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NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗

NASA NTRS1993

Conductivity As A Measure Of Degree Of Polymerization

In improved method of dielectric monitoring of process of polymerization of mixed ingredients of polymeric material, emphasis placed on measurement of conductivity rather than permittivity. Conductivity tends to change more during curing process than permittivity does, is less dependent on frequency, and more-sensitive and more-reliable indicator of progress of cure. Conductivity used to compute quantity called "ion viscosity," which relates to classical viscosity of fluid. During cure of typical polymer, ion viscosity varies over wide range, eventually rising to plateau toward end of cure.

Dean, David L.↗

NASA NTRS1992

Application of theoretical models to active and passive remote sensing of saline ice

The random medium model is used to interpret the polarimetric active and passive measurements of saline ice. The ice layer is described as a host ice medium embedded with randomly distributed inhomogeneities, and the underlying sea water is considered as a homogeneous half-space. The scatterers in the ice layer are modeled with an ellipsoidal correlation function. The orientation of the scatterers is vertically aligned and azimuthally random. The strong permittivity fluctuation theory is employed to calculate the effective permittivity and the distorted Born approximation is used to obtain the polarimetric scattering coefficients. We also calculate the thermal emissions based on the reciprocity and energy conservation principles. The effects of the random roughness at the air-ice, and ice-water interfaces are accounted for by adding the surface scattering to the volume scattering return incoherently. The above theoretical model, which has been successfully applied to analyze the radar backscatter data of the first-year sea ice near Point Barrow, AK, is used to interpret the measurements performed in the CRRELEX program.

Han, H. C.↗

NASA NTRS1992

Dielectric surface properties of Venus

It has been known for over a decade that certain high-altitude regions on Venus exhibit bizarre radar-scattering and radiothermal-emission behavior. For example, observed values for normal-incidence power reflection coefficients in these areas can exceed 0.5; enhanced back scatter in some mountainous areas in the Magellan SAR images creates a bright surface with the appearance of snow; and reduced thermal emission in the anomalous areas makes the surface there appear hundreds of degrees cooler than the corresponding physical surface temperatures. The inferred radio emissivity in several of these regions falls to 0.3 for horizontal linear polarization at viewing angles in the range 20 deg - 40 deg. Several explanations have been offered for these linked phenomena. One involves single-surface reflection from a sharp discontinuity separating two media that have extremely disparate values of electromagnetic propagation. The mismatch may occur in either or both the real (associated with propagation velocity) or imaginary (associated with absorption) components of the relevant indices of refraction, and the discontinuity must take place over a distance appreciably shorter than a wavelength. An example of such an interaction of Earth would occur at the surface of a body of water. At radio wavelengths, water has an index of refraction of 9 (dielectric permittivity of about 80), and an associated loss factor that varies strongly with the amount of dissolved salts, but is generally significant. Its single-surface radar reflectivity at normal incidence is about 0.65, and the corresponding emissivity (viewed at the same angle) is therefore 0.35. Both these values are similar to the extremes found on Venus, but in the absence of liquid water, the process on Venus requires a different explanation. Two of the present authors (Pettengill and Ford) have suggested that scattering from a single surface possessing a very high effective dielectric permittivity could explain many of the unusual characteristics displayed by the Venus surface. A second explantion relates to the volume scattering that results from successive interactions with one or more interfaces interior to the planetary surface. If the near-surface material has a moderately low index of refraction (to ensure that a substantial fraction of the radiation incident from outside is not reflected, but rather penetrates into the surface), and a very low internal propagation loss, successive internal reflections can eventually redirect much of the energy back through the surface toward the viewer. The necessary conditions for this process to be effective are a low internal propagation loss coupled with efficient internal reflection. At sufficiently low temperatures, fractured water ice displays both the necessary low loss and near-total internal reflection. The possibility that this mechanism might be acting on Venus has recently been put forward.

Pettengill, G. H.↗

NASA NTRS1993

An experimental investigation of high temperature superconducting microstrip antennas at K- and Ka-band frequencies

The recent discovery of high temperature superconductors (HTS) has generated a substantial amount of interest in microstrip antenna applications. However, the high permittivity of substrates compatible with HTS results in narrow bandwidths and high patch edge impedances of such antennas. To investigate the performance of superconducting microstrip antennas, three antenna architectures at K and Ka-band frequencies are examined. Superconducting microstrip antennas that are directly coupled, gap coupled, and electromagnetically coupled to a microstrip transmission line were designed and fabricated on lanthanum aluminate substrates using YBa2Cu3O7 superconducting thin films. For each architecture, a single patch antenna and a four element array were fabricated. Measurements from these antennas, including input impedance, bandwidth, patterns, efficiency, and gain are presented. The measured results show usable antennas can be constructed using any of the architectures. All architectures show excellent gain characteristics, with less than 2 dB of total loss in the four element arrays. Although the direct and gap coupled antennas are the simplest antennas to design and fabricate, they suffer from narrow bandwidths. The electromagnetically coupled antenna, on the other hand, allows the flexibility of using a low permittivity substrate for the patch radiator, while using HTS for the feed network, thus increasing the bandwidth while effectively utilizing the low loss properties of HTS. Each antenna investigated in this research is the first of its kind reported.

Richard, Mark A.↗

NASA NTRS1992

Feasibility of KTa(1-x)Nb(x)O3 as a dielectric or pyroelectric microcalorimeter

We are developing a dielectric microcalorimeter for X-ray spectroscopy. We will present the results of our measurement of the dielectric permittivity, the spontaneous polarization, and the pyroelectric coefficient of the mixed-crystal quantum ferroelectric KTa(1-x)Nb(x)O3 with a doping of x = 0.012, as a function of temperature and bias voltage across the device. The effects of surface layers on the permittivity and the pyroelectric coefficient are discussed. We also show the signal results from infrared LED and alpha-particle radiation.

Pfafman, T. E.↗

NASA NTRS1991

Measurement of cavity perturbation to determine the microwave absorption of a sphere in a single mode resonator

Experiments have been conducted on materials in a single mode microwave resonator to test predictions of a new theory of microwave absorption by a lossy dielectric sphere. An analysis of cavity perturbation for verifying the new absorption model revealed a limitation of a standard form of cavity perturbation theory and led to a modification which generalized its application. The cavity perturbations of a nylon sphere were used to calculate the complex permittivity using the standard perturbation theory and the modified form. These permittivity values were compared to that determined from cavity perturbation using a thin nylon rod where the standard and modified forms agree. The results show that the modification is necessary to correctly apply perturbation theory to spherical samples. A second experiment confirmed the theoretical prediction that under certain sample conditions the power absorbed by a sphere in a resonant cavity can be maximum at a location in the cavity where the empty cavity electric field intensity is a minimum.

Watkins, J. L.↗

NASA NTRS1992

Application of theoretical models to active and passive remote sensing of saline ice

The random medium model is used to interpret the polarimetric active and passive measurements of saline ice. The ice layer is described as a host ice medium embedded with randomly distributed inhomogeneities, and the underlying sea water is considered as a homogeneous half-space. The scatterers in the ice layer are modeled with an ellipsoidal correlation function. The orientation of the scatterers is vertically aligned and azimuthally random. The strong permittivity fluctuation theory is used to calculate the effective permittivity and the distorted Born approximation is used to obtain the polarimetric scattering coefficients. Thermal emissions based on the reciprocity and energy conservation principles are calculated. The effects of the random roughness at the air-ice, and ice-water interfaces are explained by adding the surface scattering to the volume scattering return incoherently. The theoretical model, which has been successfully applied to analyze the radar backscatter data of first-year sea ice, is used to interpret the measurements performed in the Cold Regions Research and Engineering Laboratory's CRRELEX program.

Han, H. C.↗

NASA NTRS1993

Polarimetric backscattering from sea ice

Polarimetric backscattering from sea ice is presented. Theoretical models for backscattering are first presented for various ice types. Then, theoretical results are compared with experimental data for new thin ice, first-year ice, and multi-year ice. Sea ice is modeled as a layer medium containing random scatterers and rough interfaces. For multi-year sea ice with snow cover, the sea ice layer is modeled as an ice background with embedded spheroidal air bubbles and the snow layer as air with ice grains. The hummocky topography on multi-year ice is characterized by a Gaussian distribution which has an averaging effect on backscattering coefficients. First-year sea ice is described by an ice medium hosting ellipsoidal brine inclusions. These inclusions are oriented preferentially in the vertical direction due to the columnar structure of first-year sea ice. Azimuthally, the orientation of the brine pockets are random corresponding to the random c-axes in sea ice, unless the axes are oriented by sea currents. For thin ice in newly opened leads, it has been observed that there exists a thin brine layer with very high salinity on the top surface of the new ice. This brine layer is depicted as a medium with high permittivity which can significantly affect electromagnetic scattering signatures from the lower thin ice layer, with a higher fractional volume of brine inclusions due to higher salinity as compared to thick first-year sea ice. The rough medium interfaces are described as Gaussian rough surfaces characterized by root-mean-square heights and surface correlation lengths. The contribution from rough surface, calculated under the Kirchhoff approximation or small perturbation method, is assumed to be independent from volume scattering. The total loss including absorption and scattering losses in the scattering media is represented by the imaginary part of effective permittivity obtained from the strong fluctuation theory. The polarimetric scattering coefficients for different ice types are then derived under the distorted Born approximation.

Nghiem, S. V.↗

NASA NTRS1993

Application of neural network to remote sensing of soil moisture using theoretical polarimetric backscattering coefficients

This paper investigates the potential application of neural network to inversion of soil moisture using polarimetric remote sensing data. The neural network used for the inversion of soil parameters is multi-layer perceptron trained with the back-propagation algorithm. The training data include the polarimetric backscattering coefficients obtained from theoretical surface scattering models together with an assumed nominal range of soil parameters which are comprised of the soil permittivity and surface roughness parameters. Soil permittivity is calculated from the soil moisture and the assumed soil texture based on an empirical formula at C-, L-, and P-bands. The rough surface parameters for the soil surface, which is described by the Gaussian random process, are the root-mean-square (rms) height and correlation length. For the rough surface scattering, small perturbation method is used for the L-band frequency, and Kirchhoff approximation is used for the C-band frequency to obtain the corresponding backscattering coefficients. During the training, the backscattering coefficients are the inputs to the neural net and the output from the net are compared with the desired soil parameters to adjust the interconnecting weights. The process is repeated for each input-output data entry and then for the entire training data until convergence is reached. After training, the backscattering coefficients are applied to the trained neural net to retrieve the soil parameters which are compared with the desired soil parameters to verify the effectiveness of this technique. Several cases are examined. First, for simplicity, the correlation length and rms height of the soil surface are fixed while soil moisture is varied. Soil moisture obtained using the neural networks with either L-band or C-band backscattering coefficients for the HH and VV polarizations as inputs is in good agreement with the desired soil moisture. The neural net output matches the desired output for the soil moisture range of 16 to 60 percent for the C-band case. The next case investigated is to vary both soil moisture and rms height while keeping the correlation length fixed. For this case, C-band backscattering coefficients are not sufficient for retrieving two parameters because the Kirchhoff approximation gives the same HH and VV backscattering coefficients. Therefore, the backscattering coefficients at two different frequency bands are necessary to find both the soil moisture and rms height. Finally, the neural nets are also applied to simultaneously invert soil moisture, rms height, and correlation length. Overall, the soil moisture retrieved from the neural network agrees very well with the desired soil moisture. This suggests that the neural network shows potential for retrieval of soil parameters from remote sensing data.

Wang, L.↗

NASA NTRS1995

Polarimetric signatures of sea ice. 1: Theoretical model

Physical, structral, and electromagnetic properties and interrelating processes in sea ice are used to develop a composite model for polarimetric backscattering signatures of sea ice. Physical properties of sea ice constituents such as ice, brine, air, and salt are presented in terms of their effects on electromagnetic wave interactions. Sea ice structure and geometry of scatterers are related to wave propagation, attenuation, and scattering. Temperature and salinity, which are determining factors for the thermodynamic phase distribution in sea ice, are consistently used to derive both effective permittivities and polarimetric scattering coefficients. Polarmetric signatures of sea ice depend on crystal sizes and brine volumes, which are affected by ice growth rates. Desalination by brine expulsion, drainage, or other mechanisms modifies wave penetration and scattering. Sea ice signatures are further complicated by surface conditions such as rough interfaces, hummocks, snow cover, brine skim, or slush layer. Based on the same set of geophysical parameters characterizing sea ice, a composite model is developed to calculate effective permittivities and backscattering covariance matrices at microwave frequencies to interpretation of sea ice polarimetric signatures.

Nghiem, S. V.↗

NASA NTRS1996

Automated Monitoring Of Dielectric Properties Of Tree Trunks

Semiautomated instrumentation system called "dielectric monitoring system" (DMS) developed for measuring microwave permittivities of selected components of plants, in particular, of active xylems in tree trunks. System set up with coaxial probes inserted in tree trunks to measure dielectric properties. Can be left to operate unattended to gather data on permittivities as function of time.

Mcdonald, Kyle C.↗

NASA NTRS1995

Polarimetric Signatures of Sea Ice: Theoretical Model - Part 1

Physical, structural, and electromagnetic properties and interrelating processes in sea ice are used to develop a composite model for polarimetric backscattering signatures of sea ice. Physical properties of sea ice constituents such as ice, brine, air, and salt are presented in terms of their effects on electromagnetic wave interactions. Sea ice structure and geometry of scatterers are related to wave propagation, attenuation, and scattering. Temperature and salinity, which are determining factors for the thermodynamic phase distribution in sea ice, are consistently used to derive both effective permittivities and polarimetric scattering coefficients. Polarimetric signatures of sea ice depend on crystal sizes and brine volumes, which are affected by ice growth rates. Desalination by brine expulsion, drainage, or other mechanisms modifies wave penetration and scattering. Sea ice signatures are further complicated by surface conditions such as rough interfaces, hummocks, snow cover, brine skim, or slush layer. Based on the same set of geophysical parameters characterizing sea ice, a composite model is developed to calculate effective permittivities and backscattering covariance matrices at microwave frequencies for interpretation of sea ice polarimetric signatures.

Nghiem, S. V.↗

NASA NTRS2000

Potential Applications of Satellite Based Low Frequency Microwave Measurements of Snow and Ice

In this presentation we will examine some potential applications of low frequency microwave radar and radiometer data to remote sensing of snow and ice conditions over land. We focus on the following low frequency bands; L-band (1.28 GHz), S-band (2.69 GHz), and C-band (5.0 GHz). To predict the effect of snow cover on microwave emission, we need to characterize the dielectric properties of the snow in terms of important physical parameters such as snow density, temperature, and wetness. For the case of dry snow, we use an empirical mixing formula which gives the effective complex permittivity of snow as a function of density, temperature, and frequency. For wet snow, we use another mixing formula which gives the effective complex permittivity as a function of snow wetness. With dry snow, the loss at low microwave frequencies is very small so the corresponding penetration depths are very large (eg., 100 m). Clearly seasonal snow covers are far too thin to have a direct scattering or emission effect on these low frequency bands. There are, however, indirect effects introduced because of altered reflection at the snow/soil boundary, and an extra reflecting interface at the snow/air boundary. For C-band, layers of snow with different densities can have an impact if the number of layers grows sufficiently large. (eg., many meters of snow pack with cm-scale density layering.) Wet snow poses a more difficult problem. Liquid water is much more effective than ice at scattering and absorbing L-band radiation, so even a small amount of wetness will greatly reduce penetration. For example, with a snow wetness of 1 percent (volume fraction), and a density of 300 kg/cu. m, the penetration depths for L-band, S-band, and C-band are about 1.6 m, 0.3 m, and 0.15 m respectively. Very wet snow has more than 10 percent liquid water, and the corresponding L-band penetration is less than 0.2 m. Because the penetration distance is a strong function of frequency, it may be possible to identify a particular class of snow where the wetness is a few percent, and the depth is around one meter by looking at the frequency gradient.

West, Richard D.↗

NASA NTRS2001

Monitoring of bacteria growth using a wireless, remote query resonant-circuit sensor: application to environmental sensing

A new technique is presented for in-vivo remote query measurement of the complex permittivity spectra of a biological culture solution. A sensor comprised of a printed inductor-capacitor resonant-circuit is placed within the culture solution of interest, with the impedance spectrum of the sensor measured using a remotely located loop antenna; the complex permittivity spectra of the culture is calculated from the measured impedance spectrum. The remote query nature of the sensor platform enables, for example, the in-vivo real-time monitoring of bacteria or yeast growth from within sealed opaque containers. The wireless monitoring technique does not require a specific alignment between sensor and antenna. Results are presented for studies conducted on laboratory strains of Bacillus subtilis, Escherichia coli JM109, Pseudomonas putida and Saccharomyces cerevisiae.

Non-NASA Center↗

NASA NTRS2005

A Tower-based Prototype VHF/UHF Radar for Subsurface Sensing: System Description and Data Inversion Results

Knowledge of subsurface characteristics such as permittivity variations and layering structure could provide a breakthrough in many terrestrial and planetary science disciplines. For Earth science, knowledge of subsurface and subcanopy soil moisture layers can enable the estimation of vertical flow in the soil column linking surface hydrologic processes with that in the subsurface. For planetary science, determining the existence of subsurface water and ice is regarded as one of the most critical information needs for the study of the origins of the solar system. The subsurface in general can be described as several near-parallel layers with rough interfaces. Each homogenous rough layer can be defined by its average thickness, permittivity, and rms interface roughness assuming a known surface spectral distribution. As the number and depth of layers increase, the number of measurements needed to invert for the layer unknowns also increases, and deeper penetration capability would be required. To nondestructively calculate the characteristics of the rough layers, a multifrequency polarimetric radar backscattering approach can be used. One such system is that we have developed for data prototyping of the Microwave Observatory of Subcanopy and Subsurface (MOSS) mission concept. A tower-mounted radar makes backscattering measurements at VHF, UHF, and L-band frequencies. The radar is a pulsed CW system, which uses the same wideband antenna to transmit and receive the signals at all three frequencies. To focus the beam at various incidence angles within the beamwidth of the antenna, the tower is moved vertically and measurements made at each position. The signals are coherently summed to achieve focusing and image formation in the subsurface. This requires an estimate of wave velocity profiles. To solve the inverse scattering problem for subsurface velocity profile simultaneously with radar focusing, we use an iterative technique based on a forward numerical solution of the layered rough surface problem. The layers are each defined in terms of a small number of unknown distributions as given above. An a priori estimate of the solution is first assumed, based on which the forward problem is solved for the backscattered measurements. This is compared with the measured data and using iterative techniques an update to the solution for the unknowns is calculated. The process continues until convergence is achieved. Numerical results will be shown using actual radar data acquired with the MOSS tower radar system in Arizona in Fall 2003, and compared with in-situ measurements.

Moghaddam, Mahta↗

NASA NTRS2004

Modeling of a Variable Focal Length Flat Lens Using Left Handed Metamaterials

Left Handed Metamaterials (LHM) were originally purposed by Victor Veselago in1968. These substances would allow a flat structure to focus electromagnetic (EM) waves because they have a negative index of refraction. A similar structure made from conventional materials, those with a positive index of refraction, would disperse the waves. But until recently, these structures have been purely theoretical because substances with both a negative permittivity and negative permeability, material properties necessary for a negative index of refraction, do not naturally exist, Recent developments have produced a structure composed of an array of thin wires and split ring resonators that shows a negative index of refraction. area smaller than a square wavelength. How small the area is can be determined by how perfectly the lens is polished and how pure the substance is that composes the lens. These lenses must also be curved for focusing to occur. The focal length is determined by the curvature of the lens and the material. On the other hand, a flat structure made from LHM would focus light because of the effect of a negative index of refraction in Snell s law. The focal length could also be varied by simply adjusting the distance of the lens from the source of radiation. This could create many devices that are adjustable to different situations in fields such as biomedical imaging and communication. the software package XFDTD which solves Maxwell s equations in the frequency domain as well as the time domain. The program used Drude models of materials to simulate the effect of negative permittivity and negative permeability. Because of this, a LHM can be simulated as a solid block of material instead of an array of wires and split ring resonators. After a flat lens is formed, I am to examine the focusing effect of the lens and determine if a higher resolution flat lens can be developed. Traditional lenses made from conventional materials cannot focus an EM wave onto an My goal was to model LHMs and create a flat lens from them. This was to be done using

Reinert, Jason↗

NASA NTRS2007

Characteristics of Coplanar Waveguide on Sapphire for High Temperature Applications (25 to 400 degrees C)

This paper presents the characteristics of coplanar waveguide transmission lines fabricated on R-plane sapphire substrates as a function of temperature across the temperature range of 25 to 400 C. Effective permittivity and attenuation are measured on a high temperature probe station. Two techniques are used to obtain the transmission line characteristics, a Thru-Reflect-Line calibration technique that yields the propagation coefficient and resonant stubs. To a first order fit of the data, the effective permittivity and the attenuation increase linearly with temperature.

Ponchak, George E.↗