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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Effective propagation constants in dense random media under effective medium approximation

The effective medium approximation is applied to study the effective propagation constants in a dense random medium. The dyadic Green's function is introduced to establish the effective medium approximation formalism for electromagnetic waves. The multiple scattering equations and the Lippmann-Schwinger equations for the transition operator are obtained in the configuration average form. The dispersion equations of multiple scattering is derived by using a standard method in quantum mechanics. To obtain an expression for the effective propagation constants the matrix elements of the configuration average dyadic transiton operator are calculated in momentum representation. Numerical illustations are carried out to demonstrate the difference in the effective propagation constants between the use of this approximation and the well-known quasi-crystalline approximation. A comparison is made with measured loss tangent in dry snow.

Zhu, P. Y.↗
NASA NTRS1986

Effective medium approximation for effective propagation constant calculation in a dense random medium

The effective medium approximation (EMA) formalism developed for scalar wave calculations in solid state physics is generalized to electromagnetic wave scattering in a dense random medium. Results are applied to compute the effective propagation constant in a dense medium involving discrete spherical scatterers. When compared with a common quasicrystalline approximation (QCA), it is found that EMA accounts for backward scattering and the effect of correlation among three scatterers which are not available in QCA. It is also found that there is not much difference in the calculated normalized phase velocity between the use of these two approximations. However, there is a significant difference in the computed effective loss tangent in a nonabsorptive random medium. The computed effective loss tangent using EMA and measurements from a snow medium are compared, showing good agreement.

Zhu, P. Y.↗
NASA NTRS2016

Applicability of the Effective-Medium Approximation to Heterogeneous Aerosol Particles.

The effective-medium approximation (EMA) is based on the assumption that a heterogeneous particle can have a homogeneous counterpart possessing similar scattering and absorption properties. We analyze the numerical accuracy of the EMA by comparing superposition T-matrix computations for spherical aerosol particles filled with numerous randomly distributed small inclusions and Lorenz-Mie computations based on the Maxwell-Garnett mixing rule. We verify numerically that the EMA can indeed be realized for inclusion size parameters smaller than a threshold value. The threshold size parameter depends on the refractive-index contrast between the host and inclusion materials and quite often does not exceed several tenths, especially in calculations of the scattering matrix and the absorption cross section. As the inclusion size parameter approaches the threshold value, the scattering-matrix errors of the EMA start to grow with increasing the host size parameter and or the number of inclusions. We confirm, in particular, the existence of the effective-medium regime in the important case of dust aerosols with hematite or air-bubble inclusions, but then the large refractive-index contrast necessitates inclusion size parameters of the order of a few tenths. Irrespective of the highly restricted conditions of applicability of the EMA, our results provide further evidence that the effective-medium regime must be a direct corollary of the macroscopic Maxwell equations under specific assumptions.

aerosols↗
NASA NTRS2014

Direct Demonstration of the Concept of Unrestricted Effective-Medium Approximation

The modified unrestricted effective-medium refractive index is defined as one that yields accurate values of a representative set of far-field scattering characteristics (including the scattering matrix) for an object made of randomly heterogeneous materials. We validate the concept of the modified unrestricted effective-medium refractive index by comparing numerically exact superposition T-matrix results for a spherical host randomly filled with a large number of identical small inclusions and Lorenz-Mie results for a homogeneous spherical counterpart. A remarkable quantitative agreement between the superposition T-matrix and Lorenz-Mie scattering matrices over the entire range of scattering angles demonstrates unequivocally that the modified unrestricted effective-medium refractive index is a sound (albeit still phenomenological) concept provided that the size parameter of the inclusions is sufficiently small and their number is sufficiently large. Furthermore, it appears that in cases when the concept of the modified unrestricted effective-medium refractive index works, its actual value is close to that predicted by the Maxwell-Garnett mixing rule.

Scattering↗
NASA NTRS1993

Review of rigorous coupled-wave analysis and of homogeneous effective medium approximations for high spatial-frequency surface-relief gratings

A review of the rigorous coupled-wave analysis as applied to the diffraction of electro-magnetic waves by gratings is presented. The analysis is valid for any polarization, angle of incidence, and conical diffraction. Cascaded and/or multiplexed gratings as well as material anisotropy can be incorporated under the same formalism. Small period rectangular groove gratings can also be modeled using approximately equivalent uniaxial homogeneous layers (effective media). The ordinary and extraordinary refractive indices of these layers depend on the gratings filling factor, the refractive indices of the substrate and superstrate, and the ratio of the freespace wavelength to grating period. Comparisons of the homogeneous effective medium approximations with the rigorous coupled-wave analysis are presented. Antireflection designs (single-layer or multilayer) using the effective medium models are presented and compared. These ultra-short period antireflection gratings can also be used to produce soft x-rays. Comparisons of the rigorous coupled-wave analysis with experimental results on soft x-ray generation by gratings are also included.

Glytsis, Elias N.↗
NASA NTRS1991

Scattering of electromagnetic waves from a half-space of randomly distributed discrete scatterers and polarized backscattering ratio law

The effective-medium approximation is applied to investigate scattering from a half-space of randomly and densely distributed discrete scatterers. Starting from vector wave equations, an approximation, called effective-medium Born approximation, a particular way, treating Green's functions, and special coordinates, of which the origin is set at the field point, are used to calculate the bistatic- and back-scatterings. An analytic solution of backscattering with closed form is obtained and it shows a depolarization effect. The theoretical results are in good agreement with the experimental measurements in the cases of snow, multi- and first-year sea-ice. The root product ratio of polarization to depolarization in backscattering is equal to 8; this result constitutes a law about polarized scattering phenomena in the nature.

Zhu, P. Y.↗
NASA NTRS2007

Aerosol Absorption and Radiative Forcing

We present a comprehensive examination of aerosol absorption with a focus on evaluating the sensitivity of the global distribution of aerosol absorption to key uncertainties in the process representation. For this purpose we extended the comprehensive aerosol-climate model ECHAM5-HAM by effective medium approximations for the calculation of aerosol effective refractive indices, updated black carbon refractive indices, new cloud radiative properties considering the effect of aerosol inclusions, as well as by modules for the calculation of long-wave aerosol radiative properties and instantaneous aerosol forcing. The evaluation of the simulated aerosol absorption optical depth with the AERONET sun-photometer network shows a good agreement in the large scale global patterns. On a regional basis it becomes evident that the update of the BC refractive indices to Bond and Bergstrom (2006) significantly improves the previous underestimation of the aerosol absorption optical depth. In the global annual-mean, absorption acts to reduce the shortwave anthropogenic aerosol top-of-atmosphere (TOA) radiative forcing clear-sky from -0.79 to -0.53 W m(sup -2) (33%) and all-sky from -0.47 to -0.13W m(sup -2 (72%). Our results confirm that basic assumptions about the BC refractive index play a key role for aerosol absorption and radiative forcing. The effect of the usage of more accurate effective medium approximations is comparably small. We demonstrate that the diversity in the AeroCom land-surface albedo fields contributes to the uncertainty in the simulated anthropogenic aerosol radiative forcings: the usage of an upper versus lower bound of the AeroCom land albedos introduces a global annual-mean TOA forcing range of 0.19W m(sup -2) (36%) clear-sky and of 0.12W m(sup -2) (92%) all-sky. The consideration of black carbon inclusions on cloud radiative properties results in a small global annual-mean all-sky absorption of 0.05W m(sup -2) and a positive TOA forcing perturbation of 0.02W m(sup -2). The long-wave aerosol radiative effects are small for anthropogenic aerosols but become of relevance for the larger natural dust and sea-salt aerosols.

Stier, Philip↗
NASA NTRS2016

Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

cloud droplets↗
NASA NTRS2021

Validation of the aerosol optical property products derived by the GRASP/Component approach from multi-angular polarimetric observations

The multi-angle polarimetric satellite observations are helpful for improving the retrievals of aerosol parameters. However, practical applications of polarization technology are still limited because of complexity of measurement and interpretation of polarimetric observations. In this study, we analyze the performance of a new component approach developed in the frame of the Generalized Retrieval of Atmosphere and Surface Properties (GRASP) algorithm. In addition to aerosol optical properties including particle size distribution, non-sphericity and index of refraction that are commonly derived from multi-angle radiance and polarization measurements, the GRASP/Component approach also provides some information about aerosol composition. Specifically, in this approach aerosol is modeled as an internal mixture of several components with distinctly different chemical compositions and known refractive indices. The approach is intended not only to provide additional insight on aerosol composition but also to improve retrieval of basic aerosol optical properties. This study presents comprehensive validation and evaluation of Aerosol Optical Depth (AOD), Ångstrom exponent (AE), fine mode AOD (AODF), coarse mode AOD (AODC), and single scattering albedo (SSA) as retrieved by the GRASP/Component approach. The GRASP/Component products include aerosol retrievals using two different aerosol component mixing rules, i.e., Maxwell-Garnett (MG) effective medium approximation and a simple Volume- Weighted averaging (VW). The differences between the results obtained using these two assumptions are also discussed. The obtained results show that the aerosol optical property products of GRASP/Component approach have good agreement with the ground-based AERONET measurements, which is comparable to other PARASOL/ GRASP approaches. Specifically, the AOD retrieved by GRASP/Component approach show high correlation and nearly no bias both over land and ocean, as compared with AERONET. The more detailed aerosol properties such as AE, AODF, AODC and SSA also show one of the best comparisons with AERONET. These improvements can probably be attributed to the use of the additional physical constraints on spectral dependence of the complex refractive index and the reduction of total number of aerosol parameters directly retrieved in the GRASP/Component approach. In addition, the choice of mixing rules had no significant effect on optical retrievals. With the exception of SSA, the results obtained based on the MG mixing rule were found to be slightly better over those obtained using VW mixing rule, especially for bias.

Brent N Holben↗
NASA NTRS1990

Thin film characterization using spectroscopic ellipsometry

The application of the multiple angle and wavelength (MAW) technique to measure the dielectric function of semiconducting films is discussed. This technique evaluates unambiguously the complex dielectric function, epsilon (E), of the film without any pre-assumptions. In some cases the effective medium approximation (EMA) was used to determine the volume fraction of the film components. Application of the MAW technique to several semiconducting films was published previously. Different applications and examples are given, including metal and insulator films.

Alterovitz, Samuel A.↗
NASA NTRS1990

Ellipsometric study of cubic SiC

Variable angle spectroscopic ellipsometry (VASE) was applied to cubic SiC. This technique gives absolute values of the refractive index (n) and the extinction coefficient (k) of a substrate and/or a thin film of unknown material. The samples were grown by chemical vapor deposition (CVD) on p-type silicon. The substrate was aligned either on the (001) axis or 1 degree of (001). Several growth temperatures and growth durations were used. The samples were divided into two groups: (1) thick films of order 10 microns grown near optimal conditions of temperature, flow, and gas ratio; and (2) thin films of order 100 A grown at various temperatures. The ellipsometric results for samples in group 1 were analyzed using a two-phase model (substrate and ambient). Results show that for wavelengths in the visible, the refractive index of these CVD samples is equal to that reported for single crystal cubic SiC, within the experimental error, which is on the order of 1 percent. However, the extinction coefficient has a relatively large value, even above the band gap. The absorption is sample dependent and has a broad peak in the visible. The results for samples in group 2 were analyzed using a three-phase model (substrate, film, and ambient). The dielectric functions of the film, deducted from the measured n and k, were further analyzed using the effective medium approximation. The results show that the films contain 30 to 40 vol. percent amorphous silicon, i.e., silicon with only short-range order.

Alterovitz, Samuel A.↗
NASA NTRS1992

Ellipsometric study of oxide films formed on LDEF metal samples

The optical constants of samples of six different metals (Al, Cu, Ni, Ta, W, and Zr) exposed to space on the Long Duration Exposure Facility (LDEF) were studied by variable angle spectroscopic ellipsometry. Measurements were also carried out on portions of each sample which were shielded from direct exposure by a metal bar. A least-squares fit of the data using an effective medium approximation was then carried out, with thickness and composition of surface films formed on the metal substrates as variable parameters. The analysis revealed that exposed portions of the Cu, Ni, Ta, and Zr samples are covered with porous oxide films ranging in thickness from 500 to 1000 A. The 410 A thick film of Al2O3 on the exposed Al sample is practically free of voids. Except for Cu, the shielded portions of these metals are covered by thin non-porous oxide films characteristic of exposure to air. The shielded part of the Cu sample has a much thicker porous coating of Cu2O. The tungsten data could not be analyzed.

Franzen, W.↗
NASA NTRS1992

Thermal oxidation of single-crystal silicon carbide - Kinetic, electrical, and chemical studies

This paper presents kinetic data from oxidation studies of the polar faces for 3C and 6H SiC in wet and dry oxidizing ambients. Values for the linear and parabolic rate constants were obtained, as well as preliminary results for the activation energies of the rate constants. Examples are presented describing how thermal oxidation can be used to map polytypes and characterize defects in epitaxial layers grown on low tilt angle 6H SiC substrates. Interface widths were measured using Auger electron spectroscopy (AES) with Ar ion beam depth profiling and variable angle spectroscopic ellipsometry (VASE) with effective medium approximation (EMA) models. Preliminary electrical measurements of MOS capacitors are also presented.

Petit, J. B.↗
NASA NTRS2006

Molecular Substrate Alteration by Solar Wind Radiation Documented on Flown Genesis Mission Array Materials

The Genesis spacecraft sampling arrays were exposed to various regimes of solar wind during flight that included: 313.01 days of high-speed wind from coronal holes, 335.19 days of low-speed inter-stream wind, 191.79 days of coronal mass ejections, and 852.83 days of bulk solar wind at Lagrange 1 orbit. Ellipsometry measurements taken at NASA s Johnson Space Center show that all nine flown array materials from the four Genesis regimes have been altered by solar wind exposure during flight. These measurements show significant changes in the optical constant for all nine ultra-pure materials that flew on Genesis when compared with their non-flight material standard. This change in the optical constant (n and k) of the material suggests that the molecular structure of the all nine ultra-pure materials have been altered by solar radiation. In addition, 50 samples of float-zone and czochralski silicon bulk array ellipsometry results were modeled with an effective medium approximation layer (EMA substrate layer) revealing a solar radiation molecular damage zone depth below the SiO2 native oxide layer ranging from 392 to 613 . This bulk solar wind radiation penetration depth is comparable to the depth of solar wind implantation depth of Mg measured by SIMS and SARISA.

Calaway, Michael J.↗
NASA NTRS2014

Optics of Water Cloud Droplets Mixed with Black-Carbon Aerosols

We use the recently extended superposition T-matrix method to calculate scattering and absorption properties of micrometer-sized water droplets contaminated by black carbon. Our numerically exact results reveal that, depending on the mode of soot-water mixing, the soot specific absorption can vary by a factor exceeding 6.5. The specific absorption is maximized when the soot material is quasi-uniformly distributed throughout the droplet interior in the form of numerous small monomers. The range of mixing scenarios captured by our computations implies a wide range of remote sensing and radiation budget implications of the presence of black carbon in liquid-water clouds. We show that the popular Maxwell-Garnett effective-medium approximation can be used to calculate the optical cross sections, single-scattering albedo, and asymmetry parameter for the quasi-uniform mixing scenario, but is likely to fail in application to other mixing scenarios and in computations of the elements of the scattering matrix.

soot↗
NASA NTRS2017

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Dlugach, Janna M.↗
NASA NTRS2022

Inferring iron-oxide species content in atmospheric mineral dust from DSCOVR EPIC observations

The iron-oxide content of dust in the atmosphere and most notably its apportionment between hematite (α-Fe2O3) and goethite (α-FeOOH) are key determinants in quantifying dust’s light absorption, its top of atmosphere UV radiances used for dust monitoring, and ultimately shortwave dust direct radiative effects (DRE). Hematite and goethite column mass concentrations and iron-oxide mass fractions of total dust mass concentration were retrieved from the DeepSpace Climate Observatory (DSCOVR) Earth Polychromatic Imaging Camera (EPIC) measurements in the ultraviolet–visible (UV–Vis) channels. The retrievals were performed for dust-identified aerosol plumes over land using aerosol optical depth (AOD) and spectral imaginary refractive index provided by the Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm over six continental regions (North America, North Africa, West Asia, Central Asia, EastAsia, and Australia). The dust particles are represented as an internal mixture of non-absorbing host and absorbing hematite and goethite. We use the Maxwell–Garnett effective medium approximation with carefully selected complex refractive indices of hematite and goethite that produce mass fractions of iron oxides species consistent with in situ values found in the literature to derive the hematite and goethite volumetric/mass concentrations from MAIAC EPIC products. We compared the retrieved hematite and goethite concentrations with in situ dust aerosol mineralogical content measurements, as well as with published data. Our data display variations within the published range of hematite, goethite, and iron-oxide mass fractions for pure mineral dust cases. A specific analysis is presented for 15 sites over the main dust source regions. Sites in the central Sahara, Sahel, and Middle East exhibit a greater temporal variability of iron oxides relative to other sites. Niger site(13.52°N, 2.63°E) is dominated by goethite over Harmattan season with median of ~2 weight percentage (wt.%) of iron-oxide. Saudi Arabia site (27.49°N, 41.98°E) over Middle East also exhibited surge of goethite content with the beginning of Shamal season. The Sahel dust is richer in iron-oxide than Saharan and northern China dust except in Summer. The Bodélé Depression area shows a distinctively lower iron-oxide concentration (~1 wt.%) throughout the year. Finally, we show that EPIC data allow to constrain the hematite refractive index. Specifically, we select 5 out of 13 different number of hematite refractive indices widely variable in published laboratory studies by constraining the iron-oxide mass ratio to the known measured values. Provided climatology of hematite and goethite mass fractions across main dust regions of the Earth will be useful for dust shortwave DRE studies and climate modeling.

Sujung Go↗
NASA NTRS2012

High Absorptance Coatings for THz Applications

High absorptance materials find application throughout the electromagnetic spectrum as radiation terminations, calibration standards, and glint reduction coatings. Successful use of materials at millimeter through submillimeter wavelengths requires an accurate knowledge and control over their thermal, mechanical, and electromagnetic properties in order to achieve the desired response while minimizing mass and volume. In practice, the achieved blackness is intimately linked to the material properties and geometry. Here, we summarize the characteristics of a variety of tunable artificial dielectric mixtures appropriate for THz applications at room and cryogenic temperatures. Theoretical guidelines for their application will be provided in the context of the effective-medium mean-field-approximation. The performance of these coatings as elements of reflectance standards, radiometric flux calibrators, passive thermal radiators, and stray light suppression baffles for imaging systems will be reviewed.

Wollack, Edward J.↗