Abbe Number Research Articles

Biobased Sulfur- and Phosphate-Containing High-Refractive-Index Polymers: Substituent Effects on Optical Properties of Polymers.

Four biobased phosphate-containing aryl monomers with methoxy, allyl, and vinyl groups as substituents have been successfully synthesized. Copolymerizing these monomers with thiophenol or mercaptans via the photoclick thiol-ene reaction gives the polymers with refractive indices (nD) of 1.63-1.70 and Abbe numbers (vD) of 12.8-38.5. An investigation of the relationship of the vD values with the substituents on the benzene rings of the monomers indicates that methoxy and vinyl groups can collectively increase the vD values. In comparison with allyl groups, vinyl groups endow the polymers with both higher nD and vD. Moreover, these polymers also display high transmittance, high thermostability, and low haze values in the visible-light region, suggesting that these biobased functional monomers are satisfactory precursors used in the fabrication of optical devices.

High-Resolution Structuring of Silica-Based Nanocomposites for the Fabrication of Transparent Multicomponent Glasses with Adjustable Properties.

Silicate-based multicomponent glasses are of high interest for technical applications due to their tailored properties, such as an adaptable refractive index or coefficient of thermal expansion. However, the production of complex structured parts is associated with high effort, since glass components are usually shaped from high-temperature melts with subsequent mechanical or chemical postprocessing. Here for the first time the fabrication of binary and ternary multicomponent glasses using doped nanocomposites based on silica nanoparticles and photocurable metal oxide precursors as part of the binder matrix is presented. The doped nanocomposites are structured in high resolution using UV-casting and additive manufacturing techniques, such as stereolithography and two-photon lithography. Subsequently, the composites are thermally converted into transparent glass. By incorporating titanium oxide, germanium oxide, or zirconium dioxide into the silicate glass network, multicomponent glasses are fabricated with an adjustable refractive index nD between 1.4584-1.4832 and an Abbe number V of 53.85-61.13. It is further demonstrated that by incorporating 7wt% titanium oxide, glasses with ultralow thermal expansion can be fabricated with so far unseen complexity. These novel materials enable for the first time high-precision lithographic structuring of multicomponent silica glasses with applications from optics and photonics, semiconductors as well as sensors.

A Facile One-Step Conversion of Biobased Magnolol (Honokiol) toward High Refractive Materials.

A series of polymers with both high refractive index and high Abbe number have been successfully synthesized through the photoclick thiol-ene reaction between the monomers derived from biobased magnolol (or honokiol) and commercial mercaptans and thiophenols. The polymer films not only exhibit a high refractive index and a high Abbe number but also display a transmittance of up to 90% in a range of wavelengths from 550 to 2000 nm and nearly 0% in the UV region. Moreover, these polymers also display low haze values in the visible-light region as well as exhibit good thermostability. These data indicate that they have potential applications for the fabrication of optical lenses and anti-UV coatings. In particular, this series of polymers are readily used for industrialization due to its excellent optical properties but low expense, simplicity, and efficiency of synthesis.

Prediction of optical properties of oxide glass combined with autoencoder and machine learning

The composition of oxide glasses is characterized by high dimensionality and sparsity, making it challenging to establish high-precision predictive models. Therefore, feature extraction is essential. This study focuses on the optical properties of oxide glasses (refractive index and Abbe number), utilizing autoencoder (AE) and machine learning techniques to achieve automated feature extraction. The results indicate that compared to standalone neural networks (NN), AE-NN transforms unsupervised learning into supervised learning, reducing feature dimensions while improving model accuracy. Specifically, for the refractive index dataset, the dimensionality was reduced from 63 to 25, with a corresponding test set coefficient of determination (R2) of 0.95. For the Abbe number dataset, the dimensionality was reduced from 61 to 30, with a corresponding test set R2 of 0.97, demonstrating the effectiveness of the feature extraction method. Regarding interpretability, analyzing the encoder weight matrix of the AE-NN identified the importance of original features, with Co and Y being the most significant for both refractive index and Abbe number. Additionally, the application of the feature extraction method in machine learning models shows its generality in improving model performance, particularly for non-ensemble models such as Support Vector Regression (SVR) or k-Nearest Neighbors (KNN), exhibiting significant accuracy enhancements. Finally, targeting lanthanide glasses, the established predictive model successfully identified novel optical glasses with high refractive index and Abbe number in the La2O3-Bi2O3 and La2O3-Ta2O5 systems, presenting new possibilities for optical component design.

Biobased Thiol-ene Networks with High Optical Transparency and Abbe Number Derived from Citric Acid

Biobased Thiol-ene Networks with High Optical Transparency and Abbe Number Derived from Citric Acid

Optically transparent and refractive thiol‐ene polymers containing cyclotriphosphazenes

AbstractA colorless, transparent thiol‐ene polymer network was developed that contains cyclic phosphazene units in the polymer chain. Hexakis (allyloxy) cyclotriphosphazene (HAP) was synthesized from the nucleophilic substitution reaction of phosphonitrilic chloride trimer and allyl alcohol. Thiol‐ene polymers (HAP‐SH) were successfully prepared without by‐products or the use of solvents through photopolymerization of the HAP and multithiol monomers with various functional group and flexible structures (e.g., 1,4‐butanedithiol (BDTH), 1,3,5‐benzenetrithiol (BTTH), trimethylolpropane tris (3‐mercaptopropionate) (TTMP) and pentaerythritol tetrakis (3‐mercaptopropionate) (PTTH)). The prepared HAP‐SH polymers showed sufficient thermal stability due to the high degree of cross‐linking. In addition, the HAP‐SH polymer films exhibited high optical transparency of over 90% in the visible region. The refractive indices of the HAP‐SH polymers measured at 637 nm were in the range of 1.5530–1.6344, and the Abbe number was calculated to be in the range of 34.5–47.1. These results are attributed to the structure of the cyclophosphazine and the polymer main chain containing aliphatic linkers with sulfur atoms. Another significant result was the transparency of the HAP‐SH polymer films in the mid‐infrared (MWIR) region. The thermal stability and excellent optical properties of the HAP‐SH polymers make them good candidates for application as a protective film for IR lenses, which are easily damaged by external factors.

Pure TeO2 glass: Influence of synthesis conditions on linear and non-linear optical, magneto-optical and structural properties

The first systematic study of linear and non-linear optical, magneto-optical and structural properties of pure TeO2 glass is presented with regard to different synthesis and material processing conditions. Prepared glasses were synthesized by the intermittent quenching from 900 ∘C in platinum or alumina crucibles and characterized prior to and after optical polishing. The position of the long-wavelength/phonon absorption edge was investigated using various optical models and experimentally obtained data of refractive index and Verdet constants were used for the estimation of magneto-optical anomaly parameter. During synthesis in alumina crucible, up to about 11 wt.% of Al2O3 incorporates into the glass (verified by EDS/XRF and Raman/FTIR spectroscopy) partially transforming the original pure TeO2 glass backbone structure composed of [TeO4] trigonal bipyramids to [TeO3+1] and [TeO3] structural units with the expected integration of Al into Te−O−Al bridges. The presence of Al2O3 results in lowered density ρ (5.60 → 4.72 g cm−3), refractive index n1550 (2.086 → 1.927) and Verdet constant V632 (36.3 → 21.9 rad T−1 m−1) and in increased optical-band-gap energy Eg (3.69 → 3.72 eV) and Abbe number νD (19.9 → 26.9) compared to pure TeO2 glass prepared in platinum crucible. A dataset of the obtained complex optical parameters (refractive index and extinction coefficient) in the wide spectral range of 193 − 11000 nm is included in the supplementary part.

Advanced linear axial wavelength spreading through cascaded double hyperchromats

This study explores the design and optimization of cascaded double-hyperchromatic optical systems (i.e., 2×2 lenses), focusing on achieving an extremely linear axial spectral decomposition characterized by an exceptionally low equivalent Abbe number. The investigation involves two double hyperchromats, considering both purely refractive systems and hybrid configurations that combine refractive and diffractive elements. For purely refractive systems, alternating focal length signs of divergent and collective lenses are crucial to achieve significant axial chromatic dispersion. In hybrid systems, the position of the diffractive optical element (DOE) and the selection of focal lengths play key roles in obtaining extremely low equivalent Abbe numbers. The optimized systems demonstrate absolute equivalent Abbe numbers of 0.983 for purely refractive and 0.65 for hybrid systems—more than four times lower than the absolute Abbe number of a single diffractive element. Notably, even systems using standard materials exhibit significantly low equivalent Abbe numbers of 2.5 and 1.4 for pure refractive and hybrid configurations, respectively. These results offer promising opportunities for improving optical applications based on axial spectral decomposition, overcoming previous limitations of axial chromatic spreading.

First highly transparent Gd2Sn2O7 pyrochlore ceramics with high refractive index: Al2O3 additive roles on structural features, sintering behaviors, and optical performances

Highly transparent novel Gd2Sn2O7 pyrochlore ceramics, for the first time, were successfully fabricated by means of oxygen-assisted pressureless sintering. First-principles calculations and experimental test analysis revealed that the polycrystalline Gd2Sn2O7 bulk material had a direct bandgap of ∼3.8 eV, low phonon energy of ∼502 cm−1, a high refractive index of ∼2.02 at 633 nm, a large Abbe's number of ∼32.7, optical basicity of 1.011 ± 0.015, and an oxygen ion polarizability of 2.53 ± 0.06 Å3. Al2O3 was observed to be a beneficial additive for Gd2Sn2O7 ceramic sintering, with an optimum concentration of 0.3 at.%. Al3+ substantially penetrated the octahedral interstice formed by Sn−O polyhedral to yield the interstitial Ali···defect, leading to lattice expansion. The point defect effect and solute drag mechanism jointly contributed to sintering densification. The grain boundary of the pure Gd2Sn2O7 ceramic was quite clean with a width of ∼1.0 nm, while a 0.3 at.% Al3+ dopant broadened the grain boundary to ∼10.8 nm. The best Gd2Sn2O7 ceramic sample exhibited a high transparency of ∼75.1 % at 633 nm and a fine average grain size of ∼3.2 μm. Upon UV excitation, the bulk samples presented green emission centering at ∼470 nm deriving from the oxygen-vacancy defect. The Al2O3 dopants enhanced the photoluminescence intensity and shortened the fluorescence lifetime. The cathodoluminescence spectra emitted a white light similar to sunlight, which covered almost the full visible spectrum. The cathodoluminescence intensity also increased as the acceleration voltage increased, while the emission intensity from the grain boundary was slightly higher than that from the grain interior at each voltage level.

Research on Off-axis Aberration Optimization Model for Bifocal Glass Lens

Presbyopia entails the gradual deterioration of the eye’s ability to focus, and bifocal lenses have become a common remedy to alleviate blurred near vision and counteract eye strain induced by prolonged usage. The refractive index and Abbe number of these lenses play a crucial role in precisely correcting focal points within the near vision range. Nevertheless, when light rays approach the lens at off-axis angles or with tilts, aberrations occur, often with uneven distribution across real glass materials. The amalgamation of bifocal lenses further compounds the complexity of these aberrations. To enhance the correction of aberrations in bifocal glass lenses, distortion and astigmatism aberration serve as input parameters to calculate the optical quality assessment of the lenses. This study introduces a novel approach to optimize the pairing of bifocal glass lenses through the Taguchi method and fuzzy inference. The experimental design involves the application of the LS9 orthogonal array, streamlining the number of experiments while upholding the reliability of experimental data. The objective is to refine the selection of glass lenses and successfully devise an optimized design model that can be effectively applied to the configuration of bifocal glass lenses.

Principal component analysis of refractive index spaces: From glass properties to residual colour prediction

Traditionally glass dispersion is described by Abbe numbers and partial dispersions, and colour correction is explained and visualized e.g. with Pg,F- and Herzberger diagrams. We have recently developed an alternative approach to colour analysis and colour correction based on principal component analysis of normalized refractive index data. The resulting diagrams can be used not only for glass selection, but also for quantitative prediction of partial refractive powers and residual colour aberrations. The method is intrinsically model-free, robust to the choice of dataset and wavelengths, and transfers easily to any spectral range.

Structural evolution of Ge<sub>20</sub>Se<sub>80–</sub><sub><i>x</i></sub>Te<sub><i>x</i></sub> glass networks and assessment of glass properties by theoretical bandgap

Infrared imaging systems are being updated towards greater performance as well as lighter and smaller devices. Developing infrared materials with special properties is a critical for enhancing the performance of optical systems as well as miniaturizing devices. Chalcogenide glass becomes a popular option for advanced IR materials due to its component-property tunability. Se—based glasses such as Ge<sub>33</sub>As<sub>12</sub>Se<sub>55</sub>, Ge<sub>10</sub>As<sub>40</sub>Se<sub>50</sub>, and As<sub>40</sub>Se<sub>60</sub>, which completely cover the mid- and long-wave infrared windows, are the most typical materials used in infrared equipment. However, these classical materials can no longer meet the requirements of high-performance imaging systems, and adding more elements such as Te, Ga, Sb, and Ag to enhance the performance is a reliable way to solve this problem. By analysing the structure and properties of the Ge<sub>20</sub>Se<sub>80–<i>x</i></sub>Te<sub><i>x</i></sub> glass system, the law of its structure and properties evolving with Te content is illustrated. The obtained typical results are shown below. With the increase of Te content, the glass transition temperature (<i>T</i><sub>g</sub>) increases and then decreases, which is caused by the network structure and the average bond energy; the density and refractive index increase in an approximately linear gradient; the Abbe number gradually increases, while the Vickers hardness hardly changes with Te content; the fracture toughness decreases with the Te content increasing. Aiming at the problem that the average coordination number is unable to evaluate the glass systems composed of two or more elements from the same main group, a theoretical bandgap-glass property evaluation system is successfully established. The functional relationships among parameters such as density, refractive index, Abbe number, and fracture toughness, and theoretical band gap are established for Ge<sub>20</sub>Se<sub>80–<i>x</i></sub>Te<sub><i>x</i></sub> glass system as shown in the summary figure, which can be used to rapidly evaluate the glass components and properties.

Preparation and properties of highly refractive SmO3/2-TiO2-HfO2 glasses by aerodynamic levitation

The SmO3/2-TiO2-HfO2 (STH) glasses system was successfully prepared using the aerodynamic levitation technique. XRD analysis confirms that the obtained samples are amorphous. Raman spectra demonstrate that the maximum phonon energy is 1060 cm−1. DSC measurements reveal that the addition of HfO2, with its high melting point, increases both Tx and Tg. The maximum ΔT reaches 75.7 °C, and the density of the glass increases from 5.0548 to 5.1097 g/cm3. When the HfO2 content is kept constant, a decrease in Sm2O3 content and an increase in TiO2 content lead to a decrease in Tg and Tx, with a corresponding increase in density. The glass exhibits a maximum Vickers hardness of 8.102 GPa, which can be attributed to the high dissociation energy of Sm2O3, TiO2, and HfO2. Furthermore, both ST and STH glasses show excellent resistance to acid and alkali corrosion. Additionally, the refractive index contribution of each oxide follows the order: TiO2 > HfO2 > Sm2O3. The refractive index increases with increasing TiO2 and HfO2 content. Therefore, it is necessary to adjust the ratio of each oxide to optimize the values of Vm, OPD, and αO2− for a positive effect on the refractive index. The transmittance of STH glass is approximately 70 %, and the internal transmittance is 90 %. This indicates good transmittance even without considering reflection. The glass has a maximum refractive index of 2.343 and an Abbe number υd in the range of 17.06–18.02, meeting the dispersion requirements of commercial optical glasses. These results suggest that STH glass is a highly refractive optical glass with promising potential for various applications.

High Refractive Index and High Abbe Number Polymer Based on Norbornadiene

High Refractive Index and High Abbe Number Polymer Based on Norbornadiene

Optical, magneto-optical properties and fiber-drawing ability of tellurite glasses in the TeO2–ZnO–BaO ternary system

The presented work is focused on the optical and magneto-optical characterization of TeO2-ZnO-BaO (TZB) tellurite glasses. We investigated the refractive index and extinction coefficient dispersion by spectroscopic ellipsometry from ultraviolet, λ ≈ 0.193 μm, up to mid-infrared, λ ≈ 25 μm spectral region. Studied glasses exhibited large values of linear (n632 ≈ 1.91–2.09) and non-linear refractive index (n2 ≈ 1.20–2.67×10−11 esu), Verdet constant (V632 ≈ 22–33 radT−1m−1) and optical band gap energy (Eg ≈ 3.7–4.1 eV). The materials characterization revealed that BaO substitution by ZnO leads (at constant content of TeO2) to an increase in linear and nonlinear refractive index as well as Verdet constant while the optical band gap energy decreases. Fiber drawing ability of TeO2–ZnO–BaO glassy system has been demonstrated on 60TeO2–20ZnO–20BaO glass with presented mid-infrared attenuation coefficient. Specific parameters such as dispersion and single oscillator energy, Abbe number, and first-/third-order optical susceptibility are enclosed together with the values of magneto-optic anomaly derived from the calculation of measured dispersion of the refractive index.

Fabrication of Plastic Optics from Chalcogenide Hybrid Inorganic/Organic Polymers for Infrared Thermal Imaging

AbstractThe development of infrared (IR) plastic optics for infrared thermal imaging, particularly, in the long‐wave IR (LWIR) spectrum (7–14 µm) is an area of growing technological interest due to the potential advantages associated with plastic optics (e.g., moldability and low cost). The development of a new class of optical polymers, chalcogenide‐based inorganic/organic hybrid polymers (CHIPs) derived from the inverse vulcanization of elemental sulfur, has enabled significant improvements in IR transparency due to reduction of IR absorbing organic comonomer units. The vast majority of effort has focused on new chalcogenide hybrid polymer synthesis and optical property improvements (e.g., refractive index, Abbe number, and LWIR transmission); however, fabrication and IR imaging methodology to prepare optical components has not been demonstrated, which remains critical to develop viable IR plastic optics. A new methodology is reported to fabricate optical components and evaluate LWIR imaging performance of this emerging class of optical polymers. New diffractive flat optics with a Fresnel lens design for these materials have been developed, along with a basic LWIR imaging system to evaluate CHIPs for LWIR imaging. This system‐based approach enables correspondence of copolymer structure‐property correlations with LWIR imaging performance, along with demonstration of room temperature LWIR imaging.

Metal-catalyzed copolymerizations of epoxides and carbon disulfide for high-refractive index low absorbance adhesives and plastics.

High-refractive index plastics are useful materials due to their optical properties, ease of processing, and low-costs compared to their inorganic counterparts. Catalytic carbon disulfide (CS2) copolymerization with epoxides is one method for producing low-cost high refractive index polymers. The reaction is accompanied by an oxygen-sulfur exchange reaction which produces irregular microstructures in the repeating units. In this study, metal salen catalysts were investigated with different metal centers (Al, Cr, Co) and salen ligand electronics, sterics, backbones, and co-catalyst in the copolymerization of CS2 with propylene oxide (PO) and cyclohexene oxide (CHO). The results reveal the essential nature of Cr metal centers on reactivity and the backbone geometry on monomer selectivity. There were no significant impacts on the O-S exchange reaction when ligand design changed, however PO and CHO/CS2 copolymers yield different monothiocarbonate microstructures. Additionally, the effects of microstructure on optical and thermal properties were investigated using spectroscopic ellipsometry and calorimetry, respectively. The CHO system produced high T g plastics (93°C) with high refractive indexes (n up to 1.64), modest absorbance (κ < 0.020), and Abbe numbers of 32.2 while PO yielded low T g adhesives (T g = 9°C) with high refractive indexes (n up to 1.73), low absorbance (κ < 0.005), and low Abbe numbers (V D = 19.1).

High Refractive Index Copolymers from Aromatic Heterocycle‐Based Vinyl Sulfides and Phthalimide/Maleimide Derivatives

AbstractHerein, the rational design and facile synthesis of high‐refractive‐index copolymers with good optical transparency and tunable thermal stability using aromatic heterocycle‐based vinyl sulfides via conventional radical copolymerization is presented. 2‐Thiazolylvinylsulfide (2TVS), 1,3,4‐thiadiazolylvinylsulfide (1,3,4‐TVS), 3‐methylimidazolylvinylsulfide (3MIVS), and 5‐methlthio‐1,3,4‐thiadiazolylvinylsulfide (MeSTVS) are selected to enhance the refractive index, and N‐vinylphthalimide (NVPI) and N‐phenylmaleimide (NPMI) are chosen as comonomers to achieve improved transparency and thermal stability while maintaining the refractive index. The sulfur, ─C═N─, and imide contents in the copolymers are varied by adjusting the monomer structures and their compositions, and their effects on the refractive index, Abbe number, and optical and thermal properties are investigated. The MeTVS monomer in poly(MeSTVS) and poly(MeSTVS‐co‐NVPI) contained three sulfur atoms and two ─C═N─ units; consequently, these polymers exhibit excellent refractive indices in the 1.7139–1.6567 range at 589 nm, Abbe numbers between 19.1–29.1, good transparency (&gt;90% at 400 nm), and tunable thermal properties (Tg = 49–138 °C, Td10 = 244–268 °C). Optically transparent poly(1,3,4‐TVS‐co‐NVPI) films (&gt;95% at 400 nm) with improved thermal stability (Tg = 89–175 °C, Td10 = 251–301 °C) are obtained while maintaining a relatively high refractive index (1.6662–1.6752).

Determination of optical constants via the single oscillator Drude-Voigt dispersion model in fluoroborate glass for optical lenses: Nonlinear optical properties

In this work, a new fluoroborate (B2O3+AlF3+NaF + CaF2) glass has been fabricated using the melt-quenching technique. Glass sample has been characterized via X-ray diffraction, scanning electron microscope, and optical spectrophotometric measurements for absorption, transmission, and reflection in the range of 350–750 nm. The optical absorption of this transparent glass is used to determine the absorption coefficients, which are then used to estimate the extinction coefficients. The refractive indices as a function of wavelengths are estimated using extinction coefficients and reflectance data of fluoroborate glass. Very important parameters such as density, molar volume, and molar polarizability have been extensively studied. Using these data, fundamental optical parameters such as average oscillator strength (6.42) and inherent absorption wavelength (119 nm) are evaluated using the Drude-Voigt single oscillator model. Compared with previously studied oxide-based glasses, the fluoroborate glass possesses a relatively high refractive index of 1.74 and an Abbe number of 49 in the visible region of 587.6 nm. The relationship between inherent absorption wavelength and Abbe number values is also discussed. Moreover, the values of refractive index and linear optical susceptibility are used to evaluate the third-order optical susceptibility (11.56 × 10−14 esu) and nonlinear refractive index (2.50 × 10−12 esu). These results suggest that fluoroborate glass is a potential material for optical lenses and nonlinear devices in the visible range.

Designing Strategy for High Refractive Index Polymers: From the Molecular Level to Bulk Structure Control

Abstract High refractive index polymers (HRIPs) are essential materials for many optical applications, including organic light-emitting diodes (OLEDs), charge-coupled devices (CCDs), complementary metal oxide semiconductors (CMOS), eyeglasses, and optical waveguides. Various molecular designs, synthetic routes, and material preparation methods have been reported to increase the refractive index (RI) of polymers; however, increasing the RI using only organic (and classical) components is difficult. Other properties, such as low or high Abbe numbers (RI dispersion), low birefringence, and high transparency, are also required for HRIPs depending on the intended wavelength usage, which ranges from visible to infrared (IR) light and X-ray applications. This review summarizes the recent developments in HRIPs, including their synthesis, properties, and applications, and provides future prospects for achieving HRIPs with the desired performances.