Linear Properties Research Articles

Effect of spirocyclization of xanthene dyes on linear and nonlinear optical properties by considering D-π-A and D-A-D Systems: DFT and TD-DFT approach

Spirocyclization, a unique feature of xanthene dyes, makes it a promising candidate for developing fluorescent ratiometric probes for sensing, imaging, tracking, and labeling. How will this feature of xanthene dyes influence the linear and nonlinear optical properties? To examine the effect of spirocyclization of xanthene dyes, we have selected both the open-close form of rhodamine B and π-extended xanthene dyes substituted with thienyl and thieno[3,2-b]thienyl group at position 3 and 6. Here, rhodamine B will serve as the (Donor)D-π-A(Acceptor) system and thiophene-substituted xanthene dyes will serve as the D-A-D system. The geometry optimization of the close-open form of xanthene dyes at B3LYP/6–311++G(d,p) and CAM-B3LYP/6–311++G(d,p) revealed that the open form is energetically more stable in the S0 state than the closed form. The vertical excitation energy (ΔE), from Time-Dependent-Density Functional Theory (TD-DFT) calculation at B3LYP/6–311++G(d,p), CAM-B3LYP/6–311++G(d,p), ωB97XD/6–311++G(d,p) revealed that (ΔE)open < (ΔE)close. Further, the open form of xanthene dyes displays red-shifted absorption compared to the closed form. The λVt of xanthene dyes (open-close forms) is mainly assigned to HOMO → LUMO transition (S0 → S1) with % orbital contribution for open form ∼ 90 % and close form ∼ 60 %. The oscillator strength of xanthene dyes is obtained in the range of 0.01 – 1.74. The λVt of xanthene dyes is in agreement with experimental absorption. The static polarizability (α0), first-order hyperpolarizability (β0), second-order hyperpolarizability (γ), molecular hyperpolarizability (µβ0), and frequency-dependent hyperpolarizability (β1064), of the open form of xanthene dyes, were found to be higher than the close form. Thus, the open form of xanthene dyes will show superior linear and nonlinear optical properties than the closed form. The thienyl[3, 2-b] thieno substituted xanthene dye with red-shifted absorption shows higher α0, β0, γ, µβ0, β1064, and γ values, show better linear and NLO properties than thienyl and diethylamine substituted xanthene dyes.

Optical characterization and dispersion analyses of plasma polymerized methyl acrylate thin films

This work reports the structural characteristics, surface morphology, linear and nonlinear optical properties of 110 to 225 nm thick plasma polymerized methyl acrylate (PPMA) thin films. X-ray diffraction analyses confirm the amorphous nature of the films. Field emission scanning electron micrographs of the films display cluster-based surface morphology. Attenuated total reflectance Fourier transform infrared spectroscopy confirms the chemical structural changes in the films. The optical properties were studied based on the absorbance, transmittance, and reflectance spectra measured by an ultraviolet–visible spectrophotometer within the wavelength ranges from 200 to 800 nm. The direct optical band gap and Urbach values are increased from 3.66 to 3.83 eV and 0.28 to 0.45 eV, respectively with increasing film thickness. The extinction coefficient and refractive index were evaluated, and discussed a correlation between the refractive index and the optical bandgap. The real and imaginary dielectric constants, volume/surface energy loss functions and skin depth were deduced. The oscillator energies and parameters were analyzed using the concept of Wemple-DiDomenico and Sellmeier models, respectively for a single oscillator. Static linear refractive index for the studied films exhibits normal dispersion behavior with film thicknesses and satisfied Moss, Ravindra-Gupta, and Herve-Vandamme rules. The linear susceptibility, third-order nonlinear susceptibility and the non-linear refractive index are considerably reduced from 0.20, 29.5 × 10−14 esu, and 5.89 × 10−12 esu with increasing optical band gap energies. The outcomes from the analyses of PPMA demonstrated their potential for usage in electronic, optoelectronic, and non-linear device applications.

Relationship between the poly(glycerol adipate) prepolymers chain microstructure and linear viscoelastic properties of the elastomers

This paper investigates the influence of the time of enzymatic polymerization of glycerol and divinyl adipate on the chain microstructure and the thermal and linear viscoelastic properties (LVE) of the poly(glycerol adipate) prepolymer (pPGA). The immobilized Candida antarctica lipase B (CALB) was used as a regioselective catalyst in the polytransesterification reaction. A series of pPGA prepolymers were synthesized at different duration times of 8, 24, 48 and 72 h and the degree of polymerization (DP) and degree of branching (DB) were determined based on a quantitative NMR analysis. Due to lack in the literature of the described relationship between the properties of the pPGA prepolymers and the PGA elastomers, the main goal of the research was to correlate the microstructure of the prepolymers with linear viscoelastic properties of the elastomers obtained by thermal crosslinking of the respective prepolymers. The respective pPGA prepolymers were cured at 110 °C for 5 days to obtain PGA elastomers. The LVE properties of the PGA elastomers were investigated based on the master curves of the storage (G') and loss (G") modulus. The differences in DP and BD for the pPGA prepolymers translated into the PGA elastomer crosslinking densities and the rubbery plateau modulus (G0). It was shown for the first time that the minor differences in the structure of the pPGA prepolymers (DP of 13 and 21, and DB of 8.4% and 9.7% for the pPGA prepolymers synthesized for 8 and 24 h, respectively) translate into significant differences in the LVE of the PGA elastomers (G0 of 116 kPa and 50 kPa for the PGA elastomers derived from pPGA8 and pPGA24 prepolymers, respectively).

Theoretical Investigation of Structural, Electronic and Optical Properties of Cs3MoO4(HCO3) with NLO Active Functional Units

AbstractEmploying functional building units with microscopic second‐order NLO response has been proposed to explore high performance NLO materials. Herein, structural, electronic and optical properties of non‐centrosymmetric molybdenyl carbonate Cs3MoO4(HCO3) with NLO active functional units have been examined based on density functional theory. Theoretical results are consistent with experimentally mentioned data, confirming the reliable method. Detailed geometric structure, electronic attributes, linear optical properties, and nonlinear optical properties of Cs3MoO4(HCO3) are provided. Analysis of structures, compositions of bands and plots of charge density suggest that asymmetric functional building units [MoO4] and [HCO3] exhibit varying degrees of second‐order Jahn‐Teller distortions, and therefore have a significant impact on the electronic structure and optical properties of Cs3MoO4(HCO3). Maximum absolute value of SHG coefficients at 1064 nm is 0.671 pm/V for d15, which is nearly twice as much as that of KDP. Further researches are needed in future to validate and enhance optical anisotropy characteristic of Cs3MoO4(HCO3) for satisfying the phase matching conditions. Analysis results indicate that microscopic origins of SHG response in Cs3MoO4(HCO3) are complicated, such as geometric environment, induced polar asymmetric functional building units, and electronic properties. Continuous research on structure‐property relationship of NLO materials is needed for exploring more competitive NLO materials.

Barium Chalcogenide Crystals: A Review

In recent decades, new nonlinear optical materials have been actively developed to create coherent tunable light sources in the mid-infrared (mid-IR) part of the spectrum used in a variety of scientific fields. In the present review, the main attention is focused on barium chalcogenide crystals, including their linear and nonlinear optical properties, laser-induced damage threshold (LIDT), and frequency down-conversion.

Tuning the optical, and dielectric properties of PVC/PEO/NiMoO4/MWCNTs/x wt %PANI blended polymers for optoelectronic applications

Nanoparticles of nickel molybdate (NiMoO4) have attracted significant interest for their application as electrode materials. Here, new hybrid blended polymers, poly (vinyl chloride)/polyethylene oxide/nickel molybdate/multi-walled carbon nanotubes/polyaniline (PVC/PEO/NiMoO4/MWCNTs/x wt %PANI) were prepared. Several techniques, including X-ray diffraction (XRD), scanning electron microscopy (SEM), diffused reflectance, fluorescence and LCR meter were used to investigate the impact of the different fillers on the structure, electrical and optical features of the PVC/PEO blend. The structures of NiMoO4 and different blends were explored using XRD technique. The linear and nonlinear optical properties and the emitted colors of host blend are found to be affected by NiMoO4, MWCNTs and different amounts of PANI fillers. The T values of PVC/PEO were reduced as it loaded with NiMoO4/MWCNTs/x wt %PANI and it reached its minimum value (21–37% in the visible range) in NiMoO4/MWCNTs/x 0.4 %PANI blend. The minimum direct and indirect optical band gap values (4.09, 4.9) eV and (1.92, 3.47, 3.94) eV, respectively, were obtained as the amount of PANI became 0.4 wt % in the doped blend. The doped PVC/PEO blend with NiMoO4 has the highest refractive index value (2.11) at 600 nm. The highest nonlinear optical parameters were acquired exclusively in the visible spectrum when PVC/PEO was doped with NiMoO4.The maximum energy density value (6.03 × 10−3 J/m3) was obtained when the host blend loaded with NiMoO4/MWCNTs. Thus, PVC/PEO/NiMoO4/MWCNTs/x wt %PANI blends are recognized as a good prospect for UV blocking, solar cell, optoelectronic, nonlinear optical devices and energy storage innovation.

Charge transfer induced linear and nonlinear optical properties in polypyrrole/ZnO@MoS2 ternary composites

Polymer-based ternary nanocomposites with tunable optical properties are the key components for optoelectronics applications. Here, we demonstrate the linear and nonlinear optical properties of polypyrrole (PPy) and its ternary composites with different concentrations of the MoS2–ZnO core–shell (ZnO@MoS2) heterostructure. The interesting observation of multiple excitons and their transportation through the interface of PPy and ZnO@MoS2 by using photoluminescence and fluorescence lifetime spectroscopy was studied. Furthermore, the third-order nonlinear optical properties of all samples were also measured by employing the z-scan technique at an excitation wavelength of 532 nm. The reverse saturable absorption of pure PPy was switched to saturable absorption after the addition of ZnO@MoS2 at the uniform linear transmittance. These ternary composites with good nonlinear responses provide an option for the development of high-performance nonlinear optical devices and open a new path for the future development of ternary systems in the optical fields.

Some results for min matrices associated with Chebyshev polynomials

Abstract In the present study, inspired by the studies in the literature, we consider Min matrix and its Hadamard exponential matrix family whose elements are Chebyshev polynomials of the first kind. Afterwards, we examine their various linear algebraic properties and obtain some inequalities. Furthermore, we shed light on the results we obtained to boost the clarity of our paper with the illustrative examples. In addition to all these, we give two MATLAB-R2023a codes that compute the Min matrix and the Hadamard exponential matrix with Chebyshev polynomials of the first kind entries, as well as calculate some matrix norms.

Nonlinear optical properties of zinc oxide thin films

This study reports the influence of deposition temperature (573 K-773 K) on the microstructural, linear and nonlinear optical properties of zinc oxide nano thin films synthesized using the chemical spray pyrolysis method. Synthesized films are polycrystalline, exhibiting a dominant (101) orientation, for which the crystallite size is found to increase with deposition temperature up to 723 K followed by a decrease. Concurrently, the deposit prepared at 723 K showed improved electrical properties, i.e. higher charge carrier concentration and mobility. Optical studies reveal increased transmittance in the visible region and a gradual increase of optical bandgap with deposition temperature. The photoluminescence studies show a near-white light emission for all thin films, however, the density of defect states was comparatively higher for thin films deposited at lower temperatures. A saturable absorption behaviour was observed due to the presence of defects. The thin films show a negative refractive index with self-defocusing phenomena. The total nonlinear susceptibility is found to decrease with increasing deposition temperature, and the solution-processed functional thin films thus have potential implications for nonlinear optical applications such as nonlinear optical switching, optical memory management, and saturable absorbers.

Nonlinear effects in manybody van der Waals interactions

Van der Waals interactions are ubiquitous and they play an important role for the stability of materials. Current understanding of this type of coupling is based on linear response theory, while optical nonlinearities are rarely considered in this context. Many materials, however, exhibit strong optical nonlinear response, which prompts further evaluation of dispersive forces beyond linear response. Here we present a approach that takes into account linear and nonlinear properties of all dipolar nanoparticles in a given system. This method is based on a Hamiltonian for nonlinear dipoles, which we apply in different systems uncovering a complex interplay of distance, anisotropy, polarizabilities, and hyperpolarizabilities in the vdW energy. This investigation broadens our basic understanding of dispersive interactions, especially in the context of nonlinear materials. Published by the American Physical Society 2024

Non-ergodic linear convergence property of the delayed gradient descent under the strongly convexity and the Polyak–Łojasiewicz condition

In this work, we establish the linear convergence estimate for the gradient descent involving the delay [Formula: see text] when the cost function is [Formula: see text]-strongly convex and [Formula: see text]-smooth. This result improves upon the well-known estimates in [Y. Arjevani, O. Shamir and N. Srebro, A tight convergence analysis for stochastic gradient descent with delayed updates, Proc. Mach. Learn. Res. 117 (2020) 111–132; S. U. Stich and S. P. Karimireddy, The error-feedback framework: Better rates for SGD with delayed gradients and compressed updates, J. Mach. Learn. Res. 21(1) (2020) 9613–9648] in the sense that it is non-ergodic and is still established in spite of weaker constraint of cost function. Also, the range of learning rate [Formula: see text] can be extended from [Formula: see text] to [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text], where [Formula: see text] is the Lipschitz continuity constant of the gradient of cost function. In a further research, we show the linear convergence of cost function under the Polyak–Łojasiewicz[Formula: see text](PL) condition, for which the available choice of learning rate is further improved as [Formula: see text] for the large delay [Formula: see text]. The framework of the proof for this result is also extended to the stochastic gradient descent with time-varying delay under the PL condition. Finally, some numerical experiments are provided in order to confirm the reliability of the analyzed results.

Wide-Band Gap Binary Semiconductor P3N5 with Highly Anisotropic Optical Linearity and Nonlinearity.

Wide-band gap binary semiconductors find extensive use in advanced optoelectronic devices due to their exceptional electronic, optical, and defect properties. This paper systematically investigates the linear and nonlinear optical and defect properties of two P3N5 structures as wide-band gap binary semiconductors and evaluates their responses to external pressure modulation using first-principles calculations. The research demonstrates that the high-pressure phase of P3N5 has a broad UV solar-blind band gap (Eg ∼ 4.9 eV) and displays highly anisotropic optical linearity and nonlinearity, including a significant second harmonic generation effect (d24 ∼ 1.8 pm/V) and large birefringence (Δn ∼ 0.12), exhibiting a relatively small change in amplitude against pressure due to unique lattice incompressibility. This material enables birefringent phase-matched second harmonic coherent output at a much shorter wavelength (down to 286 nm) than currently known wide-band gap binary semiconductors such as SiC, GaN, AlN, Ga2O3, and Si3N4. An in-depth study of the defect properties of P3N5 in relation to its UV optical properties is also provided. These results are important references for utilizing the optoelectronic functions of this binary material system.

Influence of Specimen Geometries on the Viscoelastic Properties of Bituminous Mixtures in Torsion

A standard test method for determining the linear viscoelastic properties of bituminous mixtures in torsion prescribes the use of a dynamic shear rheometer. The method uses a prismoidal specimen (rectangular cross section) sliced from a Superpave gyratory compacted sample. However, the geometry utilized in the standard is a non-axisymmetric cross section, which leads to the development of warping stress when the specimen is tested in torsion using a dynamic shear rheometer. On the other hand, axisymmetric geometry, such as cylinder (circular cross section), does not warp when subjected to torsion. This study investigates the influence of the two specimen geometries, namely prismoidal and cylindrical, on the linear viscoelastic properties of bituminous mixtures in torsion. The specimens are obtained from a bituminous mixture with a nominal maximum aggregate size of 13.2 mm, and statistical analysis is carried out to determine whether the material constitution in the specimen geometries is identical. A frequency sweep experiment is conducted at 10, 20, and 30°C with a constant strain amplitude of 0.001% in the frequency range of 0.01 Hz to 20 Hz. The absolute shear modulus of the prismoidal specimens is found to be higher than that of cylindrical specimens because of warping stresses in prismoidal specimens. It was seen that the effect of warping stress is greater at higher temperatures and lower frequencies. Correction factors are used to correct the absolute shear modulus of prismoidal specimens. These findings highlight the importance of considering correction factors for warping when characterizing prismoidal bituminous mixtures in torsion.

Silver molybdate: an excellent optical limiting material under nanoregime for photonic device application

There is a mounting demand for nonlinear optical materials with superior optical limiting performance which has a noticeable impact on protecting the delicate optical components from laser-induced damage. Transition metal molybdates have garnered attention in the nonlinear optics field due to their outstanding optical and luminescent properties, which give rise to widespread applications in next-generation optoelectronics devices. The structural confirmation of the as prepared silver molybdate nanoparticles were made by XRD and Raman spectroscopy analysis. The linear optical properties and the band gap of the synthesized material were studied using UV–Visible and photoluminescence spectroscopy. SEM analysis revealed the pebble like morphology of the silver molybdate nanostructures. The nonlinear responses of the samples were studied using open aperture z-scan approach with Nd:YAG pulsed laser (532 nm, 9 ns, 10 Hz). The sample exhibits reverse saturable absorption pattern attributed to the two photon absorption (2PA) mechanism. The obtained OL threshold value is in the order of 1012 which is suitable for fabricating optical limiters in nano second pulsed laser regime.

Explicit scheme for solving variable-order time-fractional initial boundary value problems

The creation of an explicit finite difference scheme with the express purpose of resolving initial boundary value issues with linear and semi-linear variable-order temporal fractional properties is presented in this study. The rationale behind the utilization of the Caputo derivative in this scheme stems from its known importance in fractional calculus, an area of study that has attracted significant interest in the mathematical sciences and physics. Because of its special capacity to accurately represent physical memory and inheritance, the Caputo derivative is a relevant and appropriate option for representing the fractional features present in the issues this study attempts to address. Moreover, a detailed Fourier analysis of the explicit finite difference scheme’s stability is shown, demonstrating its conditional stability. Finally, certain numerical example solutions are reviewed and MATLAB-based graphic presentations are made.

Quantitative Foveal Structural Metrics as Predictors of Visual Acuity in Human Albinism.

To assess the degree to which quantitative foveal structural measurements account for variation in best-corrected visual acuity (BCVA) in human albinism. BCVA was measured and spectral domain optical coherence tomography (SD-OCT) images were acquired for 74 individuals with albinism. Categorical foveal hypoplasia grades were assessed using the Leicester Grading System for Foveal Hypoplasia. Foveal anatomical specialization (foveal versus parafoveal value) was quantified for inner retinal layer (IRL) thickness, outer segment (OS) length, and outer nuclear layer (ONL) thickness. These metrics, participant sex, and age were used to build a multiple linear regression of BCVA. This combined linear model's predictive properties were compared to those of categorical foveal hypoplasia grading. The cohort included three participants with type 1a foveal hypoplasia, 23 participants with type 1b, 33 with type 2, ten with type 3, and five with type 4. BCVA ranged from 0.08 to 1.00 logMAR (mean ± SD: 0.53 ± 0.21). IRL ratio, OS ratio, and ONL ratio were measured in all participants and decreased with increasing severity of foveal hypoplasia. The best-fit combined linear model included all three quantitative metrics and participant age expressed as a binary variable (divided into 0-18years and 19years or older; adjusted R2 = 0.500). This model predicted BCVA more accurately than a categorical foveal hypoplasia model (adjusted R2 = 0.352). A quantitative model of foveal specialization accounts for more variance in BCVA in albinism than categorical foveal hypoplasia grading. Other factors, such as optical aberrations and eye movements, may account for the remaining unexplained variance.

Robust stability analysis for uncertain systems with time‐varying delay via variable augmentation approach

AbstractThis paper investigates the problem of robust stability analysis for systems with time‐delays and time‐varying structured uncertainties. The variable augmentation approach and the free‐matrix‐based inequality are employed to retain the linear property of the estimation of the derivative of the Lyapunov–Krasovskii functionals. Moreover, with the use of the variable augmentation approach related to the time‐varying structured uncertainties, the time‐varying S‐Procedure combined with the time‐varying delay and its derivative is employed. As a result, less‐conservative robust stability conditions are derived. In addition, the merits of the augmentation of the time‐varying structured uncertainties over the traditional methods are theoretically demonstrated. Finally, two numerical examples are given to verify the benefits of the proposed methods.

Crystal growth and characterization of glycine chlorzoxazone nonlinear optical crystal for energy storage capacitor applications

This research presents the synthesis of a glycine chlorzoxazone (GC) organic single crystal through a slow evaporation process using a mixed solvent of water and ethanol at room temperature. The crystal's functional group coordination is examined via fourier-transform infrared (FTIR) spectroscopy. The study delves into the linear optical properties through UV–visible spectroscopy, and thermal analyses provide insights into the material's thermal behavior. Optical nonlinearity is confirmed using the Kurtz-Perry powder technique. The investigation extends to the electrical properties of prepared crystals, incorporating a combination of AC and DC electrical studies. This comprehensive approach enhances our understanding of the multifaceted characteristics of synthesized crystal, positioning it as a promising candidate for different electronic and optical applications.

Optical and structural characterization of zinc oxide thin films upon ion beam assisted smoothing

Wurtzite zinc oxide (ZnO) has a preferential growth direction along the c-axis of the hexagonal unit cell, which, especially in combination with underlying (amorphous) heterostructures, can lead to a high surface roughness for the ZnO layers. This poses a significant challenge to the construction of e.g. photonic waveguides or gratings. Here, we propose an efficient way for smoothing ZnO surfaces after deposition using a collimated beam of Argon ions. Furthermore, the influence of this treatment at different angles of incidence and fluence of the ions on the morphological, structural and linear optical emission properties is investigated using atomic force microscopy, X-ray diffraction, spectroscopic ellipsometry and photoluminescence (PL) experiments. Our results suggest that using an ion beam incident at an angle of 85° reduces the surface roughness by around 70% while keeping the ZnO crystal structure intact. Though such a treatment leads to a reduced intensity and to a broadening of the PL-emission, excitonic transitions are still prominently observable.

Tunable structure and linear viscoelastic properties of poly(glycerol adipate urethane)-based elastomeric composites for tissue regeneration

Elastomeric biocomposites based on poly(glycerol adipate urethane) and hydroxyapatite were fabricated for tissue regeneration. The poly(glycerol adipate urethane) (PGAU) elastomeric composite matrices were obtained by chemical crosslinking of the poly(glycerol adipate) prepolymer (pPGA) with diisocyanate derivative of L-lysine. Two series of composites varying in the amount of L-lysine diisocyanate ethyl ester (LDI) used as a crosslinking agent were manufactured. As a ceramic filler both unmodified and L-lysine surface-modified hydroxyapatite (HAP) particles were used. The novelty of our research consists in the manufactured elastomeric materials and characterization of their linear viscoelastic (LVE) properties. The LVE properties of the composites were investigated by means of dynamic thermomechanical analysis. Frequency sweep and amplitude sweep measurements were performed in shear mode. The influence of the crosslinking agent (LDI) amount, HAP content and surface modification of HAP on the LVE properties of the composites was determined based on the analysis of the master curves of storage (G′) and loss (G″) moduli and of tanδ of the composites. Depending on the amount of LDI, HAP and surface modification, the materials differ in the values of rubber elasticity plateau modulus (G0) and G′ and G″ determined at selected shear frequencies and at the glassy state. G0 ranges from 278 kPa to 3.98 MPa, G′ in the glassy state is within the range of 219 MPa–459 MPa. The G0 values of the PGAU-based composites are within the stiffness range of soft tissue. In view of the choice of HAP as the ceramic component and the G0 values, elastomeric composites have the potential to be used as filling materials in small bone defects (due to their mechanical similarity to osteoid) as well as materials for cartilage tissue regeneration.