Equation For Refractive Index Research Articles

Dielectric Characterization of Fabric Aggregates around the 2.45 GHz ISM Band under Various Humidity, Density, and Temperature Conditions.

Fabric permittivity is critical for the manufacturing of wearable sensors and antennas as well as predicting how fabrics interact with electromagnetic fields. Engineers should also understand how permittivity changes under different temperatures, densities, and moisture content values, or when several fabrics are mixed in aggregates, when designing future applications such as microwave dryers. The permittivity of cotton, polyester, and polyamide fabric aggregates is investigated in this paper for a wide range of compositions, moisture content levels, density values, and temperature conditions around the 2.45 GHz ISM band using a bi-reentrant resonant cavity. The obtained results show extremely comparable responses for all characteristics investigated for single and binary fabric aggregates. Permittivity always increases as temperature, density, or moisture content levels rise. Moisture content is the most influential characteristic, causing enormous variations in the permittivity of aggregates. Fitting equations are supplied for all data, with exponential functions used to accurately model variation in temperature and polynomial functions employed to precisely model density and moisture content variations with low error levels. The temperature permittivity dependence of single fabrics without the influence of air gaps is also extracted from fabric and air aggregates by using complex refractive index equations for two-phase mixtures.

A Novel System for the Measurement of an Evaporation Duct Using the Magnetic Coupling Principle for Power Feeding and Data Transmission.

Since the evaporation duct height (EDH) only covers the antenna height of most shipborne microwave radars, mastering the EDH in advance has great significance in achieving long-range target detection. In this paper, a set of hydrological and meteorological sensors based on the gradient meteorological instrument (GMI) were built to monitor the evaporation duct of the South China Sea (SCS). However, the monitoring needed to be interrupted during the battery replacement of the sensor, which could result in the loss of some important data collection. On the basis of the inductively coupled power transfer (ICPT) technology, the resonance principle was used to compensate the inductive reactance on the closed steel ring (CSR), and the energy stored in the super capacitor was introduced for data collection and return. A novel measuring system for the detection of an evaporation duct was proposed. To avoid iterative calculation by setting the initial value of the current evaporation duct models in large-scale and multi time evaporation duct prediction and diagnosis, on the basis of the non-iterative air–sea flux (NAF) model, the EDH was obtained by introducing the K theoretical flux observation method into the atmospheric refractive index equation. Finally, preliminary experimental results are presented for the detection of evaporation duct to demonstrate the feasibility and effectiveness of the proposed system. The communication accuracy rate of the proposed system was 99.7%. The system transmission power reached 22.8 W. The research results of the NAF model adaptability showed that the mean value of the EDH was 8.7 m, which was lower than the mean EDH of the SCS. The EDH calculated by the NAF model in the unstable air–sea stratification state was slightly lower than that calculated by the NPS model. The diagnosis of the EDH by the NAF model was similar to that of the NPS model, but the calculation stability of the NAF model was better.

Refractive index characteristics of edible oils based on spectrometry and effects of oil dispersion on OCT

It is necessary to investigate the wavelength-dependent variation rules of the refractive index of edible oils so as to explore the specificity of the dispersion in light propagation, imaging, and interference processes among different types of edible oil products. In this study, by deriving the refractive index equations of the double glass sheet holding device and oil, the reflectance spectra of three different types of oil samples, namely, peanut oil, colza oil, and kitchen waste oil, were measured via a spectrometer. Furthermore, the refractive index model of these different types of oil samples was investigated. Additionally, based on the oil dispersion characteristics, the dispersion of oil in optical coherence tomography (OCT) was compensated via deconvolution. In the wavelength range of [Formula: see text] (380, 1500)[Formula: see text]nm, the analytical expressions of the double glass sheet holding device and oils are featured by practical reliability. The refractive indexes of three different types of oils [Formula: see text] (1.38, 1.52) show normal dispersion characteristics. The Cauchy coefficient matrix of the oil refractive index can be used for oil identification; in particular, the healthy oil and waste oil differ significantly in terms of the Cauchy coefficient matrix in the infrared band. Oil dispersion has almost no influence on the phase spectra of oils but can enhance their amplitude spectra. The dispersion mismatch can be eliminated by calculating the convolution kernel. The envelope broadening factors of OCT interference signals of oil products are 0.84, 0.64, and 0.91, respectively. According to the present research results, the refractive index model of oil can effectively remove the influence of the holding device. The refractive indexes of three different types of oil samples show similar wavelength-dependent variation characteristics, which confirms the existence of many correlated components in these oil samples. The established refractive index model of oil in a wide spectral range, from the ultraviolet to the infrared band, can be adequately employed for identifying different types of oils. The numerical dispersion compensation based on the established refractive index model can enhance the axial resolution in OCT imaging.

Measurement of multiple physical parameters of dense gaseous hydrogen-deuterium mixture under double-shock compression: Evaluating theoretical models from multiple views

A series of reverberating shock experiments on the precompressed hydrogen-deuterium (H-D) mixture were performed by using a two-stage light gas gun, and an elaborately designed diagnostic configuration was presented to probe the multishock states of dense fluid H-D mixtures. The particular diagnostics allowed multiple physical parameters, including the equation of state (EOS), refractive index, reflectivity, molecular polarizability, and energy gap, of H-D mixtures under double-shock compression to be simultaneously determined in a single shot. The multiple parameters obtained provide a comprehensive evaluation for existing theoretical models from multiple perspectives. It is found that, compared with the semilocal Perdew–Burke–Ernzerhof xc functional, the EOS data predicted by a nonlocal van der Waals exchange-correlation (xc) functional (vdW-DF1) are in much better agreement with the experimental results. Furthermore, the commonly used Gladstone–Dale relation is not appropriate for describing the refractive index in high-pressure-temperature regions, and the refractive index and reflectivity can be well reproduced by the Heyd–Scuseria–Ernzerhof hybrid xc functional. These observations may provide insights into future theoretical developments and a better understanding of material properties under extreme pressure-temperature conditions.

Refractive index of lithium fluoride to 900 gigapascal and implications for dynamic equation of state measurements

Lithium fluoride (LiF) is a unique crystal possessing the largest reported bandgap of any material and is predicted to remain transparent to visible light under stresses in excess of 1000 GPa. Dynamic compression experiments often utilize LiF as a window material to maintain stress on a sample while enabling direct measurements of interface velocity. However, typical velocimetry diagnostics measure changes in the optical path length; therefore, an accurate understanding of LiF’s equation of state and refractive index is needed. Here, we present a measurement of the LiF refractive index up to 900 GPa from a low-temperature ramp-compression experiment at the National Ignition Facility. To demonstrate propagation of optical uncertainty from this work to equation of state measurements, simulations in which a tin–LiF interface reaches a peak stress of 825 GPa show that the principal isentrope of tin can be determined up to 1450 GPa with a 1.2% uncertainty in density while considering uncertainties in the optical response of LiF.

Soliton dynamics in finite nonlocal media with cylindrical symmetry

The effect of finite boundaries in the propagation of spatial nonlocal solitons in media with cylindrical symmetry is analyzed. Using Ehrenfest's theorem together with the Green's function of the nonlinear refractive index equation, we derive an analytical expression for the force exerted on the soliton by the boundaries, verifying its validity by full numerical propagation. We show that the dynamics of the soliton are determined not only by the degree of nonlocality, but also by the boundary conditions for the refractive index. In particular, we report that a supercritical pitchfork bifurcation appears when the boundary condition exceed a certain threshold value.

Manipulating light trace in a gradient-refractive-index medium: a Lagrangian optics method.

Light propagation obeys Fermat's principle, and an important inference of Fermat's principle is the optical Lagrange equation, from which the light trace can be determined with a given refractive index. Here, we consider the inverse problem of how to derive the refractive index distribution of a planar geometric optical system once the trace is predetermined. Based on the optical Lagrange equation, we propose a dynamic equation model which associates the refractive index with the light trace. With the consideration of a certain trace, we illustrate the process of solving the partial differential equation of refractive index through first integral method. By setting the distribution function of a gradient-refractive-index (GRIN) medium, one can control the light traveling along a desirable curve, adjust the incoming and outgoing rays, and also use the trace to paint geometrics. This method develops the Lagrangian optics in the application of ray dynamic system design, such as lens, beam splitter, metasurface and optical waveguide. It provides a theoretical guidance to manipulate the ray in a GRIN medium.

Solving Fresnel equation for refractive index using reflected optical power obtained from Bessel beam interferometry.

This work demonstrates an interferometric technique to estimate the reflected powers from dielectric interfaces and the reflection coefficient using the Fresnel equation for measurement of the refractive index (RI) of liquid samples. It uses low-coherence common-path optical interferometry that is commonly used for optical imaging. A uniquely designed optical fiber tip generating a high-quality non-diffractive Bessel beam probes liquid samples in a glass container non-invasively. The light reflected from different interfaces of the container is recollected by the same optical fiber tip. The reflected beams interfere with the reference beam generated at the fiber tip itself. This interference spectrum is further processed using fast-Fourier transform to measure reflected powers from the respective interfaces. The acquired powers are used to solve the Fresnel equation to find RI of liquid samples. As a proof of concept, experiments have been performed on several liquid samples including turbid media such as blood. This non-invasive interferometric technique could also be an ideal example confirming the Fresnel equation for reflection of light. Unlike other optical fiber-based RI sensors, this technique does not require temperature compensation. The method can be employed for inspection of the production process in terms of RI in pharmaceutical and chemical process plants, etc.

Average value of the shape and direction factor in the equation of refractive index

The theoretical calculation of the refractive indices is of great significance for the developments of new optical materials. The calculation method of refractive index, which was deduced from the electron-cloud-conductor model, contains the shape and direction factor [Formula: see text]. [Formula: see text] affects the electromagnetic-induction energy absorbed by the electron clouds, thereby influencing the refractive indices. It is not yet known how to calculate [Formula: see text] value of non-spherical electron clouds. In this paper, [Formula: see text] value is derived by imaginatively dividing the electron cloud into numerous little volume elements and then regrouping them. This paper proves that [Formula: see text] when molecules’ spatial orientations distribute randomly. The calculations of the refractive indices of several substances validate this equation. This result will help to promote the application of the calculation method of refractive index.

Rapid fabrication of organic/organic photonic bandgap films with robust mechanical properties using blended polymer spheres

Photonic crystals were fabricated using self-assembled polystyrene (PS) submicrospheres with different content of nanospheres with different glass transition temperatures ( Tg: 100 to −54°C) and their opalescent and mechanical properties were investigated. PS spheres (185.4 nm) and nanospheres were prepared by soap-free emulsion polymerization. Nanospheres were prepared using one or two types of monomers, styrene, n-butyl methacrylate, and butyl acrylate with sodium p-styrenesulfonate. Surface morphology, particle size ( Dn), and wavelength ( λ) of photonic crystals were determined from scanning electron microscopy (SEM), effective refractive index equation, and modified Bragg’s law, respectively. The reflection wavelength ( λmax) was measured from ultraviolet-visible spectroscopy. SEM results showed that hard nanospheres were distributed around PS spheres in their photonic crystals. On the other hand, soft nanospheres were coated onto PS spheres in their photonic crystals. With increasing weight fraction of hard or soft nanospheres in the photonic crystals, Dn and λ were increased. The value of λmax corresponded to that of λ. The mechanical property of the photonic crystals was measured by the pencil hardness (PH) test. The result showed that by decreasing the Tg and increasing the weight fraction of nanospheres, PH was increased. The opal film prepared from PS spheres with 20% N-54 nanospheres had the highest PH (H).

Solid–liquid equilibria and the physical properties of binary systems of diphenyl carbonate, dimethyl carbonate, methyl phenyl carbonate, anisole, methanol and phenol

Non-phosgene diphenyl carbonate (DPC) can be synthesized via many routes. A preferable green route of synthesis consists of a two-step reaction from dimethyl carbonate (DMC) and phenol because the direct synthesis of DPC is limited due to the low equilibrium constants of the forward reaction. In this synthesis process, the reaction products with intermediates should be separated from each other for higher yields of DPC and to recycle the reactants. However, relatively few studies have examined the separation design properties, particularly, the phase equilibria and the physical properties for systems containing the reaction intermediate methyl phenyl carbonate (MPC). In the present work, we analytically determined the binary solid–liquid equilibria (SLE) for the {DMC (1)+DPC (2)}, {DPC (1)+MPC (2)}, {phenol (1)+MPC (2)} and {methanol (1)+DPC (2)} systems. The former three systems showed a simple eutectic point, while the {methanol (1)+DPC (2)} system did not. The determined SLE data correlated well with a non-random two-liquid (NRTL) activity coefficient model. In addition, the temperature dependence of the physical properties of the reaction products densities, refractive indices and kinematic viscosities were reported. The experimental properties were correlated well with the Daubert and Danner (DIPPR) equation for density, the linear equation for refractive index, and the Goletz and Tassion equation for kinematic viscosity, respectively.

Equation of state, refractive index and polarizability of compressed water to 7 GPa and 673 K

The equation of state (EoS), refractive index n, and polarizability α of water have been determined up to 673 K and 7 GPa from acoustic velocity measurements conducted in a resistively heated diamond anvil cell using Brillouin scattering spectroscopy. Measured acoustic velocities compare favorably with previous experimental studies but they are lower than velocities calculated from the extrapolation of the IAPWS95 equation of state above 3 GPa at 673 K and deviations increase up to 6% at 7 GPa. Densities calculated from the velocity data were used to propose an empirical EoS suitable in the 0.6-7 GPa and 293-673 K range with a total estimated uncertainty of 0.5% or less. The density model and thermodynamic properties derived from the experimental EoS have been compared to several EoS proposed in the literature. The IAPWS95 EoS provides good agreement, although underestimates density by up to 1.2% at 7 GPa and 673 K and the thermodynamic properties deviate greatly (10%-20%) outside the estimated uncertainties above 4 GPa. The refractive index n of liquid water increases linearly with density and do not depend intrinsically on temperature. The polarizability decreases with pressure by less than 4% within the investigated P-T range, suggesting strong intermolecular interactions in H(2)O that are consistent with the prevalence of the hydrogen bond network in the fluid. The results will allow the refinement of interaction potentials that consider polarization effects for a better understanding of solvent-solvent and ion-solvent interactions in aqueous fluids at high pressure and temperature conditions.

Refractive index of a transparent liquid measured with a concave mirror

This paper describes the spherical concave mirror method for measuring the index of refraction of transparent liquids based on locating the actual and apparent radii of curvature of the mirror. We derived the refractive index equation using Snell’s law and the small-angle approximation.

Temperature-dependent second harmonic generation process based on an MgO-doped periodically poled lithium niobate waveguide

The temperature dependency of a 5-mol% MgO-doped periodically poled lithium niobate waveguide was investigated in this paper. We started with the temperature-dependent refractive index equation for the waveguide. Secondly, the temperature dependency of the second harmonic generation effect was experimentally researched under different temperatures and pump powers. The quasi-phase matched wavelengths, efficiency bandwidths and peak efficiencies of the waveguide were measured. The experimental results agreed with theoretical simulations, which are indispensable in the following all-optical sampling studies based on the cascaded second harmonic generation/difference-frequency generation process in the current device.

Erratum to: Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3

Erratum to: Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3

Equation of state and refractive index of argon at high pressure by confocal microscopy

Using confocal microscopy, we determined the high-pressure equation of state and refractive index of argon at 300 K, in the same experiment. The results show that, within the experimental uncertainty, the polarizability depends only on the density, and not on the phase (fluid or solid).

Padé approximant for refractive index and nonlocal envelope equations

Padé approximation is superior to Taylor expansion when functions contain poles. This is especially important for response functions in complex frequency domain, where singularities are present and intimately related to resonances and absorption. Therefore, we introduce a rational Padé approximant for the complex medium refractive index n ( ω ) . The approximant is calculated using only local information of medium dispersion properties close to a carrier frequency ω 0 . In return it typically offers an accurate global representation of medium dispersion and absorption. Moreover, the fulfillment of the causality principle and the Kramers–Kronig relation can be established. In practice, our results are relevant if n ( ω ) is known only for ω ≃ ω 0 whereas optical field is spectrally broad such that (i) the resonance absorption becomes important and (ii) a traditional polynomial dispersion operator diverges and induces huge errors. As an exemplary application we use the approximant to derive a nonlocal envelope model for ultrashort pulses. The model provides a natural bridge between the commonly used local envelope equations and the most general non-envelope models operating directly with the electric field.

Dependence of Arc Plasma Dispersion Capability on its Temperature

The relationship between the dispersion capability and the temperature of argon arc plasma at 1 atm is deduced in view of the plasma's refractive index equation. The results indicate that argon arc plasma has a normal dispersion and its dispersion capability is nonlinear to the plasma's temperature in a wide range of temperature and wavelength region. According to the results of numerical calculation, the preferred optical methods are believed to be suitable for the diagnosis of argon arc plasma in different temperature regions.

Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3

We present wavelength- and temperature-dependent refractive index equations for 5% MgO-doped congruent PPLN and for 1% MgO-doped stoichiometric PPLN crystals valid for a wide spectral and temperature range. The dispersion equations were derived from quasi-phase-matched nonlinear interactions with these two crystal compositions in the near and mid-infrared. The results show a good agreement with previously published frequency conversion experiments.

Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3

Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3