Dispersion Formula Research Articles

Structural, stoichiometric and optical constants of crystalline undoped lead iodide films prepared by the flash-evaporation method

The flash-evaporation method was used to deposit several thin films (1, 1.2, and 1.35 µm thick) of undoped lead iodide on glass slides held at $$150$$ °C and $$200$$ °C. Their X-ray diffraction patterns, scanning electron microscope micrographs, and energy-dispersive spectroscopy spectra revealed crystalline hexagonal 2H-polytypic structure and high stoichiometry ( $${\text{PbI}}_{x} ;x \cong 1.9$$ ). Their as-measured normal-incidence transmittance $$T_{\text{exp}} (\lambda)$$ –wavelength $$\lambda$$ curves exhibited above a specific wavelength $$\lambda_{{\text{c}}} \approx 520{\text{ nm}}$$ and many well-resolved interference-fringe maxima and minima, indicating good film uniformity. Below $$\lambda_{{\text{c}}}$$ , these $$T_{\text{exp}} (\lambda) - \lambda$$ curves declined sharply toward $$T_{\text{exp}} (\lambda) \cong 0$$ , signifying high film crystallinity. The $$\lambda$$ dependency of optical constants $$n(\lambda)$$ and $$\kappa (\lambda)$$ retrieved from numeric iterative curve fitting of $$T_{\text{exp}} (\lambda) - \lambda$$ data to theoretical $$T_{{{\text{theor}}}} (\lambda)$$ formula describe an air-supported {film/substrate} structure, combined with O’Leary–Johnson–Lim (OJL) interband transition dispersion model and a set of harmonic-like oscillator dispersion formulas. The retrieved bandgap energy $$E_{{\text{g}}}^{{{\text{opt}}}}$$ and band-tail breadth $$\gamma$$ were around $$2.4\,{\text{ eV}}$$ and $$100\,{\text{ meV}}$$ , respectively. The determined $$n(\lambda) - \lambda$$ data gave best curve fits to the Wemple–DiDomenico (WDD) equation with reasonable bandgap energy parameter $$E_{{\text{o}}} \cong 3.8\,{\text{ eV}} \cong 1.6\,E_{{\text{g}}}^{{{\text{opt}}}}$$ , single-oscillator energy strength $$E_{{\text{d}}} \cong 18\,{\text{ eV}}$$ and static index of refraction $$n_{{\text{o}}} \cong 2.4$$ . The calculated optical absorption coefficient $$\alpha (\lambda) = 4{\uppi }\kappa (\lambda)/\lambda$$ was found to obey the direct interband transition with bandgap energy $$E_{{\text{g}}} \cong 2.45\,{\text{ eV}}$$ in the absorption edge region, near which the curve fits of $$\alpha (\lambda)$$ to Urbach formula gave an Urbach tail parameter $${\Gamma }_{{\text{U}}}$$ of $$45\,{\text{ meV}}$$ , consistent with the results of numerical analysis of $$T_{\text{exp}} (\lambda) - \lambda$$ curves. The film thickness and substrate temperature had a slight effect on the determined optical parameters.

Estimating transmitted wavefronts in a broad bandwidth based on Zernike coefficients

Existing technologies and methods for measuring transmitted wavefronts typically operate at only a few specific wavelengths. In this paper, we propose a new method for estimating the wavefront distortion of an optical transmission system in a broad bandwidth. We establish the relationship between the transmitted wavefront and wavelength, using Zernike fringe coefficients to represent the wavefront. From simulations of several different types of optical systems, we found that two formulas can be used to express Zernike-wavelength curves: the Conrady dispersion formula and a new formula that we have named the apochromatic characteristic formula. To reduce the influence of measurement errors on predictions, fitting method is biased in favor of simulation rather than experimental data. We illustrate the validity of this technique by reconstructing a wavefront transmitted at 671 nm using Zernike polynomials, demonstrating that the predicted wavefront is very similar to the wavefront measured experimentally. Using the Conrady formula, we illustrate that the wavefront of a monochromatic system can be predicted for any wavelength in a broad range, using data from three standard wavelengths. As Seidel coefficients correspond to Zernike coefficients, the relationship between optical aberration and wavelength detailed here can also be applied to areas, such as optical design, optical computing and adaptive optics.

ENHANCEMENT OF GLIBENCLAMIDE DISSOLUTION RATE BY SOLID DISPERSION METHOD USING HPMC AND PVP

Objective: The aim of this study was to investigate the effects of changing in the proportions of the solid dispersion formula on the dissolution rate of glibenclamide.
 Methods: Solid dispersions were prepared by solvent evaporation method by using methanol as solvent, hydroxypropyl methylcellulose (HPMC) and polyvinyl pyrrolidone (PVP) as polymers. The prepared product was evaluated by the saturated solubility test and the dissolution rate test. The prepared product was characterized by Fourier transform infrared spectroscopy (FT-IR), differential scanning calorimetry (DSC), and powder X-ray diffraction (PXRD) and Scanning Electron Microscopy (SEM).
 Results: The result showed solid dispersion with a ratio of glibenclamide: PVP: HPMC (1: 3: 6) has the highest increase in solubility (20 fold) compared to pure glibenclamide. This formula also showed an improvement in dissolution rate from 19.9±1.19% (pure glibenclamide) to 99±1.60% in 60 min. Characterization of FT-IR showed that no chemical reaction occurred in solid dispersion of glibenclamide. The results of X-ray diffraction analysis showed an amorphous form in all solid dispersion formulas. The results of DSC analysis showed that endothermic peak melting point of solid dispersion occurred, and the morphology of solid dispersion was more irregular than pure glibenclamide based on SEM characterization
 Conclusion: The solid dispersion of glibenclamide using PVP: HPMC as carriers can increase the solubility and dissolution rate compared to pure glibenclamide.

Photonic Band Gap Properties of One-dimensional Generalized Fibonacci Photonic Quasicrystal Containing Superconductor Material

In this work, we theoretically investigate the transmission properties of one-dimensional (1D) Fibonacci photonic quasicrystal (PQC) by using the transfer matrix modeling (TMM) method. The PQC structure is composed of alternated layers of isotropic dielectric (SiO2) and a high-Tc superconductor (YBCO). Frequency-dependent dispersion formula according to the two-fluid Gorter–Casimir theory has been adopted to describe the optical response of the superconducting material. Within the framework of the TMM method, we studied the effect of many parameters such as the thicknesses of the dielectric and superconductor layers, Fibonacci lattice parameters, and the operating temperature on the transmission behaviors of the PQC structure. Our numerical results reveal the transmission cutoff frequency can be tuned efficiently by the operating temperature as well as by the thicknesses of the constituent materials. We found that increasing the temperature and the angle of incidence, maintaining materials thicknesses constant, there is a shift of the cutoff frequency to lower frequency values. Nevertheless, this cutoff frequency is shifted to higher values with increasing the superconductor layer thickness. Moreover, we found that the width and the number of the photonic bandgaps can be controlled by order of Fibonacci sequence. Our results are promising for the design of tunable filtering devices.

Temperature-dependent quasi phase-matching properties of periodically poled LaBGeO5

We report accurate Sellmeier equations at 22℃ for LaBGeO5, which reproduce well our experimental results for the quasi phase-matching conditions with the ee-e, oe-o, eo-o, and oo-e interactions in the 0.2660 − 1.0642 µm spectral range. In addition, the thermo-optic dispersion formula (dn/dT) of this material is also presented.

Peningkatan Kadar Ketoprofen Terdisolusi melalui Pembentukan Dispersi Padat menggunakan Polivinil Alkohol (PVA)

Ketoprofen is included in the Class II of Biopharmaceutical Classification System (BCS) which has low solubility. Low solubility will affect the dissolution rate and the dissolved concentration, so the absorption and bioavailability are low as well. Several studies have been conducted to improve the solubility and the dissolution of drugs from these group, such as by solid dispersion system. This study aims to determine the effect of polyvinyl alcohol (PVA) on the dissolved concentration of ketoprofen in solid dispersion and in physical mixture, and to decidethe optimum formula.Solid dispersion and physical mixture of ketoprofen - PVA were formulated with the ratio of 1:1, 1:2 and 1:4, and then compared with the standard ketoprofen. Evaluation of solid dispersion was performed by the intervention test of PVA as a matrix on the maximum wavelength of standard ketoprofen using a UV-Vis spectrophotometer and the dissolution test in artificial gastric fluid media without pepsin using a basket stirrer at pH ± 1,2, the temperature of 37 ± 0.5ºC, and device speed of 50 rpm. The sample was collected at 10, 20, 30, 45, and 60 minutes. The amount of dissolved ketoprofen was determined by a UV-Vis spectrophotometer at a wavelength of 260 nm. The results showed that there was no shifting on maximum wavelength point in both solid dispersions and physical mixtures. The dissolved ketoprofen concentration that was represented in solid dispersion was greater than in physical mixture and standard ketoprofen. The highest dissolved ketoprofen concentration was indicated in solid dispersion formula with the ratio of 1:1.

New Sellmeier and Thermo-Optic Dispersion Formulas for AgGaS2

This paper reports on the new Sellmeier and thermo-optic dispersion formulas that provide a good reproduction of the temperature-dependent phase-matching conditions for second-harmonic generation (SHG) and sum-frequency generation (SFG) of a CO2 laser and a Nd:YAG laser-pumped KTiOPO4 (KTP) optical parametric oscillator (OPO) in the 0.8859–10.5910 μm range as well as those for difference-frequency generation (DFG) between the two diode lasers in the 4.9–6.5 μm range and DFG between the two periodically poled LiNbO3 (PPLN) OPOs in the 5–12 μm range thus far reported in the literature.

Natamycin niosomes as a promising ocular nanosized delivery system with ketorolac tromethamine for dual effects for treatment of candida rabbit keratitis; in vitro/in vivo and histopathological studies

Objectives: This study was aimed to develop dual-purpose natamycin (NAT)-loaded niosomes in ketorolac tromethamine (KT) gels topical ocular drug delivery system to improve the clinical efficacy of natamycin through enhancing its penetration through corneal tissue and reducing inflammation associated with Fungal keratitis (FK).Significance: Nanosized carrier systems, as niosomes would provide great potential for improving NAT ocular bioavailability.NAT niosomal dispersion formulae were prepared and then incorporated in 0.5%KT gels using different mucoadhesive viscosifying polymers.Methods: Niosomes were prepared using the reverse-phase evaporation technique. In vitro experimental, and in vivo clinical evaluations for these formulations were done for assessment of their safety and efficacy for treatment of Candida Keratitis in Rabbits. In vitro release study was carried out by the dialysis method. In vivo and histopathological studies were performed on albino rabbits.Results: NAT niosomes exhibited high entrapment efficiency percentage (E.E%) up to96.43% and particle size diameter ranging from 181.75 ± 0.64 to 498.95 ± 0.64 nm, with negatively charged zeta potential (ZP). NAT niosomal dispersion exhibited prolonged in vitro drug release (40.96–77.49% over 24h). NAT-loaded niosomes/0.5%KT gel formulae revealed retardation in vitro release, compared to marketed-product (NATACYN®) and NAT-loaded niosomes up to57.32% (F8). In vivo experimental studies showed the superiority for F8 in treatment of candida keratitis and better results on corneal infiltration and hypopyon level. These results were consistent with histopathological examination in comparison with F5 and combined marketed products (NATACYN® and Ketoroline®).Conclusions: This study showed that F8 has the best results from all pharmaceutical in vitro evaluations and a better cure percent in experimental application and enhancing the prolonged delivery of NAT and penetrating the cornea tissues.

Thermo-optic dispersion formula for LiGaS2.

This paper reports on new experimental results on the temperature-dependent phase-matching properties of LiGaS2 for second-harmonic generation and sum-frequency generation in the 0.820-10.5910μm spectral range. In addition, we present a thermo-optic dispersion formula that provides a good reproduction of the present experimental results when combined with the Sellmeier equations presented in our previous paper, Kato etal. [Opt. Lett.42, 4363 (2017)OPLEDP0146-959210.1364/OL.42.004363].

Coherent Multiple-Antenna Block-Fading Channels at Finite Blocklength

In this paper, we consider a channel model that is often used to describe mobile wireless scenarios: multiple-antenna additive white Gaussian noise channels subject to random (fading) gains with full channel state information at the receiver. The dynamics of the fading process are approximated by a piecewise-constant process (frequency non-selective isotropic block fading). This paper addresses the finite blocklength fundamental limits of this channel model. Specifically, we give a formula for the channel dispersion—a quantity governing the delay required to achieve capacity. The multiplicative nature of the fading disturbance leads to a number of interesting technical difficulties that required us to enhance traditional methods for finding the channel dispersion. Alas, one difficulty remains: the converse (impossibility) part of our result holds under an extra constraint on the growth of the peak-power with blocklength. Our results demonstrate, for example, that while the capacities of $n_{t}\times n_{r}$ and $n_{r} \times n_{t}$ antenna configurations coincide (under fixed received power), the coding delay can be sensitive to this switch. For example, at the received SNR of 20 dB, the $16\times 100$ system achieves capacity with codes of length (delay) which is only 60% of the length required for the $100\times 16$ system. Another interesting implication is that for the MISO channel, the dispersion-optimal coding schemes require employing orthogonal designs such as Alamouti’s scheme—a surprising observation considering the fact that Alamouti’s scheme was designed for reducing demodulation errors, not improving coding rate. Finding these dispersion-optimal coding schemes naturally gives a criteria for producing orthogonal design-like inputs in dimensions where orthogonal designs do not exist.

Modeling the Temperature-Dependent Material Dispersion of Imidazolium-Based Ionic Liquids in the VIS-NIR

A thorough analysis of the refractive index of 11 1-alkyl-3-methylimidazolium-based ionic liquids with three different anions, tetrafluoroborate (BF4), bis(trifluoromethylsulfonyl)imide (NTf2), and trifluoromethanesulfonate (OTf), is reported. Refractive indices were estimated, in the temperature interval from 298.15 to 323.15 K, using an Abbe refractometer to determine the value at the sodium D line and white light spectral interferometry to obtain dispersion in the range of wavelengths from 400 to 1000 nm. The first part of the manuscript is focused on the dependence of refractive index with wavelength, temperature, cation alkyl chain length, and anion nature. Once the main features are detailed, and in order to explain the experimental trends, a model for the refractive index is considered where its square is expressed by a single resonance Sellmeier dispersion formula. This formula has two coefficients: the first one identifies the position of the resonance in the spectral axis, and the second one spe...

Optical properties of p-type SnOx thin films deposited by DC reactive sputtering

Refractive index (n), extinction coefficient (k), effective complex dielectric function (e) and band gap energy (Eg) of p-type SnOx thin films from 0.75 to 4 eV are studied. 25 nm thick films were deposited by direct current (DC) magnetron sputtering in reactive argon and oxygen atmosphere at different relative oxygen partial pressure (OPP) followed by a post annealing treatment at 250 °C in air atmosphere for 30 min. The relative high Hall effect mobility (μ) of the SnOx was attributed to the dominant SnO phase in films grown at 15% OPP. Films deposited at 5 and 11% OPP showed incomplete Sn oxidation resulting in a mixture of Sn and SnO phases with lower hole mobility. Optical transmittance (T) and reflectance (R) are described by assuming a model where the p-type SnOx films are defined by a dispersion formula based on a generalization of the Lorentz oscillator model. The roughness of the films (r) was modeled by a Bruggeman effective medium approximation (BEMA). From the optical analysis, k in the visible spectral region show high values for films with phase mixture, while films with single SnO phase presented negligible values. Films with single SnO phase have low n, this latter result from the lower compact microstructure of these films. Also, energies associated to direct and indirect transitions of the Brillouin zone of the SnOx films were identified from the evaluated e. Finally, the increase in the values of Eg energy was related to the increase in the SnO phase.

Dispersion and anisotropy of thermo-optical properties of Alexandrite laser crystal

Dispersion and anisotropy of thermal coefficients of the optical path (TCOP) and thermo-optic coefficients (TOCs) of Alexandrite laser crystal (Cr3+:BeAl2O4) are studied for the three principal light polarizations, E || a, E || b and E || c. Thermo-optic dispersion formulas are presented for the spectral range of 0.4-1.1 µm. All TOCs are positive and show a notable polarization-anisotropy, dna/dT = 5.9, dnb/dT = 6.9 and dnc/dT = 15.2 × 10−6 K−1 at 0.75 µm. Thermal lensing was characterized in a continuous-wave Alexandrite laser pumped at 0.532 µm and operating at 0.7509 µm (for E || b). The measured thermal lens was weak, positive and slightly astigmatic. The sensitivity factors of the thermal lens were found to be Mx = 1.74 and My = 2.38 [m−1/W].

On an attenuation obeying a frequency power law

An attenuation obeying a frequency power law scales as |ω|^β, where ω is angular frequency and β is a real constant. According to the strain-hardening shear-wave equation in the grain-shearing theory, the attenuation of the shear wave supported by a marine sediment follows a frequency power law. The associated dispersion formula, which is a causal transform, predicts that the phase speed is also a power law and that the product of the phase speed and the attenuation divided by ω is a constant, independent of frequency. From the dispersion formula, along with the conditions that the phase speed and attenuation must both be positive and the propagation factor must exhibit conjugate symmetry, it follows that the exponent β can take only certain values that fall in well-defined intervals extending indefinitely with no upper or lower limit. However, to satisfy the requirement that Green’s function be causal, β is further constrained to lie in the interval [0.5 1), under which condition the Green’s function is maximally flat at the time the source is activated. With other values of β the Green’s function is non-causal, exhibiting non-zero values at times preceding the onset of the source. [Research supported by ONR.]An attenuation obeying a frequency power law scales as |ω|^β, where ω is angular frequency and β is a real constant. According to the strain-hardening shear-wave equation in the grain-shearing theory, the attenuation of the shear wave supported by a marine sediment follows a frequency power law. The associated dispersion formula, which is a causal transform, predicts that the phase speed is also a power law and that the product of the phase speed and the attenuation divided by ω is a constant, independent of frequency. From the dispersion formula, along with the conditions that the phase speed and attenuation must both be positive and the propagation factor must exhibit conjugate symmetry, it follows that the exponent β can take only certain values that fall in well-defined intervals extending indefinitely with no upper or lower limit. However, to satisfy the requirement that Green’s function be causal, β is further constrained to lie in the interval [0.5 1), under which condition the Green’s function is ...

The dispersion formula and the Green's function associated with an attenuation obeying a frequency power law.

An attenuation obeying a frequency power law scales as , where ω is angular frequency and β is a real constant. A recently developed dispersion formula predicts that the exponent β can take only certain values in well defined, disjoint intervals. It is shown here that these admissible values of β are consistent with the physical requirement, stemming from the second law of thermodynamics, that the work done during the passage of a wave must always be positive. Since the dispersion formula, which is derived from the strain-hardening wave equation, is a causal transform, it is expected that the associated Green's function should also satisfy causality for all the permitted values of β. Such is not the case, however: the Green's function is maximally flat at the time of source activation, and hence is causal, but only for values of β in the interval (0.5, 1). This restriction supersedes the weaker constraints on β derived from the dispersion formula alone. For the previously admissible values of β outside the interval (0.5, 1), although the dispersion formula satisfies causality, the Green's function is non-causal. Evidently, causality may be satisfied by the dispersion formula but violated by the Green's function.

Characterizations and morphology of sodium tungstate particles.

A solid-state reaction technique was used to synthesize polycrystalline Na2WO4. Preliminary X-ray studies revealed that the compound has a cubic structure at room temperature. The formation of the compound has been confirmed by X-ray powder diffraction studies and Raman spectroscopy. Electrical and dielectric properties of the compound have been studied using complex impedance spectroscopy in the frequency range 209 Hz–1 MHz and temperature range 586–679 K. The impedance data were modellized by an equivalent circuit consisting of series of a combination of grains and grains boundary. We use complex electrical modulus M* at various temperatures to analyse dielectric data. The modulus plots are characterized by the presence of two relaxation peaks thermally activated. The morphologies and the average particle size of the resultant sodium tungstate sample were demonstrated by atomic force microscopy, scanning electron microscopy and transmission electron microscopy. The thicknesses and optical constants of the sample have been calculated using ellipsometric measurements in the range of 200–22 000 nm by means of new amorphous dispersion formula which is the objective of the present work. The results were obtained for Na2WO4 particles from experimental (EXP) and measured (FIT) data showed an excellent agreement. In addition, the energy gap of the Na2WO4 sample has been determined using ellipsometry and confirmed by spectrophotometry measurements.

How valid is Taylor dispersion formula in slugs?

How valid is Taylor dispersion formula in slugs?

New thermo-optic dispersion formula for LiB3O5

This paper reports on the new thermo-optic dispersion formula for LiB3O5 that provides a good reproduction of the temperature dependent phase-matching conditions for second-harmonic generation, sum-frequency generation, and optical parametric oscillator thus far reported in the literature when combined with the Sellmeier equations presented in the previous paper (Kato 1994 IEEE J. Quantum Electron. 30 2950–2).

Empirical Formulae for Dispersion and Effective Mode Area in Hollow-Core Antiresonant Fibers

We present empirical formulae that provide dispersion and effective area of the fundamental mode in hollow-core antiresonant fibers. The formulae draw on the structural parameters of the fiber and allow one to obtain the guiding properties over a wide spectral bandwidth, without the need for time consuming numerical simulations. The formulae are validated by comparing their results with those obtained using the finite-element method. We also analyze the effects of changing the number of antiresonant tubes, as well as adding nested elements in the antiresonant tubes on the guiding properties.

Properties of Ferrite Garnet (Bi, Lu, Y)₃(Fe, Ga)₅O12 Thin Film Materials Prepared by RF Magnetron Sputtering.

This work is devoted to physical vapor deposition synthesis, and characterisation of bismuth and lutetium-substituted ferrite-garnet thin-film materials for magneto-optic (MO) applications. The properties of garnet thin films sputtered using a target of nominal composition type Bi0.9Lu1.85Y0.25Fe4.0Ga1O12 are studied. By measuring the optical transmission spectra at room temperature, the optical constants and the accurate film thicknesses can be evaluated using Swanepoel’s envelope method. The refractive index data are found to be matching very closely to these derived from Cauchy’s dispersion formula for the entire spectral range between 300 and 2500 nm. The optical absorption coefficient and the extinction coefficient data are studied for both the as-deposited and annealed garnet thin-film samples. A new approach is applied to accurately derive the optical constants data simultaneously with the physical layer thickness, using a combination approach employing custom-built spectrum-fitting software in conjunction with Swanepoel’s envelope method. MO properties, such as specific Faraday rotation, MO figure of merit and MO swing factor are also investigated for several annealed garnet-phase films.