Dispersion Analysis of Perpendicular Modes Using a Hybrid Two-Trace Two-Dimensional (2T2D) Smart Error Sum.

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.

Polarization-dependent effects in vibrational absorption spectra of 2D finite-size adsorbate islands on dielectric substrates.

In the last few years, infrared reflection-absorption spectroscopy (IRRAS) has become a standard technique to study vibrational excitations of molecules. These investigations are strongly motivated by potential applications in monitoring chemical processes. For a better understanding of the adsorption mechanism of molecules on dielectrics, the polarization-dependence of an interaction of infrared light with adsorbates on dielectric surfaces is commonly used. Thus, the peak positions in absorption spectra could be different for s- and p-polarized light. This shift between the peak positions depends on both the molecule itself and the dielectric substrate. While the origin of this shift is well understood for infinite two-dimensional adsorbate layers, finite-size samples, which consist of 2D islands of a small number of molecules, have never been considered. Here, we present a study on polarization-dependent finite-size effects in the optical response of such islands on dielectric substrates. The study uses a multi-scale modeling approach that connects quantum chemistry calculations with Maxwell scattering simulations. We distinguish the optical response of a single molecule, a finite number of molecules, and a two-dimensional adsorbate layer. We analyze CO and CO2 molecules deposited on CeO2 and Al2O3 substrates. The evolution of the shift between the polarization-dependent absorbance peaks is first studied for a single molecule, which does not exhibit any shifting at all, and for finite molecular islands, where it increases with increasing island size, as well as for an infinite two-dimensional adsorbate layer. In the latter case, the agreement between the obtained results and the experimental IRRAS data and more traditional three/four-layer model theoretical studies supports the predictive power of the multi-scale approach.

Sophisticated Attenuated Total Reflection Correction Within Seconds for Unpolarized Incident Light at 45°.

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.

Dielectric metasurface-assisted cavity ring-down spectroscopy for thin-film circular dichroism analysis.

Chiral molecules show differences in their chemical and optical properties due to the different spatial arrangements of the atoms in the two enantiomers. A common way to optically differentiate them is to detect the disparity in the absorption of light by the two enantiomers, i.e. absorption circular dichroism (CD). However, the CD of typical molecules is very small, limiting the sensitivity of chiroptical analysis based on CD. Cavity ring-down spectroscopy (CRDS) is a well-known ultrasensitive absorption spectroscopic method for low-absorbing gas-phase samples because the multiple reflections of light in the cavity greatly increase the absorption path. By inserting a prism into the cavity, the optical mode undergoes total internal reflection (TIR) at the prism surface and the evanescent wave (EW) enables the absorption detection of condensed-phase samples within a very thin layer near the prism surface, called EW-CRDS. Here, we propose an ultrasensitive chiral absorption spectroscopy platform using dielectric metasurface-assisted EW-CRDS. We theoretically show that, upon linearly polarized and oblique incidence, the metasurface exhibits minimum scattering and absorption loss, introduces negligible polarization change, and locally converts the linearly polarized light into near fields with finite optical chirality, enabling CD detection with EW-CRDS that typically works with linearly polarized light. We evaluate the ring-down time in the presence of chiral molecules and determine the sensitivity of the cavity as a function of total absorption from the molecules. The findings open the avenue for the ultrasensitive thin film detection of chiral molecules using CRDS techniques.

Understanding Refractive Index Changes in Homologous Series of Unbranched Organic Compounds Based on Beer's Law.

Changes of the refractive index for homologous series of hydrocarbons are usually plotted versus the density. While there is a clear linear dependence for alkanes and alkenes, the linearity deteriorates for homologous series with functional groups involving heteroatoms. The slope can even become negative, e. g., for carboxylic acids. For gaining a deeper understanding and to establish a more general correlation, we reinvestigate the corresponding theories starting with the Newton-Laplace, Gladstone-Dale and the Lorentz-Lorenz rules. We revisit the concept of molar refractivity pioneered by Landolt and Brühl and show that it is closely connected with a twin of Beer's law. We conclude that the refractive index of homologues series should better be plotted versus the molar concentration of the main UV-chromophore, the C-H bond, which actually causes the refractive index changes. This new approach is not limited to alkanes and alkenes but holds for homologous series with functional groups including heteroatoms.

Unveiling chiral optical constants of α-pinene and propylene oxide through ATR and VCD spectroscopy in the mid-infrared range.

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.

SpectIR-fluidics: completely customizable microfluidic cartridges for high sensitivity on-chip infrared spectroscopy with point-of-application studies on bacterial biofilms.

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.

Simple, Fast and Convenient Magnetic Bead-Based Sample Preparation for Detecting Viruses via Raman-Spectroscopy.

We introduce a magnetic bead-based sample preparation scheme for enabling the Raman spectroscopic differentiation of severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2)-positive and -negative samples. The beads were functionalized with the angiotensin-converting enzyme 2 (ACE2) receptor protein, which is used as a recognition element to selectively enrich SARS-CoV-2 on the surface of the magnetic beads. The subsequent Raman measurements directly enable discriminating SARS-CoV-2-positive and -negative samples. The proposed approach is also applicable for other virus species when the specific recognition element is exchanged. A series of Raman spectra were measured on three types of samples, namely SARS-CoV-2, Influenza A H1N1 virus and a negative control. For each sample type, eight independent replicates were considered. All of the spectra are dominated by the magnetic bead substrate and no obvious differences between the sample types are apparent. In order to address the subtle differences in the spectra, we calculated different correlation coefficients, namely the Pearson coefficient and the Normalized cross correlation coefficient. By comparing the correlation with the negative control, differentiating between SARS-CoV-2 and Influenza A virus is possible. This study provides a first step towards the detection and potential classification of different viruses with the use of conventional Raman spectroscopy.

Correcting systematic errors by hybrid 2D correlation loss functions in nonlinear inverse modelling.

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.

Smart Error Sum Based on Hybrid Two-Trace Two-Dimensional (2T2D) Correlation Analysis.

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.

Dispersion related coupling effects in IR spectra on the example of water and Amide I bands.

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 ß-sheet structures.

The Global Polarity of Alcoholic Solvents and Water - Importance of the Collectively Acting Factors Density, Refractive Index and Hydrogen Bonding Forces.

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, 129 Xe 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.

Infrared spectroscopy of quasi-ideal binary liquid mixtures: The challenges of conventional chemometric regression.

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.

To generate a photonic nanojet outside a high refractive index microsphere illuminated by a Gaussian beam.

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 Negative Solvatochromism of Reichardt's Dye B30 - A Complementary Study.

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/λmax ) with the molar absorption coefficient ϵ as function of solvent polarity are demonstrated for several derivatives of B30. The approach presented is only applicable to negative solvatochromism. Therefore, while the approach is vital to fully understand solvatochromism, it needs to be complemented by other approaches, e. g., to describe the changes of the chemical interactions based on the nature of the solvent, to explain all its various aspects.

Detection of siloxane thin films on glass substrate using IR ratio-reflectance spectrum.

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-1, can be correlated to the film morphology and bridging oxygen number. We support our conclusions using principal component analysis of reflectance spectra, contact angle, AFM and SEM measurements.

Infrared refraction spectroscopy - Kramers-Kronig analysis revisited.

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.

Hybrid 2D Correlation-Based Loss Function for the Correction of Systematic Errors.

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 (CaF2) and silicon (Si), which do not suffer from the systematic errors.

Beyond Beer's Law: Quasi-Ideal Binary Liquid Mixtures.

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.

Infrared Refraction Spectroscopy.

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.