Determination Of Complex Refractive Index Research Articles

Determination of complex refractive index of plastics from ultraviolet to mid-infrared by ellipsometry

Plastic litter is a pervasive issue in the ocean, posing threats to both marine ecosystems and human health. In the field of marine remote sensing detection, one common method for detecting and identifying marine plastics is by analyzing their optical characteristics, specifically their spectral remote sensing reflectance. This reflectance is dependent on the complex refractive index of plastics. Therefore, understanding the complex refractive index, which is an intrinsic optical property of plastics, holds significant importance in marine plastics research. In this study, we utilized spectroscopic ellipsometry to measure the complex refractive index of 9 common ploymers including polymethyl methacrylate (PMMA), methyl methacrylate–styrene copolymer (MS), polyethylene (PE), poly (ethylene glycol-co-cyclohexane-1,4-dimethanol terephthalate) (PETG), polybutylene terephthalate (PBT), polyoxymethylene (POM), perfluoroalkoxy (PFA), acrylonitrile butadiene styrene (ABS), and styrene-acrylonitrile copolymer (SAN). In addition, we have expanded the complex range of refractive index measurements to include UV and MIR bands with wavelengths up to 32 μm. To ensure the reliability and accuracy of the measurements, experimental results for polycarbonate (PC) were compared with data from the existing literature. The variation of refractive index with wavelength is studied and the causes of absorption peaks in the infrared range are discussed. Furthermore, Considering the dispersion relationship and monomer composition of PMMA, MS, ABS and SAN plastics, a comparative analysis of plastics with commonly used monomers is conducted, and the influence of monomers on refractive index is discussed. Our study indicates that the presence of styrene monomers leads to an increase in the refractive index of plastics in the visible to near-infrared band, while the presence of butadiene monomers results in a decrease.The findings from this study provide fundamental data for future research on marine plastic remote sensing detection applications.

Determination of complex refractive index using maximum deviation angle through prism

Light-absorbing materials are widely used, and their optical properties are an important factor. Snell's law does not hold in materials that partially absorb light. Hence, the optical path in refraction is calculated from Maxwell's law. We used the optical path to obtain the deviation angle when a light passes through a prism made of light-absorbing material. The deviation angle has a local maximum. The deviation angle near the maximum is sensitive to the real and imaginary parts of the refractive index. The local maximum deviation angle and its incident angle are used to determine the complex index of refraction. This measurement has the same advantages as measuring the minimum deviation angle of a transparent prism. The detection is easy. Then, it is necessary to determine the complex refractive index from the measured maximum deviation angle and its incident angle. These two angles are plotted parametrically by varying the real part of the refractive index under a fixed imaginary part. The similar curves are drawn under the fixed real parts. Each curve has a fixed value for the real or imaginary part of the refractive index. Drawings of these many curves are made prior to measurement. Then we select the four curves that are closest to the measured local maximum deviation angle and its incident angle. Four fixed values attached to each of the four curves determine the complex index of refraction. The method in this paper can easily determine the complex refractive index and can be used for material identification.

Determination of complex refractive index using prism composed of absorbing medium

In light refraction between two transparent media, Snell’s law describes the relationship between the incident angle and refraction angle. The refractive index is usually determined from Snell’s law using the minimum deviation angle through a prism. A medium that partially absorbs light has complex permittivity (or permeability), and its refractive index has an imaginary part. Because of the imaginary part, Snell's law does not hold for light-absorbing media. Accordingly, other methods are required to determine the complex value of the refractive index in a light-absorbing medium. The exact solution of Maxwell’s equations was obtained for light passing through a prism composed of a light-absorbing medium. Thereby the optical path was determined. The difference of optical paths between light-absorbing medium and transparent medium was calculated numerically. The difference is very large in the neighborhood of perfect reflection area of transparent medium. We found two methods to determine the complex value of the refractive index using the optical path. Both methods analyzed the solutions in detail for two specific incident angles. The deviation angles corresponding to the two incident angles determined the complex value of the prism’s refractive index. Of course, the obtained refractive index depends only on the material making up the prism, not on the apex angle of the prism.

Determination of complex refractive indices and optical properties of volcanic ashes in the thermal infrared based on generic petrological compositions

The spaceborne detection of volcanic ash clouds at infrared wavelengths helps to avoid regions with enhanced volcanic ash concentrations that pose a threat to aviation. Current volcanic ash data retrievals require detailed information on microphysical properties and the refractive index of volcanic ash, which are highly variable. Uncertainties in the latter currently limit the quality of volcanic ash nowcasts. Here, we introduce a novel method to calculate the complex refractive indices of volcanic ashes at wavelengths from 5 to 15 μm from measurements of their individual components based on generic petrological ash compositions. Thereby the refractive indices for volcanic glasses and bulk volcanic ashes of different chemical compositions are derived. The variability of the latter is mainly influenced by the silica content and the porosity and to a minor degree by the glass-to-crystals ratio. Calculating optical properties exhibits an equally large impact of bulk composition and grain size distribution, whereas particle shape is considered less important for particle sizes of the order 1 μm. Using these optical properties to determine brightness temperature differences between the 11 μm and 12 μm channels we show that the effect of ash composition is non-negligible for modern satellite instruments. Particularly, the dependence of the volcanic ash on the silica content (and to a much smaller extent on the glass-to-crystals ratio) is observable in its refractive index, its optical properties and the brightness temperature difference, indicating that composition might be retrievable to some degree by remote sensing methods.

An analytical method to determine the complex refractive index of an ultra-thin film by ellipsometry

We proposed a completely analytical method to determine the complex refractive index of an ultra-thin film on an arbitrary substrate by ellipsometry. The method is based on directly solving the polynomial equation derived from the 2nd-order Taylor expansion of ellipsometric functions without any prior knowledge about electronic transitions of the material. Numerical simulations demonstrate that the proposed method can be applied to deal with ultra-thin films with a wide thickness range from a single atomic layer to 5 nm over an ultra-broad spectral range from deep ultraviolet to infrared regions. With the proposed method, complex refractive indices of typical two-dimensional (2D) materials, including the monolayer graphene and 1–3 layer WSe2, were experimentally investigated over an ultra-wide spectral range (193–1690 nm). The proposed method shows great potential in the accurate determination of complex refractive indices of ultra-thin films especially the emerging 2D materials.

Determination of complex refractive index of SU-8 by Kramers–Kronig dispersion relation method at the wavelength range 2.5–22.0 µm

Accurate determination of the complex refractive index of SU-8 epoxy has significant for the wide variety of applications in optical sensor technology at IR range. The complex refractive index of SU-8 is determined by recording the transmission of light spectra for the wavelength range of 2.5–22.0 µm. The data analysis is based on the Kramers–Kronig dispersion relation method. The method has several merits, such as ease of operation, non-contact technique, measurement accuracy, and rapid measurement. The present method is not restricted to the case of SU-8 but it is also proposed to be applicable across a broad range of applications, such as assessment of the optical properties of paints and biomedical samples.

Modeling approach to derive the anisotropic complex refractive index of polymer:fullerene blends for organic solar cells utilizing spectroscopic ellipsometry

The knowledge of the complex refractive indices of all thin layers in organic solar cells (OSCs) is a prerequisite for comprehensive optical device simulations that are particularly important for sophisticated device architectures, such as tandem OSCs. Therefore, refractive indices are often determined via spectroscopic ellipsometry and subsequent time-consuming modeling. Here, we investigate a modeling approach that allows for the determination of complex refractive indices of bulk-heterojunctions by superimposing the optical models of the respective fullerenes and polymers. The optical constants of neat [6,6]-phenyl C71-butyric acid methyl ester (PC71BM), poly{[4,4’-bis(2-ethylhexyl)dithieno(3,2-b;2’,3’-d)silole]-2,6-diyl-alt-(2,1,3-benzothidiazole)-4,7-diyl} (PSBTBT) and poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′′]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole) (PCPDTBT) are determined, covering the OSC relevant spectral region from 250 to 1,000 nm. Then the blends PSBTBT:PC71BM and PCPDTBT:PC71BM are described within an effective medium approximation. From this approximation, the mass density ratio of polymer and fullerene can be derived. This approach furthermore allows for a uniaxial anisotropic optical description of the polymers and provides insight into thin-film morphology. In contrast to x-ray diffraction experiments, this method also allows for probing amorphous materials. Spectroscopic ellipsometry can be a valuable tool for the investigation of bulk-heterojunction morphologies of the latest high-performance OSC materials that exhibit a low degree of crystallinity.

Infrared Optical Constants and Computational Studies of Neat Liquid -Butylethylether

Aliphatic ethers are of interest to researchers due to their wide application in the fuel, chemical, and pharmaceutical industry. In this paper we studied vibrational properties of neat liquidn-butylethylether (NBEE), including the determination of complex refractive index in the NIR and MIR range (11700–560 cm−1). The high absorption of neat liquid in the MIR range required the use of thin-film transmission recordings. The spectra analysis was based on conformational analysis and anharmonic calculations on B2PLYP/N07D level of theory. Final band assignments procedure was based on potential energy distributions. The theoretical investigation revealed that although 26 conformers of NBEE can be expected to exist in the liquid phase at 298 K, only few of them are essential for the forming of the spectrum. This study is important for the proper understanding of vibrational properties of other aliphatic ethers.

Analysis of optical properties of porous silicon nanostructure single and gradient-porosity layers for optical applications

The porous silicon (PS) layers with different porosities were prepared by electrochemical anodization method to obtain the desired refractive index in a given range. The optical response of the PS layer has been performed by the reflectance measurements. The obtained data were coupled to Kramers-Kronig analysis and allowed determination of complex refractive index in spectral range extending from 400 to 850 nm. In addition, the dispersion of refractive index of PS was determined from optical reflection measurements experimentally utilizing the relationship between the optical path in the plane-parallel film and the position of extrema. These results were compared and the agreement of them was discussed. The Bruggeman’s effective medium approximation was also used to estimate the porosity of each PS sample from calculated optical characteristics. FESEM analyses revealed vertically aligned silicon nanopillars with diameters on the order of 50 nm perpendicular to the Si substrate surface. A gradient-porosity PS layer was fabricated by modulating applied current density during anodization. Indeed, the elaborated structure is consisted of porous layers with modulated refractive indices. For this structure, normal incident and reflecting light through the layers provide an effective refractive index.

Refractive Index Measurements of Films with Biaxial Symmetry. 1. Determination of Complex Refractive Indices Using Polarized Reflectance/Transmittance Ratio

A new method to extract complex refractive indices of films with biaxial symmetry from polarized transmission and reflection spectra is described. Theoretical analysis demonstrates that the reflectance/transmittance ratio (R/T ratio) of two films of different thicknesses but with the same optical anisotropy is a simple function of the refractive index (n) and extinction coefficient (k). For films with biaxial symmetry, components of n and k on symmetric axes can be extracted from either s- or p-polarized R/T ratios if the film thickness values are known. The R/T ratio method can generate n and k spectra within a particular wavelength range without assuming a specific relationship among n, k, and wavelength, which is an advantage over many currently available techniques. The R/T ratio method is used to extract the anisotropic complex refractive indices of a polyimide film with known uniaxial symmetry. The resultant n and k spectra compare well with simulations based on known n and k values. The accuracy of n and k spectra is affected mostly by data error in reflection and transmission spectra collection, thickness variation across sample films, and error in sample alignment.

Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm

We introduce an inverse method for determining simultaneously the real and imaginary refractive indices of microspheres based on integrating sphere measurements of diffuse reflectance and transmittance, and Monte Carlo modelling in conjunction with the Mie theory. The results for polystyrene microspheres suspended in water are presented.

Determination of complex refractive index and thickness of a homogeneous layer by combined reflection and transmission ellipsometry

Analytic inversion of combined reflection and transmission ellipsometric data is demonstrated. When the thickness is eliminated between the equations that give the reflection and transmission ratios ρ = rp/rs and τ = tp/ts, an algebraic equation for the unknown dielectric constant e of the layer is obtained. After removal of some factors, this reduces to a linear equation in e. The solution for unsupported films agrees with that previously obtained by Azzam [ J. Phys. (Paris)C10, 67 ( 1993)]; it can be simplified to e = e1 sin2θ1/(cos2θ1 − ρ/τ), where e1 is the dielectric constant of the ambient medium and θ1 is the angle of incidence. Stability of the solution with respect to noise in the data is analyzed.

Simple and direct determination of complex refractive index and thickness of unsupported or embedded thin films by combined reflection and transmission ellipsometry at 45° angle of incidence

Measurements of the polarization states (represented by complex numbers χr and χt, respectively) of light reflected and transmitted by an unsupported or embedded thin film, for totally polarized light (with nonzero p and s components) incident at 45°, permit simple, direct, and explicit determination of the film’s complex refractive index N1independently of film thickness or input polarization. If α = χr/χt, we find that α = rs + rs−1, where rs is Fresnel’s complex reflection coefficient of the ambient–film interface for the s polarization at 45° incidence. From α, rs is determined, and from rs we get N1 = N0(1 + rs2)1/2/(1 + rs), where N0 is the refractive index of the transparent medium surrounding the film. Knowledge of the incident polarization χi allows the film thickness to be determined, also explicitly, by using either of the ratios χi/χr or χi/χt.

The determination of complex refractive indices with fourier transform interferometry—VI: Error analysis of liquid-cell experiments

An error analysis of far infrared (∼ 5–500 cm −1) dispersive interferometric experiments is presented, in which the complex refractive index spectrum N̆ s (σ) of a liquid is determined using a cell type specimen holder. For several practical evaluation methods expressions are developed that relate the error in n̆ s to the error sources. With our interferometric system optical constants of very absorbing liquids can be measured quite accurately; errors in n s are of the order of 0.01 and relative errors in k s are about 5%. For moderately absorbing and transparent liquids the accuracy of n s will be an order of magnitude better. The complex refractive index spectrum of methanol (from 10–60 cm −1) is given as an illustration.

The determination of complex refractive indices with fourier-transform interferometry—V. Methods for the determination of complex refractive index spectra of liquids in the far infrared spectral region (5–500 cm −1) using a variable pathlength, variable temperature cell

Several methods are given for the determination of complex refractive index spectra n̆ s(σ), where σ is the wavenumber, of transparent as well as very absorbing liquids in the FIR (5–500 cm −1), from dispersive interferograms obtained with a Michelson interferometer of which the fixed-mirror arm is terminated by a variable pathlength, variable temperature cell. The liquid specimen is confined between a displaceable mirror and a fixed plane-parallel window (of e.g. hyperpure silicon, crystal quartz). The complex refractive index spectrum of the window of which a knowledge is required in most of the methods for determining n̆ s(σ), is determined from an empty-cell interferogram. The cell and the interferometric setup are briefly described. Some experimental results are given (silicon, chlorobenzene, methanol).

The determination of complex refractive indices with Fourier-transform interferometry—IV: Error analysis of free layer experiments

An analysis is presented of the errors in the complex refractive index spectrum of liquids in the far i.r. spectral region (∼ 5–500 cm −1) as determined by free layer experiments. The specimen transmission method, most popular in present practice, is found to be the most reliable one if editing methods can be applied. It is further concluded that the repeating of single measurements in order to minimize random errors is not necessary in practice, but that experiments at several specimen thicknesses are obligatory. It is shown that the error due to the vapour above the liquid specimen can be quite substantial.

The particle size determination of pigments with the disc centrifuge

In view of the influence of particle size on the technological properties of pigments, several aspects of the determination of size distributions with the disc centrifuge have been investigated. A detailed analysis of photodensitometric measurements and their interpretation is given for two methods, one with all particles starting at the same line, the other with the particles initially being distributed uniformly. An empirical relation for fine pigments is pointed out, which can simplify the evaluation for the former. It is also shown that this method can be used for the determination of complex refractive indices of a pigment. It is further established that in both methods a density gradient is necessary to guarantee turbulence-free sedimentation. Finally an automatic data acquisition system is described.

The determination of complex refractive indices with Fourier-transform interferometry: II. Expressions for the experimentally accessible quantities; characteristic features in the interferogram

With the help of the basic equations of part I of this paper theoretical expressions connecting the experimental quantities obtained by Fourier-transform interferometry using a Michelson interferometer to the complex refractive index of a material investigated by this method are derived and discussed. The characteristic signatures to be expected in the interferograms are analyzed in terms of the experimental conditions and discussed in view of the possibilities of deriving from them the relevant material constants in the far-infrared region of the spectrum. Different experimental setups are examined: material systems with and without window positioned on the fixed mirror in the Michelson interferometer (reflection measurements) and material systems positioned in front of the detector (transmission measurements). In the former case methods are proposed to determine the frequency-dependent refractive index and the absorption coefficient, and in the latter only methods for the absorption coefficient.

The determination of complex refractive indices with Fourier-transform interferometry: I. Basic equations

A general description of a Michelson-type interferometric system suitable for the determination of complex refractive indices is presented using linear response theory. Expressions are given from which it is possible to calculate the complex refractive indices of stratified media with the help of measured interferograms.