Determination of the refractive index of n- and p-type porous Si samples

Photochemical etching of porous Si layers has been shown to be able to create micrometer or submicrometer-scale lateral gratings very promising for photonic applications. However, the reduced size of this lateral periodicity hinders standard measurements of refractive index variations. Therefore accurate characterizations of such gratings are usually difficult. In this paper we address this problem by reproducing on a larger scale (millimeter) the micrometer scale light-induced refractive index variations associated to the lateral periodicity. Using this procedure we perform standard X-ray and optical reflectivity measurements on our samples. One can then proceed to the determination of light-induced variations of porosity and refractive index. We present results for p-type samples, where the photo-dissolution can only be realized after the formation of the porous layer, as well as for n⁺-type samples, where light action can only be effective during the formation of the porous layer.     

折光率法测定四氢呋喃溶液的组成

应用阿贝折射仪测量THF(四氢呋喃)溶液的折光率,以此确定THF溶液的组成。实验研究表明,测试数据与文献值吻合良好;THF与水、乙醇及甲醇的两组分溶液折光率与组成之间有很好的规律性,前者可以用抛物线关系式描述,后两者可以用线性关系式描述,其相关系数R在0.99以上,标准偏差SD在0.0015以下,完全适合用于相关溶液组成的测定。     

Determination of refractive index increments of PMMA particles dispersed in liquid phase

The refractive index increments of poly(methyl methacrylate) (PMMA) particles with sizes ranging from submicron to several microns were determined by measuring different concentrations of the solution and using a refractometer and microbalance calibrated by accurate traceability source. Conventionally, it was common to measure only the difference in refractive index between solvent and solution using a Bryce-type cell system, but it is difficult to perform traceable calibration since there is no reference material for refractive index increment. In this paper, we accurately quantify the refractive index increment by making individual measurements of the solvent and solution refractive indices, respectively, using Abbe-type refractometer. In addition, an uncertainty analysis was performed, and the results clarified the main factor of the variance in the refractive index increment measurements. The most important factor of variation of refractive index increment measurement is the measured apparent values at dilute concentration region including fluctuation of the system. This method was able to be applied to the determination of water content existing in particles. The percentage of the water content was determined using two different solvents, and the water content values were in good agreement within their uncertainties.     

Electro-optic properties of c-axis oriented LiNbO3 films grown on Si(1 0 0) substrate

We developed a spectroscopic–ellipsometric approach to evaluate the electro-optic coefficient of highly c-axis oriented LiNbO₃ films on an Si(1 0 0) substrate grown by electron cyclotron resonance plasma sputtering. Applying an electric field between the TiN transparent top electrode and Si substrate, the interference fringe appearing in the tan Ψ spectrum was slightly modulated by phase retardation in the wavelength domain. The change in effective wavelength was converted to refractive index change, yielding dispersion in the Pockels coefficient (r₃₃) between 0.3 and 0.8 μm. At 633 nm, we obtained an r₃₃ that was 57% of the bulk LN crystal value.     

The structure and optical dispersion of the refractive index of tellurite glass

The structure and optical properties of a 80TeO₂-(20−x)Li₂O-xTiO₂ glass system where x = 0, 5, 10, and 15 mol% has been investigated using FTIR spectroscopy and Brewster angle measurements. The sample preparation, linear refractive index and density measurements, and infrared spectroscopic analysis are described. The refractive index and density of the studied tellurite glass samples increase when the amount of Ti in the glass is increased. The dispersion of the phase refractive index was analyzed using Wemple’s model. The dispersion energy E_d is significantly affected by the addition of Ti to TeO₂-based glass. The analysis of FTIR spectra indicate a Te coordination change that is in agreement with the increase of the Te coordination number determined from dispersion data using Wemple’s equation.     

Model for calculating the refractive index of a III–V semiconductor

An empirical relationship modeled by a theoretical numerical model has been presented for estimating the refractive indices of semiconductors, especially the III–V semiconductors, relative to their energy gaps.

This model is based on the fact that there is a strong correlation between the energy gap and the refractive index of a given material. This physical relationship remains strictly intrinsic and specific to the material considered.

The performance of this model is compared with that of some other numerical models established by other authors. An analysis based on calculations of the errors between this model and the experimental data has also been carried out.

For the first time, the present model is applicable to the whole range of energy gaps, taking into account the fact that the refractive index for an infinite energy gap is equal to one.

Good agreement is observed between the computed values and the refractive indices reported in the literature for well-known semiconductors.     

Optical properties of BaTiO3/ZnO heterostructures under the effect of an applied bias

We report electro-optical measurements of BaTiO₃/ZnO heterostructures grown by pulsed laser deposition. The optical properties of the heterostructures were examined with and without an applied bias. A change in the heterostructure optical properties is found and attributed to a linear electro-optical effect causing a change in the band gap. Moreover the formation of an electric polarization in the BaTiO₃ layer causes a remanent change in the dielectric function if the bias is removed. The change could be estimated to be around 5 meV.     

Origin of crystallization-induced refractive index changes in photo-thermo-refractive glass

Photo-thermo-refractive (PTR) glass is a multi-component silicate that undergoes localized refractive index decrease after UV-exposure and thermal treatment for partial crystallization. Based on this refractive index change, high efficiency volume Bragg gratings have been developed in PTR glass and have been successfully used for laser beam control. However, despite the fact that this type of glass has been widely studied and used over the last 20 years, the origin of the refractive index change upon crystallization is poorly understood. In this paper, we introduce three possible mechanisms (the precipitation of nano-sized NaF crystals and the associated local chemical changes of the glass matrix, the volumetric changes due to relaxation, and the local residual stresses) for the refractive index decrement in PTR glass and estimate the partial refractive index change due to each mechanism. Refractive index measurements are compared with high temperature XRD experiments and a general approach for the simulation of the refractive index change in PTR glass is proposed. We show that among the studied variables the residual stresses surrounding the crystals are the main responsible for the local refractive index decrement in this glass.     

High refractive index and good mechanical property UV-cured hybrid films containing zirconia nanoparticles

UV-curable zirconia (ZrO₂) nanoparticle coatings, prepared by dispersing highly-crystalline zirconia nanoparticles (4 nm) in tetrahydrofuran with the aid of 3-glycidoxypropyltrimethoxysilane (GPTMS) and following addition of a cationic photoinitiator, were cast on silicon wafers (or glass substrates) by dip-coating or spin-coating and photopolymerized to get transparent ZrO₂ nanoparticle films. Ellipsometrical characterization indicates that the refractive index of the film changes from 1.63 to 1.77 at wavelength of 632 nm when the molar ratio of GPTMS-to-ZrO₂ decreases from 0.30 to 0.15. Nano-indentation tests show that the films exhibit robust mechanical performance though they are not heat-treated.     

Understanding the mechanism of refractive index modulation in materials undergoing photo-Fries rearrangement

Molecules and polymers that undergo a photo-Fries rearrangement are studied by using DFT calculation in order to predict the refractive index modulation which accompanies this light induced process. In particular, monomeric units of polystyrene derivatives (such as poly(p-formyloxystyrene) and poly(4-acetoxystyrene)) are considered and the refractive index calculated starting from the molecular polarizability and following the Lorentz–Lorenz approach. The results demonstrate that the conversion of ester groups to ketone/alcohol provides just a small modulation of the refractive index that does not fit the experimental results reported in the literature. A change in material density is therefore considered as main source of the modulation of the refractive index. Theoretical and experimental evidences are reported to support the picture.     

New Er-doped phosphate glass for ion-exchange active waveguides: accurate determination of the refractive index

The optical properties of a new Er-doped glass for ion-exchange active waveguides have been characterized, including fluorescence lifetime, Ag–Na diffusion coefficient, and refractive index. In particular, the Sellmeier curve was determined from the visible to the near infrared by means of a non-conventional method based on the measurement of the output angle of radiation modes propagating within the substrate. An accuracy of about 1×10⁻⁴ for the determination of the refractive index is obtained.     

Temperature dependence of the band gap, refractive index and single-oscillator parameters of amorphous indium selenide thin films

InSe thin films are obtained by evaporating InSe crystal onto ultrasonically cleaned glass substrates under pressure of 10⁻⁵ Torr. The structural and compositional analysis revealed that these films are of amorphous nature and are atomically composed of 51% In and 49% Se. The reflectance and transmittance of the films are measured at various temperatures (300–450 K) in the incident photon energy range of 1.1–2.1 eV. The direct allowed transitions band gap – calculated at various temperatures – show a linear dependence on temperature. The absolute zero value band gap and the rate of change of the band gap with temperature are found to be (1.62 ± 0.01) eV and −(4.27 ± 0.02) × 10⁻⁴ eV/K, respectively. The room temperature refractive index is estimated from the transmittance spectrum. The later analysis allowed the identification of the static refractive index, static dielectric constant, oscillator strength and oscillator energy.     

Comparison of different dispersion models for single layer optical thin film index determination

We here determine the optical properties of different single-layer thin films containing Ta₂O₅, Si, Indium Tin Oxide and Au in the ultraviolet-visible and near infrared ranges. More specifically, we deduce the complex refractive index and thickness from the reflectance and transmittance measured using a spectrophotometer at normal incidence. One major difficulty is to find an appropriate selection of dispersion laws for various types of material (dielectric, semiconductors, and metals). For this purpose, a number of models have been investigated from a theoretical point of view in consideration of the Kramers-Kronig relation. These include the Forouhi-Bloomer model, combined with the modified Drude, Tauc-Lorentz and multiple-oscillator Tauc-Lorentz models. A global optimization procedure had to be employed because of the large number of parameters (from 3 to 15) required to describe the optical dispersion laws. The calculated reflectance and transmittance are in good agreement with experimental data and the complex refractive index is consistent with our knowledge and that already reported.     

Temperature dependent model dielectric function of highly disordered Ga0.52In0.48P

We report on the temperature dependence of the dielectric function of Ga_0.52In_0.48P from room temperature to 500°C, and for photon energies from 0.75 eV to 5 eV. The undoped, highly disordered Ga_0.52In_0.48P thin film was grown by metal-organic vapor phase epitaxy lattice matched onto a (001) GaAs substrate. The dielectric function of Ga_0.52In_0.48P was measured by in-situ spectroscopic ellipsometry, and analyzed using Adachi's composite critical point model. We provide a second-order temperature expansion parameter set for calculation of the Ga_0.52In_0.48P dielectric function and its temperature dependence, and which may become useful for in situ growth control or optoelectronic device performance evaluation at elevated temperatures. We discuss the temperature-induced shift of critical point transition energy parameters.     

Phase-modulated ellipsometry for probing the temperature-induced phase transition in ruthenium-doped lead zinc niobate-lead titanate single crystal

Phase-modulated ellipsometry was applied to measure changes in the refractive index of pure and ruthenium (Ru)-doped 0.9Pb (Zn_1/3Nb_2/3)O₃ (PZN)-0.1PbTiO₃ (PT) during the heating process in real time. Both samples were heated from room temperature to 200 °C in a thermally insulated chamber. In both samples, the phase transitions were observed to change from tetragonal to cubic. The temperature region at which the phase transition (Curie region) of Ru-doped 0.9PZN-0.1PT occurred not only broadened but also shifted to a lower temperature. The refractive indices were extremely stable in this region, meaning that Ru-doped 0.9PZN-0.1PT is a more favorable medium for the fabrication of optical memories.     

Refractive index measurement of cerium-doped LuxY2−xSiO5 single crystal

Principal refractive indices of the biaxial cerium-doped Lu_xY_2−xSiO₅ (LYSO) crystal were determined with high accuracy at seven different wavelengths between 400 and 700 nm using the classical minimum angle of deviation method. The reliability of the measured data permitted to deduce parameters of a common dispersion formula, by which the refractive indices can be extrapolated for wavelengths up to 1100 nm, an important range for laser applications. The extent of axial dispersion was precisely measured by ellipsometry, its effects on the anisotropic refractive index has been calculated. Examples are given to demonstrate the influence of anisotropy on the operation of optical devices.     

Extraction of complex refractive index of absorbing films from ellipsometry measurement

Numerical extraction of complex refractive index of an unknown absorbing layer inside a multilayer sample from ellipsometry measurement is discussed. The approach of point by point extraction considering all points of spectroscopic data as independent data points is investigated. This problem has typically multiple solutions and the standard method consisting in fitting calculated to experimental point is likely to converge to a wrong solution if a precise guess value is not given. An alternate method is proposed, based on the determination of contours of the ellipsometric function, to provide all solutions in an as extended as wanted range of complex refractive index values. The method is tested through different kinds of sample examples. Errors relative to any of the parameters used in the sample model are calculated and discussed. This method should be helpful in many practical cases of ellipsometry data interpretation.     

Behavior of the refractive index of lithium disilicate glass ceramic processed at high pressure and high temperature

The aim of this work was to investigate the effect of high pressure and high temperature on the refractive index of lithium disilicate glass ceramic with the stoichiometric composition Li₂O·2SiO₂ (LS₂). A first group of monolithic LS₂ glass samples were processed at 2.5 GPa, 4 GPa and 7.7 GPa at room temperature and a second group was submitted to high pressure and, simultaneously, to heat treatments for nucleation and growth of the crystalline phases. For comparison, samples submitted to the same heat treatments at 1 atm were also investigated. The refractive index of the samples was obtained by spectral ellipsometry and the results were clearly dependent on the particular pressure and temperature conditions. The crystallization of the samples was investigated by X-ray diffraction. For the samples processed under high temperature at 1 atm and at 2.5 GPa a fraction of the originally amorphous glass was transformed to a monoclinic phase of lithium disilicate. For the samples processed under high temperature and at 4 GPa, a large fraction of the originally amorphous glass transformed to an orthorhombic phase while, at 7.7 GPa, it was observed the formation of lithium metasilicate.     

Influence of gamma irradiation on the refractive index of Fe-doped barium titanate thin films

Polycrystalline Fe-doped barium titanate (Fe-doped BaTiO₃) thin films were grown by thermal decomposition of the precursors deposited from a sol-gel system onto quartz substrates. The changes in the transmittance spectra induced by gamma irradiation on the Fe-doped BaTiO₃ thin films were quantified. The values for the optical energy band gap were in the range of 3.42-3.95 eV depending on the annealing time. The refractive index of the film, as measured in the 350-750 nm wavelength range was in the 2.17-1.88 range for the as prepared film, and this increased to 2.34-1.95 after gamma irradiation at 15 kGy. The extinction coefficient of the film was in the order of 10⁻² and increased after gamma irradiation. We obtained tuneable complex refractive index of the films by exposure to various gamma rays doses.     

Measurement of the refractive index and thickness of a transparent film from the shift of the interference pattern due to the sample rotation

A method is described for the simultaneous measurement of the refractive index and thickness of a transparent film. The method is based on the rotational shift of the interference pattern caused by the change of the light incidence angle. The refractive index is evaluated without any prior information about film thickness or about the substrate and its refractive index. In addition, the roughness of the interfaces and/or the presence of an unidentified thin layer are not important. In two experimental examples, the refractive index and thickness are measured for a GaN thin film and a cling-film.