Normal Incidence Reflectivity Research Articles

Permittivity evaluation of multilayered hyperbolic metamaterials: Ellipsometry vs. reflectometry

Metal-dielectric nanolaminates represent a class of hyperbolic metamaterials with uniaxial permittivity tensor. In this study, we critically compare permittivity extraction of nanolaminate samples using two techniques: polarized reflectometry vs. spectroscopic anisotropic ellipsometry. Both Au/MgF2 and Ag/MgF2 metal-dielectric stacks are examined. We demonstrate the applicability of the treatment of the multilayered material as a uniaxial medium and compare the derived optical parameters to those expected from the effective medium approximation. We also experimentally compare the effect of varying the material outer layer on the homogenization of the composite. Additionally, we introduce a simple empirical method of extracting the epsilon-near-zero point of the nanolaminates from normal incidence reflectance. The results of this study are useful in accurate determination of the hyperbolic material permittivity and in the ability to tune its optical properties.

Preparation and optical characterization of Cu2ZnGeSe4 thin films

Cu2ZnGeSe4 (CZGSe) films have been fabricated by ion beam sputtering onto glass substrates at a substrate temperature of 300 and 420K. CZGSe films were characterized by X-ray diffraction (XRD), energy dispersive X-ray spectroscopy, scanning electron microscopy and by the method of normal incidence transmittance and reflectance. XRD studies reveal an improved crystallinity of the polycrystalline CZGSe films with tetragonal structure when the substrate temperature was increased. The refraction index and extinction coefficient were extracted from the optical measurements. Spectral dependence of the absorption coefficient and the energy band gaps values of CZGSe films were also determined.

Angle of incidence of minimum reflectance of a dielectric-conductor interface for incident unpolarized or circularly polarized light.

The angle of incidence ϕ=ϕu min of minimum reflectance for incident unpolarized or circularly polarized light at a dielectric-conductor interface is determined for any complex relative refractive index N=(n,k), and contours of constant ϕu min in the nk plane are presented. The minimum reflectance Ru min at ϕu min is also plotted as a function of the polar angle 0≤θ=arg(N)≤90° along each constant ϕu min contour. Also presented are families of Ru-versus-ϕ curves for values of complex N at θ=30°, ϕu min=45° to 85° in steps of 10°, and values of complex N at ϕu min=75°, θ=0° to 90° in steps of 10°. Finally, a nonpolarimetric method for the determination of n and k of optical materials, which is based on measurements of ϕu min and the normal-incidence reflectance R0, is proposed.

Normal incidence measurement in a subaqueous sand dune field in the South China Sea.

Regions with subaqueous sand dunes have been discovered on the upper continental slope of the northern South China Sea. These large subaqueous sand dunes are expected to cause errors in the measurement of normal incidence reflection. This letter presents experiment results of two normal incidence survey tracks conducted in 2013, and the errors in reflection coefficient estimation and the resulting sediment properties induced by sand dune bedforms. The results demonstrate that the reflected energy is focused and scattered by different parts of sand dune bedforms and that they produce significant variation in the estimated reflection coefficients and the inverted geoacoustic properties.

Seismic attribute for hydrocarbon expressions in stack section

Stacking process in seismic data processing is a simple and powerful tool commonly used to remove undesired random noise and enhance signal to noise ratio. Basically, the process averages traces from prestack gathers (angles or CDPs) so that they present normal-incidence reflections in stack sections. Experience has showed that hydrocarbons-bearing sediments are generally characterized by anomalous amplitude changes relative to their background from an offset to another. This can result in interesting seismic expressions in the stack section that can help identify reservoirs and delineate their extensions.This paper investigates the conceptual assumptions behind stacking and amplitude variation with offset (AVO). A new attribute is presented and used to detect and extract anomalies associated with hydrocarbon sand reservoirs from their background. The attribute has been examined on real datasets from different fields. The seismic-weighted instantaneous energy attribute showed excellent results in delineating bright spots associated with shallow gas accumulations as well as revealing stratigraphic features of two productive sand-filled channels. Indeed, the paper provides a new insight into seismic stack data analysis and interpretation.

Normal incidence reflection measurements (TREX13): Inferences for lateral heterogeneity over a range of scales

Normal incidence seabed reflection data suffer from a variety of ambiguities that make quantitative interpretation difficult. The reflection coefficient has an inseparable ambiguity between bulk density and compressional sound speed. Even more serious, reflection data are a function of other sediment characteristics including interface roughness, volume heterogeneities, and local bathymetry. Seafloor interface curvature is especially important and can lead to focusing/defocusing of the reflected field. An attempt is made with ancillary data including bathymetry, 400 kHz backscatter, and wide angle seabed reflection data to separate some of the mechanisms. Resulting analysis of 1–12 kHz reflection data suggest: (1) strong lateral sediment heterogeneity exists on scales of 10–100 m; (2) there are distinct geoacoustic regimes on the lee and stoss side of the ridge crest, and also between crest and the swale, and (3) the ridge crest geoacoustic properties are similar across distances of 6 km along two perpendicular transects (1 correlation). [Research supported by ONR Ocean Acoustics.]

Spectroscopic ellipsometry study of Cu2ZnSnSe4 bulk crystals

Using spectroscopic ellipsometry we investigated and analyzed the pseudo-optical constants of Cu2ZnSnSe4 bulk crystals, grown by the Bridgman method, over 0.8–4.5 eV photon energy range. The structures found in the spectra of the complex pseudodielectric functions were associated to E0, E1A, and E1B interband transitions and were analyzed in frame of the Adachi's model. The interband transition parameters such as strength, threshold energy, and broadening were evaluated by using the simulated annealing algorithm. In addition, the pseudo-complex refractive index, extinction coefficient, absorption coefficient, and normal-incidence reflectivity were derived over 0.8–4.5 eV photon energy range.

Optical constants and electronic energy-band structure of AgGaSe2

The complex dielectric-function spectra, ε(E) = ε1(E) + iε2(E), of the AgGaSe2 chalcopyrite semiconductor have been measured by spectroscopic ellipsometry (SE) for light polarizations perpendicular (E ⊥ c) and parallel to the c-axis (E ∥ c) in the 1.6–5.3 eV photon-energy range at room temperature. The measured ε(E) spectra reveal distinct structures of critical points in the Brillouin zone. Analysis of the numerically derived ε(E) spectra facilitates the precise determination of critical-point energies. By performing the band-structure and dielectric-function calculations, these critical points are successfully assigned to specific points in the Brillouin zone. The dielectric-related optical constants of AgGaSe2, such as the complex refractive index n* = n + ik, the absorption coefficient α, and the normal-incidence reflectivity R, are presented.

Multilayer reflectometry and quantitative analysis of higher order diffraction impurities of grating monochromator

Spectral impurity of the beam delivered by a soft X-ray synchrotron beamline is often a problem because higher order components of a grating monochromator cause some error in quantitative measurements. To achieve a correct data analysis, characterization of the higher order diffraction impurities is needed. This paper describes a simple and easy method, where a reflective multilayer is used to pick one out of a series of diffraction orders with the angle of incidence adjusted. The reflectance of the multilayer is first measured at harmonic energies 2E, 3E and 4E at an angle of incidence φn satisfying the Bragg condition in the first order, where E is the fundamental energy. Then, setting sequentially the angle of incidence of the multilayer at φn, reflectance is measured around E, where the measured value is reflectance for the energy nE multiplied by the proportion of the nth order component. Thus, impurity spectrum is obtained. The present method can be generally used for any beamline and any energy. Experiments were performed at BL-11D of the Photon Factory, KEK, at 282eV using a Cr/C multilayer, and the proportion of the first order was found to be 0.915. The normal incidence reflectance of the multilayer was measured, and the intrinsic value for pure 282eV light was estimated to be 20.4% by purity factor correction.

Quantification of signal and noise in two-way transmitted wavefields to improve well ties in Cooper Basin, Australia

Permian coal beds at 2400–2900 m depth in Cooper Basin, Australia have normal-incident reflection coefficient values as large as [Formula: see text]. If internal multiples are included in synthetic seismograms, excellent correlations exist between the synthetic seismogram and seismic, even when more than 50 coal beds are present. However, neither the synthetic seismogram nor the seismic tie the well-log lithologic boundaries because the incident wavefield that strikes a lithologic boundary and returns to the surface contains a signal wavelet followed by high-amplitude noise, which are interbed multiple reflections. Because the spectra of the signal and noise coda at a given two-way time normally do not overlap, time-varying Gaussian filters applied to the near-offset stack enhance the signal and suppress the noise coda. After filtering, the apparent time delay of reflections introduced by the coal beds is removed with variable time shifts (time compression), based on the estimated time-varying signal wavelets. The two-step process of low-pass filtering and compression yields seismic events that successfully tie the lithologic boundaries in the borehole, although with limited resolution. Our preliminary tests on a seismic line indicate that the horizon event associated with the base of a 500-m-thick coal sequence is more coherently imaged with our processing than with conventional processing.

Thermal stability studies of short period Sc/Cr and Sc/B4C/Cr multilayers

The stability of short period Sc/Cr and Sc/B₄C/Cr multilayers was investigated over a large temperature range. The aim was to find a stable reflective coating for an off-axis parabola for focusing x rays from a soft x-ray free-electron laser. Normal incidence reflectivity, surface roughness, and intrinsic stress were investigated as a function of annealing temperature and two samples were also studied with a high-resolution transmission electron microscope (TEM), a scanning TEM, and through electron energy loss spectroscopy (EELS). Interface-engineered Sc/B₄C/Cr multilayers showed increased thermal stability and higher reflectivity as compared to pure Sc/Cr multilayers.

Reflection by absorbing periodically stratified media

Existing theory gives the optical properties of a periodically stratified medium in terms of a two by two matrix. This theory is valid also for absorbing media, because the matrix remains unimodular. The main effect of absorption is that the reflection (of either polarization) becomes independent of the number of periods N, and of the substrate properties, provided N exceeds a certain value which depends on the absorption. The s and p reflections are then given by simple formulae. The stop-band structure, which gives total reflection in bands of frequency and angle of incidence in the non-absorbing case, remains influential in weakly absorbing media, causing strong variations in reflectivity. The theory is applied to the frequency dependence of the normal-incidence reflectivity of a quarter-wave stack in which the high-index and low-index layers both absorb weakly. Analytical expressions are obtained for the frequency at which the reflectivity is maximum, the maximum reflectivity, and also for the reflectivity at the band edges of the stop band of the non-absorbing stack.

Ellipsometric studies of AlxGa1−xAs0.5Sb0.5 (0.0 ≤ x ≤ 0.6) alloys lattice-matched to InP(100)

We report on the optical properties of AlxGa1−xAs0.5Sb0.5 (0.0 ≤ x ≤ 0.6) alloys grown by metal-organic vapor phase epitaxy on InP(100) substrates for InP-based multi-junction photovoltaic device applications. Spectroscopic ellipsometry is used to determine the complex dielectric function ε = ε1 + iε2, complex refractive index N = n + ik, normal-incidence reflectivity R, and absorption coefficients α from 0.73 to 6.45 eV at room temperature. The measured spectra exhibit four above-bandgap critical point (CP) structures E1, E1 + Δ1, E0′, and E2, and the CP energies are accurately obtained from the standard lineshape analysis. The fundamental bandgap E0 CP energies are estimated from the multilayer modeling of ellipsometric data. Dependence of the CP energies on composition x is discussed.

Short period La/B and LaN/B multilayer mirrors for ~68 nm wavelength

In the first part of this article we experimentally show that contrast between the very thin layers of La and B enables close to theoretical reflectance. The reflectivity at 6.8 nm wavelength was measured from La/B multilayer mirrors with period thicknesses ranging from 3.5 to 7.2 nm at the appropriate angle for constructive interference. The difference between the measured reflectance and the reflectance calculated for a perfect multilayer structure decreases with increasing multilayer period. The reflectance of the multilayer with the largest period approaches the theoretical value, showing that the optical contrast between the very thin layers of these structures allows to experimentally access close to theoretical reflectance. In the second part of the article we discuss the structure of La/B and LaN/B multilayers. This set of multilayers is probed by hard X-rays (λ = 0.154 nm) and EUV radiation (λ = 6.8 nm). The structure is reconstructed based on a simultaneous fit of the grazing incidence hard X-ray reflectivity and the EUV reflectivity curves. The reflectivity analysis of the La/B and LaN/B multilayer mirrors shows that the lower reflectance of La/B mirrors compared to LaN/B mirrors can be explained by the presence of 5% of La atoms in the B layer and 63% of B in La layer. After multi-parametrical optimization of the LaN/B system, including the nitridation of La, the highest near normal incidence reflectivity of 57.3% at 6.6 nm wavelength has been measured from a multilayer mirror, containing 175 bi-layers. This is the highest value reported so far.

Optical properties of unprotected and protected sputtered silver films: Surface morphology vs. UV/VIS reflectance

Abstract The optical properties of opaque sputtered silver films are investigated and related to their surface morphology. As reference, an evaporated sample produced by thermal flash evaporation has been studied, too. Standard optical and electrical characterizations as well as scanning electron microscopy (SEM) and X-ray reflectometry have been carried out with unprotected silver films directly after deposition and reveal strong correlations between the corresponding characterization results. The aging behavior of the normal incidence reflectance has been studied over a time period of 36 weeks. Protected silver mirrors have been prepared by sputtering using silica and alumina as the protective coating. It is shown by model calculations that the main spectral features occurring in the reflectance spectra of as-deposited unprotected coatings, unprotected coatings after aging, and protected coatings can be reproduced assuming a rough silver surface covered by a corresponding ultrathin absorbing interface layer or overlayer.

Perfect dielectric-metamaterial reflector

We exploit the Mie resonance in dielectric microparticles to design a single-negative metamaterial monolayer with near-unity reflectivity and negligible absorptivity. In contrast to Bragg reflectors and photonic band gap materials, which require multiple layers for high reflection, this metamaterial is both highly reflective and subwavelength in thickness. We identify the underlying physics necessary to design near-perfect all-dielectric reflectors at virtually any wavelength band of interest. Using full-wave, finite-element analysis and realistic optical constants for the constitutive materials, we develop a 0.45-$\ensuremath{\mu}$m-thick, silicon-based metamaterial monolayer with normal-incidence reflectivity over 99.999% and absorptivity less than 0.001% at a short-wave infrared wavelength of 1.5 $\ensuremath{\mu}$m.

Modeling and analysis of seismic wave dispersion based on the rock physics model

Seismic wave attenuation and dispersion are largely related to the fluid content in reservoirs, which has been verified by rock physics models, numerical modeling and some field case studies. The main mechanism of seismic wave dispersion is wave-induced fluid flow due to the heterogeneity at different scales, including ‘macroscopic’, ‘microscopic’ and ‘mesoscopic’. Recently, studies on dispersion have focused on mesoscopic rock. Previous studies have shown that there are many factors influencing seismic wave dispersion and attenuation, and amongst all the parameters, gas saturation is a very important one. Based on the White model, in this paper we firstly model the seismic wave dispersion and attenuation characteristics with varying gas saturation and porosity, and then analyze the velocity and normal-incidence (NI) reflection coefficient using three sandstone models. The results show that the frequency-dependent reflection coefficient (FDRC) is influenced by gas saturation, which corresponds to the frequency-dependent velocity characteristic. Finally, we derive approximate FDRC expressions using the NI reflection coefficient method, which can be used to estimate the dispersion characteristic. Analysis of the cross-plots of NI and dispersion indicates that dispersion and attenuation are more sensitive to gas saturation and porosity. Therefore, dispersion and NI cross-plots provide a potential way to predict the gas saturation. The modeling results of different consolidated sandstone reservoirs also indicate that there is a critical gas saturation point at which the dispersion magnitude reaches maximum value. Based on the critical point, the cross-plot can be divided into two parts and we can predict the gas saturation in either of them.

The Mohorovičić discontinuity beneath the continental crust: An overview of seismic constraints

Abstract The seismic signature of the Moho from which geologic and tectonic evolution hypotheses are derived is to a large degree a result of the seismic methodology which has been used to obtain the image. Seismic data of different types, passive source (earthquake) broad-band recordings, and controlled source seismic refraction, densely recorded wide-angle deep seismic reflection, and normal incidence reflection (using VibroseisTM, explosives, or airguns), have contributed to the description of the Moho as a relatively complex transition zone. Of critical importance for the quality and resolution of the seismic image are the acquisition parameters, used in the imaging experiments. A variety of signatures have been obtained for the Moho at different scales generally dependent upon bandwidth of the seismic source. This variety prevents the development of a single universally applicable interpretation. In this way source frequency content, and source and sensor spacing determine the vertical and lateral resolution of the images, respectively. In most cases the different seismic probes provide complementary data that gives a fuller picture of the physical structure of the Moho, and its relationship to a petrologic crust–mantle transition. In regional seismic studies carried out using passive source recordings the Moho is a relatively well defined structure with marked lateral continuity. The characteristics of this boundary change depending on the geology and tectonic evolution of the targeted area. Refraction and wide-angle studies suggest the Moho to be often a relatively sharp velocity contrast, whereas the Moho in coincident high quality seismic reflection images is often seen as the abrupt downward decrease in seismic reflectivity. The origin of the Moho and its relation to the crust–mantle boundary is probably better constrained by careful analysis of its internal details, which can be complex and geographically varied. Unlike the oceanic Moho which is formed in a relatively simple, well understood process, the continental Moho can be subject to an extensive variety of tectonic processes, making overarching conclusions about the continental Moho difficult. Speaking very broadly: 1) In orogenic belts still undergoing compression and active continental volcanic arcs, the Moho evolves with the mountain belt, 2) In collapsed Phanerozoic orogenic belts the Moho under the collapse structure was formed during the collapse, often by a combination of processes. 3) In regions having experienced widespread basaltic volcanism, the Moho can result from underplated basalt and basaltic residuum. In Precambrian terranes the Moho may be as ancient as the formation of the crust, in others Precambrian tectonic and magmatic processes have reset it. We note that seismic reflection data in Phanerosoic orogens as well as from Precambrian cratonic terranes often show thrust type structures extending as deep as the Moho, and suggest that even where crust and mantle xenoliths provide similar age of formation dates, the crust may be semi-allochothonous.

Stability and normal incidence reflectivity of W/B4C multilayer mirror near the boron K absorption edge

A multilayer structure consisting of alternate layers of W and B4C has been deposited using a magnetron sputtering system. The structure of the as-deposited and vacuum-annealed W/B4C multilayer sample has been characterized using grazing incidence x-ray reflectivity, grazing incidence diffraction, and the normal incidence reflectivity has been measured using synchrotron radiation. A two-layer model consisting of tungsten and boron carbide is presented. The multilayer structure was found to be stable after 800°C annealing. Grazing incidence x-ray diffraction measurements suggested that W is polycrystalline with small grain size. No signature of tungsten carbide or tungsten boride formation could be observed during the annealing treatments. A near normal incidence soft x-ray reflectivity (SXRR) of ~8.3% was obtained at 6.8 nm wavelength. A little drop (~1%) in SXRR after 800°C annealing suggested that there were no compositional changes within the layers during the annealing treatments.

Quantitative seismic pre-stack analysis of potential gas-hydrate resources in the Makran Accretionary Prism, offshore Iran

Gas hydrates are classified as a major unconventional resource and assumed to be a future potential energy source. High pressures, low temperature stability conditions of the hydrates restrict their occurrence to the permafrost and deep sea regions (from the continental slop to the abyssal). In these regions where the well information is most often absent or sparse, the amplitude-variation-with-angle (AVA) is a common method of hydrate/free gas assessment. In this method, various linear reflection coefficient equations are fitted to a series of data points to compute some pre-stack attributes. These attributes have the advantage of being an interface property rather than a layer property which makes them an easy to use characterization tool in lack of well data. In recent years, rock physics templates (nomograms) have been presented to estimate the hydrate/free gas saturations solely based on these interface properties. AVA inversion approach was applied to the seismic data in the Makran Accretionary Prism, offshore Iran, to estimate the bottom simulating reflector (BSR)-vicinity hydrate and gas saturations. This inversion process included four pre-stack attributes of the intercept, gradient, normal incidence (NI) and Poisson reflectivity (PR) and was limited to the BSR. Estimated BSR-vicinity saturations were ranged from 7%–8.5% for hydrate and 5%–6.5% for free gas at three representative locations. Accuracy of each attribute was analyzed by a synthetic modeling. In this modeling, the effective medium theory (EMT) was considered to calculate the physical properties of hydrate and gas-bearing sediments. Lithological properties and the acquisition geometry were set to the corresponding values of the field data. Results of the synthetic AVA inversion showed that if the hydrate saturation does not exceed 30%, the error of the estimation for pre-stack attributes would be in acceptable range. The expected estimation errors for actual attributes were derived from this synthetic modeling.