aware of its limitations. Since he died too early, it is the goal of this review to complete his work in this regard.

CaF2 seems to be the ideal substrate material for organic and biological layers, since its refractive index is very similar to that of these materials. As a consequence of this similarity, the base...

In this contribution we show how the Lorentz‐Lorenz and the Clausius‐Mosotti equations are related to Beer's law. Accordingly, the linear concentration dependence of absorbance is a consequence of neglecting the difference between the local and the applied electric field. Additionally, it is necessary to assume that the absorption index and the related refractive index change is small. By connecting the Lorentz‐Lorenz equations with dispersion theory, it becomes obvious that the oscillators are coupled via the local field. We investigate this coupling with numerical examples and show that, as a consequence, the integrated absorbance of a single band is in general no longer linearly depending on the concentration. In practice, the deviations from Beer's law usually do not set in before the density reaches about one tenth of that of condensed matter. For solutions, the Lorentz‐Lorenz equations predict a strong coupling also between the oscillators of solute and solvent. In particular, in the infrared spectral region, the absorption coefficients are prognosticated to be much higher due to this coupling compared to those in the gas phase., Lorentz‐Lorenz equation revisited: The local field of Lorentz shifts the oscillator position to lower wavenumber and leads to coupling. Therefore, absorbance is no longer depending linearly on concentration.

Absorption, scattering, and fluorescence are processes that increase with electric field intensity. The most prominent way to enhance electric field intensity is to use localized or propagating surface plasmon polaritons (SPPs) based on metallic particles and nanostructures. In addition, several other, much less well-known, photonic structures that increase electric field intensity exist. Interference enhancement provided by thin dielectric coatings on reflective substrates is able to provide electric field intensity enhancement over the whole substrate and not only at certain hotspots, thereby being in particular suitable for the spectroscopy of thin surface layers. The same coatings on high refractive index substrates may be used for interference-enhanced total internal reflection-based spectroscopy in much the same way as Kretschmann or Otto configuration for exciting propagating SPPs. The latter configurations can also be used to launch Bloch surface waves on 1D photonic crystal structures for the enhancement of electric field intensity and thereby absorption, scattering, and fluorescence-based spectroscopies. High refractive index substrates alone can also, when nanostructured, enhance infrared absorption or Raman scattering via Mie-type resonances. As a further method, this review will cover recent developments to employ phonon polaritons in the reststrahlen region.

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.

It has been well recognized that infrared spectra of microscopically heterogeneous media do not merely reflect the absorption of the sample but are influenced also by geometric factors and the wave nature of light causing scattering, reflection, interference, etc. These phenomena often occur simultaneously in complex samples like tissues and manifest themselves as intense baseline profiles, fringes, band distortion and band intensity changes in a measured IR spectrum. The information on the molecular level contained in IR spectra is thus entangled with the geometric structure of a sample and the optical model behind it, which largely hinders the data interpretation and in many cases renders the Beer-Lambert law invalid. It is required to recover the pure absorption (i.e., absorbance) of the sample from the measurement (i.e., apparent absorbance), that is, to remove the 'artefacts' caused merely by optical influences. To do so, we propose an artefact removal approach based on a deep convolutional neural network (CNN), specifically a 1-dimensional U-shape convolutional neural network (1D U-Net), and based our study on poly(methyl methacrylate) (PMMA) as materials. To start, a simulated dataset composed of apparent absorbance and absorbance pairs was generated according to the Mie-theory for PMMA spheres. After a data augmentation procedure, this dataset was utilized to train the 1D U-Net aiming to transform the input apparent absorbance into the corrected absorbance. The performance of the artefact removal was evaluated by the hit-quality-index (HQI) between the corrected and the true absorbance. Based on the prediction and the HQI of two experimental and one simulated independent testing datasets, we could demonstrate that the network was able to retrieve the absorbance very well, even in cases where the absorbance is completely overwhelmed by extremely large 'artefacts'. As the testing datasets bear different patterns of absorbance and 'artefacts' to the training data, the promising correction also indicated a good generalization performance of the 1D U-Net. Finally, the reliability and computational mechanism of the trained network were illustrated via two interpretation approaches including a direct visualization of layer-wise outputs as well as a saliency-based method.

As derived by Max Planck in 1903 from dispersion theory, Beer's law has a fundamental limitation. The concentration dependence of absorbance can deviate from linearity, even in the absence of any interactions or instrumental nonlinearities. Integrated absorbance, not peak absorbance, depends linearly on concentration. The numerical integration of the absorbance leads to maximum deviations from linearity of less than 0.1 %. This deviation is a consequence of a sum rule that was derived from the Kramers‐Kronig relations at a time when the fundamental limitation of Beer's law was no longer mentioned in the literature. This sum rule also links concentration to (classical) oscillator strengths and thereby enables the use of dispersion analysis to determine the concentration directly from transmittance and reflectance measurements. Thus, concentration analysis of complex samples, such as layered and/or anisotropic materials, in which Beer's law cannot be applied, can be achieved using dispersion analysis., Absorbance at a particular spectral point does not necessarily depend linearly on the concentration. Based on electromagnetic theory, it can be demonstrated, however, that for the integrated absorbance, Beer's law still holds.

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.

In case of thin films of siloxane obtained from different organo-silane derivatives (alkoxy and chloro) on soda lime silica glass substrates, IR-ATR and IR-SR could not detect the organic functional groups of the coating. This becomes even more problematic for the case of tetraethoxysilane (when fully hydrolyzed), the coating of which possesses the same functional groups as the glass substrate. In this work we propose to employ the so-called ratio-reflectance spectra in the v(Si-O) wavenumber region, where both glass and the siloxane coating give most prominent bands, important for the evaluation of the quality of coating formation and qualitative knowledge on its structure. We show that the reflectance-absorbance spectra obtained from the ratio-reflectance spectra are in direct connection to the structure of the siloxane network which depends not only on the chemical nature of the parent silane, but also on the dipping time and the solvent composition. Some characteristics of the reflectance-absorbance spectra, like the appearance of a two well defined bands at 1110 and 975 cm

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.

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.

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].

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.

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 Na2Cr2O7·2H2O and by that the dielectric tensor function. The gained oscillator parameters were verified by forward-calculation of spectra using different crystal faces.

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.

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.

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Beer's empiric law states that absorbance is linearly proportional to the concentration. Based on electromagnetic theory, an approximately linear dependence can only be confirmed for comparably weak oscillators. For stronger oscillators the proportionality constant, the molar attenuation coefficient, is modulated by the inverse index of refraction, which is itself a function of concentration. For comparably weak oscillators, the index of refraction function depends, like absorbance, linearly on concentration. For stronger oscillators, this linearity is lost, except at wavenumbers considerably lower than the oscillator position. In these transparency regions, linearity between the change of the index of refraction and concentration is preserved to a high degree. This can be shown with help of the Kramers–Kronig relations which connect the integrated absorbance to the index of refraction change at lower wavenumbers than the corresponding band. This finding builds the foundation not only for refractive index sensing, but also for new interferometric approaches in IR spectroscopy, which allow measuring the complex index of refraction function., Linear or not? Like the absorbance, the change of the index of refraction at a particular spectral point can depend linearly on concentration for low oscillator strength or concentration.

The interaction of light with matter at surfaces of dielectrics strongly depends on polarization. Here, we present the first infrared spectroscopic evidence for significant polarization effects in the spectroscopic detection of adsorbate vibrational frequencies. In addition to much larger peak intensities for p-polarized light relative to s-polarization, a small but distinct blue shift was identified for CO adsorbed at the surfaces of two prototype dielectric substrates, CeO$_{2}$(111) and CaCO$_{3}$(10.4). A simulation using a layer model yields very good agreement with experiment.

This work demonstrates a membrane-based chiral plasmonic metamaterial with two plasmonic absorption bands which can be used for broadband surface-enhanced infrared absorption (SEIRA) and vibrational circular dichroism (VCD) sensing in the spectral range ∼1000–4000 cm–1 (SEIRA) and ∼2000–4000 cm–1 (VCD). Based on finite-difference time-domain simulations, the chiral plasmonic response was optimized for enhancement at around 3200 cm–1. Accordingly, the chiral cross-slit array was adjusted for application in conventional transmission measurement setups and covers an area of 1 mm2. Polyethylene was used as a model analyte to simulate the SEIRA broadband response and the results were compared with octadecanethiol measurements due to their spectral similarity. Signal enhancement was observed from 3000 cm–1 down to 1400 cm–1 by tuning the polarization of the incoming radiation. Due to the inherent chirality of the design, a strong VCD absorbance of 0.83 at ∼3500 cm–1 could be observed for the unloaded substrate....

Raman spectroscopy in combination with appropriate sample preparation strategies, for example, enrichment of bacteria on metal surfaces, has been proven to be a promising approach for rapidly diagnosing infectious diseases. Unfortunately, the fabrication of the required chip substrates is usually very challenging due to the lack of feasible instruments that can be used for quality control in the surface modification process. The intrinsically weak Raman signal of the biomolecules, employed for the enrichment of the micro-organisms on the chip surface, does not allow for monitoring of the successful immobilization by means of a Raman spectroscopic approach. Within this contribution, we demonstrate how a simple modification of a plain aluminum surface enables enhancement (or a decrease, if desired) of the Raman signal of molecules deposited on that surface. The manipulation of the Raman signal strength is achieved via exploiting interference effects that occur, if the highly reflective aluminum surface is modified with thin layers of transparent dielectrics like aluminum oxide. The thicknesses of these layers were determined by theoretical considerations and calculations. For the first time, it is shown that the interference effects can be used for the detection of biomolecules as well by investigating the siderophore ferrioxamine B. The observed degree of enhancement was approximately 1 order of magnitude. Moreover, the employed aluminum/aluminum oxide layers have been thoroughly characterized using atomic force and scanning electron microscopy as well as X-ray reflectometry and UV-Vis measurements.

We report the observation of an enormous circular dichroism (CD) response in broadband surface-enhanced infrared absorption sensing arrays. In our experiment, a 2D-metamaterial chiral cross-slit array adjusted for application in conventional measurement setups was used. The inherent chirality of the design results in a very strong CD absorbance of 0.83 at around 2.86 μm (3500 cm–1). This far surpasses our predictions based on the finite-difference time-domain simulations. This is probably the highest CD response ever reported for the mid-infrared region. Our observation was rigorously validated; thus most error sources were ruled out. Further, this Letter discusses our results in view of possible remaining artifacts that might have had an influence on our observations, as both chiral enantiomers and an achiral counterpart with similar structure were created and measured. A giant CD 2D-metamaterial might lead toward surface-enhanced vibrational circular dichroism spectroscopy, a field that is subject to li...

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.

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Dispersion analysis is applicable to arbitrarily cut monoclinic crystals of unknown orientation in order to find the symmetry axis. By this it is possible to differentiate between the transition moments oriented parallel and normal to the b-axis and to determine the dielectric tensor functions of those two principal directions. Dispersion analysis of arbitrarily cut monoclinic crystals is based on an extension of the evaluation scheme developed for arbitrarily cut orthorhombic crystals. We present dispersion analysis of monoclinic crystals exemplarily on spodumene (LiAl(SiO3)2) and yttrium orthosilicate (Y2SiO5).

We developed a measurement and evaluation scheme to perform dispersion analysis on arbitrarily cut orthorhombic crystals based on the schemes developed for triclinic and uniaxial crystals. As byproduct of dispersion analysis the orientations of the crystal axes are found. In contrast to the spectra of arbitrarily cut uniaxial crystals, where the fit routine has to separate two independent principal spectra, the spectra of arbitrarily cut orthorhombic crystals are a combination of three independent spectra and the evaluation scheme gets more complex. Dispersion analysis is exemplary performed on two different crystals, which show different spectral features and different levels of difficulties to evaluate. Neodymium gallate (NdGaO3) has broad overlapping reflections bands while topaz (Al2SiO4 [F, OH]2) has a quite high total number of infrared active bands.

The discovery of the enhancement of Raman scattering by molecules adsorbed on nanostructured metal surfaces is a landmark in the history of spectroscopic and analytical techniques. Significant experimental and theoretical effort has been directed toward understanding the surface-enhanced Raman scattering (SERS) effect and demonstrating its potential in various types of ultrasensitive sensing applications in a wide variety of fields. In the 45 years since its discovery, SERS has blossomed into a rich area of research and technology, but additional efforts are still needed before it can be routinely used analytically and in commercial products. In this Review, prominent authors from around the world joined together to summarize the state of the art in understanding and using SERS and to predict what can be expected in the near future in terms of research, applications, and technological development. This Review is dedicated to SERS pioneer and our coauthor, the late Prof. Richard Van Duyne, whom we lost during the preparation of this article., Funding is acknowledged from the European Research Council (ERC Advanced Grant No. 787510-4DBIOSERS to L.M.L.-M., ERC Advanced Grant No. 789104-eNANO to F.J.G.A., ERC Starting Grant No. 259432-MULTIBIOPHOT to J.K., ERC Consolidator Grant No. 772108-DarkSERS); the Department of Education of the Basque Government (Grant No. IT1164-19 to J.A.); the Spanish MINECO (CTQ2017-88648-R to R.A.-P., MAT2016-77809-R to I.P.-S. and J.P.-J.); the EPSRC (EP/P034063/1 to S.B., EP/L027151/1 to J.B., EP/L014165/1 to D.G. and K.F.); IDUN-Danish National Research Foundation (DNRF122) and Villum Fonden (Grant No. 9301) to A.B.; the National Research Foundation of Korea (Grant No. 2019R1A2C3004375 to J.B.); the German Science Foundation, DFG (SFB 1278 Polytarget (Project B4) to V.D., Grant No. SCHL 594/13-1 to S.S., Germany’s Excellence Strategy (EXC 2089/1-390776260) to S.M.); the Federal Ministry of Education and Research, Germany (BMBF) (Grant InfectoGnostics 13GW0096F to D.C.-M. and J.P.); DARPA-16-35-INTERCEPT-FP-018 to L.F.; the UK BBSRC (Grant No. BB/L014823/1 to R.G.); the Department of Science and Technology (DST Nanomission Project SR/NM/NS-23/2016 to K.G.T.); the U.S. National Science Foundation (Grant No. CHE-1707859 to A.J.H., Center for Sustainable Nanotechnology CHE-1503408 (Centers for Chemical Innovation Program) to C.L.H., Center for Chemical Innovation Chemistry at the Space-Time Limit (CaSTL) CHE-1414466 to G.C.S. and R.P.V.D., Grant No. CHE-1807269 to K.A.W.); the Knut and Alice Wallenberg Foundation to M.K.; the Office of Naval Research (Grant No. N00014-18-1-2876 to N.A.K.); Royal Society of New Zealand Te Apa̅rangi to E.L.R. and B.A.; Singapore Ministry of Education, Tier 1 (RG11/18) to X.Y.L.; the Photoexcitonix Project in Hokkaido Univ., Japan, to K.M.; BioNano Health-Guard Research Center funded by the Ministry of Science and ICT (MSIT) of Korea as Global Frontier Project (Grant No. H-GUARD_2013M3A6B2078947) to J.-M.N.; NSFC of P. R. China (Grant No. 21705015 to Y.O., Grant No. 21633005 to B.R.); National Key R&D Program (2017YFA0206902) to C.X. This work was coordinated under the Maria de Maeztu Units of Excellence Program from the Spanish State Research Agency—Grant No. MDM-2017-0720.

Beer's law assumes a linear dependence of absorbance on concentration, accordingly the index of absorption and the molar attenuation coefficient are material properties and the absorption cross section, including absorbance itself, must be additive if chemical interactions are excluded. Under the “no interaction” condition, a linear dependence should also exist between macroscopic polarization and the number of induced dipole moments per unit volume. The latter linear dependence is the basis for dispersion theory. Invoking Maxwell's wave equation, Beer's law has been derived recently from dispersion theory. As a result, Beer's law is a limiting law. Accordingly, indices of absorption and molar attenuation coefficients including absorption cross sections are no material properties and the latter can per se not be additive. Indeed, as we show in this contribution, not even for particles very small compared to wavelength, where the scattering cross sections can be neglected, is this additivity a given, except for comparably large distances between the particles. We investigate the magnitude of these critical distances with the help of finite difference time domain calculations for amorphous SiO2 spheres in the infrared spectral range. Based on electric field maps, we conclude that the deviations scale with oscillator strengths and, correspondingly, with local electric fields and nearfield effects.

In contrast to the extensive molecular and crystal structure investigations on oxalic acid dihydrate (C2H2O4·2H2O, 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 Bu and Au 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.

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.

Beer's law assumes a strictly linear dependence of the absorbance from concentration. Usually, chemical interactions and instrumental imperfection are made responsible for experimental deviations from this linearity. In this contribution we show that even in the absence of such interactions and instrumental errors, absorbance should be only approximately proportional to concentration. This can be derived from the quadratic dependence of the complex refractive index, and, by that, of the molar attenuation coefficient, from the dielectric constant and its frequency dispersion. Following dispersion theory, it is the variation of the real and the imaginary part of the dielectric function that depends linearly on concentration in the absence of interactions between the oscillators. We show that this linear correlation translates into a linear dependence of the absorbance for low concentrations or molar oscillator strengths based on an approximation provided by Lorentz in 1906. Accordingly, Beer's law can be derived from dispersion theory.

We present a dispersion analysis of the orthorhombic peptide single crystal Z-Aib-Aib-Aib-L-Ala-OtBu (N-benzyloxycarbonyl-α-aminoisobutyryl-α-aminoisobutyryl-α-aminoisobutyryl-L-alanine tert-butyl ester, C

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.

We present the theoretical basis for a profound upgrade of the method of absorbance band fitting ("band deconvolution"), which requires only minute changes in the code of corresponding spectrometer software. This upgrade is based on a (re-)connection of the damped harmonic oscillator model ("Lorentz oscillator") and the Lorentz profile used for band fitting. Based on this reconnection, we provide a proper extension to multiple oscillators. As a result, band fitting allows directly obtaining all oscillator parameters with very good accuracy, at least for the not too strong oscillators present in organic and biological matter. Accordingly, this could be the initial spark to open the way to a long-awaited paradigm shift in infrared spectroscopy: Away from a mere oscillator position-based, towards an also intensity-based quantitative interpretation of spectra. As an extra, absorbance band fitting ("Poor Man's Dispersion Analysis"), allows to obtain the index of refraction function in one go.

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.

A single crystal of yttrium orthosilicate was investigated by FTIR-spectroscopy in the spectral region of 150⬜2000 cm ↙1 to properly characterize this laser medium. The five reflection spectra of the crystal in principal orientation were evaluated by dispersion analysis and with the dispersion parameters the dielectric tensor function was obtained. Based on the dielectric tensor function the refractive and absorption indices as example for the optical properties were calculated.

Extraordinary optical transmission and perfect absorption are two plasmonic-based optical phenomenona that are both accompanied by high local field enhancements that can be exploited for biological and chemical sensing. Here we merge both phenomenona in a slit array metamaterial perfect absorber consisting of a dielectric layer sandwiched between two metallic layers of which the upper layer is perforated with a periodic array of slits. Period and dimensions of the slits and thickness of the dielectric layer are tuned in a way that virtually all light of a certain wavelength incident on the surface passes through the slits and is subsequently absorbed. As a consequence, light–matter interaction is greatly enhanced in the slits. Thus, already small concentrations of analytes down to a monolayer attached to the sidewalls of the slits can be detected by refractive index sensing and identified by their spectral fingerprints with a standard mid-infrared lab spectrometer.