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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 NTRS1976

Multilayered models for electromagnetic reflection amplitudes

The remote sensing of snowpack characteristics with surface installations or with an airborne system could have important applications in water resource management and flood prediction. To derive some insight into such applications, the electromagnetic response of multilayer snow models is analyzed. Normally incident plane waves are assumed at frequencies ranging from 10 to the 6th power to 10 to the 10th power Hz, and amplitude reflection coefficients are calculated for models having various snow-layer combinations, including ice sheets. Layers are defined by a thickness, permittivity, and conductivity; the electrical parameters are constant or prescribed functions of frequency. To illustrate the effect of various layering combinations, results are given in the form of curves of amplitude reflection coefficients, versus frequency for a variety of models. Under simplifying assumptions, the snow thickness and effective dielectric constant can be estimated from the reflection coefficient variations as a function of frequency.

Linlor, W. I.↗

NASA NTRS1975

Electromagnetic reflection from multi-layered snow models

The remote sensing of snow-pack characteristics with surface installations or an airborne system could have important applications in water-resource management and flood prediction. To derive some insight into such applications, the electromagnetic response of multilayered snow models is analyzed in this paper. Normally incident plane waves at frequencies ranging from 1 MHz to 10 GHz are assumed, and amplitude reflection coefficients are calculated for models having various snow-layer combinations, including ice layers. Layers are defined by thickness, permittivity, and conductivity; the electrical parameters are constant or prescribed functions of frequency. To illustrate the effect of various layering combinations, results are given in the form of curves of amplitude reflection coefficients versus frequency for a variety of models. Under simplifying assumptions, the snow thickness and effective dielectric constant can be estimated from the variations of reflection coefficient as a function of frequency.

Linlor, W. I.↗

NASA NTRS1985

Dispersion characteristics for wide slotlines on low-permittivity substrates

A spectral-domain Galerkin method is used to calculate the dispersion characteristics of wide slotlines on low-permittivity substrates that are electrically thin. The range of parameters covered are d/lambda sub 0 = 0.006-0.06, W/lambda sub 0 = 0.005-2.0, and epsilon sub r = 2.22, 3.0, 3.8, and 9.8. The choice of expansion and testing functions makes possible the extraction of the asymptotic form of the infinite integrals, resulting in a computationally efficient solution. The agreement between calculated and measured slot wavelengths on narrow and wide slots is generally within 2.0 percent over 2-6 GHz.

Janaswamy, R.↗

NASA NTRS2011

Comment on "An Analysis of VLF Electric Field Spectra Measured in Titan's Atmosphere by The Huygens Probe" By J. A. Morente et al.

Morente et al. have recently revisited the VLF electric field measurements made with the Permittivity, Wave and Altimetry (PWA) instrument during the descent of the Huygens Probe through the atmosphere of Titan. They assert that they have identified several harmonics of the transverse resonance mode of the surface?]ionosphere cavity, which would prove the existence of an electrical activity in the atmosphere of the largest satellite of Saturn. We refute this finding on the basis that it results from an artifact due to an improper analysis of the data set. [2] The investigators of the Permittivity, Wave and Altimetry (PWA) experiment on the Huygens Probe have reported the extremely low frequency (ELF) and very low frequency (VLF) electric signals recorded during the descent through the atmosphere of Titan. The PWA data are archived in the Planetary Science Archive (PSA) of ESA, and an extensive description of the instrument is at the disposal of the scientific community. Morente and his coworkers have revisited this data set and reported the results of their investigations in two papers. In a first paper, they claim that they have detected in the ELF range (0.100 Hz) several harmonics of a global resonance allegedly generated by lightning activity in the spherical cavity guide formed by the surface of Titan and the inner boundary of the ionosphere, a phenomenon similar to the Schumann resonance observed at EartH In the second paper dedicated to the VLF electric signal recorded by PWA, in the range 0.10 kHz, they argue that they can also bring out the transverse resonance and its harmonics, a more local phenomenon that develops around the excitation source and whose frequency is controlled by the separation between Titan?fs surface and the inner ionospheric boundary. [3] The PWA investigators have analyzed the narrowband ELF signal at about 36 Hz effectively observed during the entire descent. They have not endorsed, however, the alternative approach of Morente et al. that discloses additional ELF narrow-band signals and numerous related harmonics. Hamelin et al. and Beghin et al. have questioned the work of Morente and his coworkers and demonstrated unambiguously that their findings are mere artifacts entirely due to a faulty procedure. Morente et al. refuted this critical analysis of their ELF paper in a rebuttal. The present comment draws a parallelism between the ELF and VLF papers and demonstrates that the VLF signal carries no evidence whatever of any transverse resonance. The analyses of the ELF and VLF signals by Morente and his coworkers are flawed, and their conclusions are shown here to be invalid. A more comprehensive and thorough assessment of the numerical approaches proposed by Morente et al. is given by Berthelin et al..

Grard, Rejean↗

NASA NTRS1976

Studies of earth simulation experiments

The low gravity environment of earth orbit offers the potential for performing experiments involving baroclinic Geophysical Fluid Dynamics (GFD) on spherical surfaces. These experiments in turn have the potential for providing deeper understanding of large scale planetary and solar circulations. However, to perform these experiments, one requires an experimental technique whereby a radially directed body force can be generated to simulate a radial gravitational force field. One viable technique is the use of dielectric fluids with temperature dependent dielectric permittivity in a radially directed electric field. Application of the Boussinesq approximation to the equations of motion for this system and restrictions on the size of certain electrodynamic terms in the energy equations yields a set of equations which are analogous to the equations of motions of geophysical systems like the earth's atmosphere on term by term basis. The theoretical design of GFD experiments for performance in earth orbit are described along with results of preliminary tests of a prototype.

Hart, J. E.↗

NASA NTRS2003

Perovskite Superlattices as Tunable Microwave Devices

Experiments have shown that superlattices that comprise alternating epitaxial layers of dissimilar paraelectric perovskites can exhibit large changes in permittivity with the application of electric fields. The superlattices are potentially useful as electrically tunable dielectric components of such microwave devices as filters and phase shifters. The present superlattice approach differs fundamentally from the prior use of homogeneous, isotropic mixtures of base materials and dopants. A superlattice can comprise layers of two or more perovskites in any suitable sequence (e.g., ABAB..., ABCDABCD..., ABACABACA...). Even though a single layer of one of the perovskites by itself is not tunable, the compositions and sequence of the layers can be chosen so that (1) the superlattice exhibits low microwave loss and (2) the interfacial interaction between at least two of the perovskites in the superlattice renders either the entire superlattice or else at least one of the perovskites tunable.

Christen, H. M.↗

NASA NTRS1990

Modified Hilbert transform pair and Kramers-Kronig relations for complex permittivities

Modified versions of the Hilbert transform pair and the Kramers-Kronig relations are derived for the complex permittivity of a plasma/dielectric medium which is singular at the frequency of the applied electric field equal to 0. Such a complex permittivity exists when the plasma/dielectric model allows a loss term but no restoring term. Permittivity, in which both loss and restoring terms are included, is shown to satisfy the standard Hilbert transform pair and, thus, the Kramers-Kronig relations.

Cockrell, C. R.↗

NASA NTRS1974

Electrical properties of sample 70215 - Low-frequency corrections

Dielectric permittivity, loss tangent, and direct current conductivity of solid sample 70215,14 were measured at temperatures ranging from 100 to 373 K and vacuums of .01 to .1 microtorr; alternating current measurements were made in the 30 Hz to 100 kHz frequency range. It is concluded that dc conductivity undergoes a three order-of-magnitude change between lunar day and lunar night. The assumption is made that strong k' increments at the lower frequencies are partially induced by electrode and dc conductivity effects. Corrections were applied to the experimental data; corrected results suggest relaxation processes occurring at frequencies below 1 kHz.

Alvarez, R.↗

NASA NTRS1989

Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

Cockrell, C. R.↗

NASA NTRS2012

Open Circuit Resonant (SansEC) Sensor for Composite Damage Detection and Diagnosis in Aircraft Lightning Environments

Composite materials are increasingly used in modern aircraft for reducing weight, improving fuel efficiency, and enhancing the overall design, performance, and manufacturability of airborne vehicles. Materials such as fiberglass reinforced composites (FRC) and carbon-fiber-reinforced polymers (CFRP) are being used to great advantage in airframes, wings, engine nacelles, turbine blades, fairings, fuselage and empennage structures, control surfaces and coverings. However, the potential damage from the direct and indirect effects of lightning strikes is of increased concern to aircraft designers and operators. When a lightning strike occurs, the points of attachment and detachment on the aircraft surface must be found by visual inspection, and then assessed for damage by maintenance personnel to ensure continued safe flight operations. In this paper, a new method and system for aircraft in-situ damage detection and diagnosis are presented. The method and system are based on open circuit (SansEC) sensor technology developed at NASA Langley Research Center. SansEC (Sans Electric Connection) sensor technology is a new technical framework for designing, powering, and interrogating sensors to detect damage in composite materials. Damage in composite material is generally associated with a localized change in material permittivity and/or conductivity. These changes are sensed using SansEC. Unique electrical signatures are used for damage detection and diagnosis. NASA LaRC has both experimentally and theoretically demonstrated that SansEC sensors can be effectively used for in-situ composite damage detection.

Wang, Chuantong↗

NASA NTRS1988

Material parameter determination from scattering measurements

The electrical, macroscopic performance of isotropic material can generally be described through their constitutive scalar parameters, permittivity and permeability which are symbolically represented by epsilon and mu, respectively. These parameters relate the electric and magnetic flux densities to the electric and magnetic fields through the following relationships: (1) D=epsilonE; and (2) B=muH. It is through these parameters that the interaction of electromagnetic waves with material can be quantized in terms of reflection and transmission coefficients, and propagation and attenuation factors.

Dominek, A.↗

NASA NTRS2021

Temperature and Frequency Dependent Electrical Properties of AVCOAT and Shuttle Tile Material

This technical memorandum presents the data and results from a series of tests performed on AVCOAT, charred AVCOAT, and different Shuttle Thermal Protection System (TPS) tile coatings to determine their electrical properties as a function of temperature and frequency. Initially, the samples were assumed to be insulators and the complex permittivities were measured from data collected by sandwiching each sample between two conductors to form a sandwich. However, the AVCOAT sample data showed that the material becomes conductive as it begins to char. To get an accurate conductivity reading on these charred samples, a four-point resistance probe was used to collect data. Overall, this testing showed that the virgin AVCOAT starts out as a material that is a good insulator but transitions to one with a conductivity on the order of 1860 S/m as it chars. The deeper layers of AVCOAT (un-charred) all exhibited a temperature and frequency dependence that is possibly indicative of a dielectric relaxation in the material. As the sample temperatures were increased, a knee appears in the real permittivity data sets below 1 kHz. Both the real permittivity and resistivity drop up to several orders of magnitude yet show that the material remains an insulator. The Shuttle High Temperature Reusable Surface Insulation (HRSI) tile coatings studied included Reac- tion Cured Glass (RCG), Aluminum Enhanced Thermal Barrier (AETB), and Toughened Unipiece Fibrous Insulation (TUFI). The purely glass fiber parts of the tile were removed leaving only the outer layers con- taining just the coating. The data collected shows that the RCG, AETB, and outermost layer of the TUFI have similar electrical properties. The real permittivity plots show that there appears to be a relaxation that shows up at frequencies below 1 kHz. The relaxation frequency increases with increasing temperature. Also, the real permittivity increases up to about a factor of four between room temperature and 650K. Likewise, the resistivity (related to the imaginary permittivity) decreases up to five orders of magnitude over the same temperature interval, but still remains an insulator. This data was collected to support a NASA Engineering and Safety Center (NESC) assessment team investigating the source of thermocouple anomalies in both Shuttle TPS material and AVCOAT used for on the Orion spacecraft for Exploration Flight Test 1 (EFT-1). The details of their findings will be documented in a separate report with this document serving as a reference.

Mark A Nurge↗

NASA NTRS1989

A moment method solution of a volume-surface integral equation using isoparametric elements and point matching

Three integral equations for TE (transverse electric) scattering by dielectric cylinders having large values of permittivity are examined. A moment-method solution of the volume-surface integral equation is developed employing isoparametric elements and point matching. The solution is shown to be more accurate and stable than the traditional solutions using pulse basis, particularly in the case of scatterers having large refractive indices.

Jin, Jian-Ming↗

NASA NTRS1985

Characteristic Impedance of a Wide Slot Line on Low Permittivity Substrates

Computed results on the characteristic impedance of wide slots etched on an electrically thin substrate of low dielectric constant epsilon sub r are presented. Results are given for epsilon sub r = 2.22, 3.0, 3.8 and 9.8. Comparison is shown for the characteristic impedance between the present calculations and those available in the literature for high-epsilon sub r substrates.

Janaswamy, R.↗

NASA NTRS1986

Characteristic impedance of a wide slot line on low permittivity substrates

Computed results on the characteristics impedance of wide slots etched on an electrically thin substrate of low dielectric constant epsilon sub r are presented. These results are used to help provide design data for slotlines. Curves are presented for epsilon sub r = 2.22, 3.0, 3.8, and 9.8. Comparison is shown for the characteristic impedance between the present calculations and those available in the literature for high-epsilon sub r substrates. Empirical formulas, based on least square curve fitting, are presented for the normalized slot wavelength lambda prime/lambda sub 0 and the characteristic impedance Z sub 0 over the range: 0.0015 is equal to or less than W/lambda sub 0 equal to or less than 1.0, 0.006 is equal to or less than d/lambda sub 0 equal to or less than 0.06, 2.22 is equal to or less than epsilon sub 0 equal to or less than 9.8.

Janaswamy, R.↗

NASA NTRS1986

Characteristic impedance of a wide slotline on low-permittivity substrates

Janaswamy, R.↗

NASA NTRS2009

The Thermal Electrical Conductivity Probe (TECP) for Phoenix

The Thermal and Electrical Conductivity Probe (TECP) is a component of the Microscopy, Electrochemistry, and Conductivity Analyzer (MECA) payload on the Phoenix Lander. TECP will measure the temperature, thermal conductivity and volumetric heat capacity of the regolith. It will also detect and quantify the population of mobile H2O molecules in the regolith, if any, throughout the polar summer, by measuring the electrical conductivity of the regolith, as well as the dielectric permittivity. In the vapor phase, TECP is capable of measuring the atmospheric H2O vapor abundance, as well as augment the wind velocity measurements from the meteorology instrumentation. TECP is mounted near the end of the 2.3 m Robotic Arm, and can be placed either in the regolith material or held aloft in the atmosphere. This paper describes the development and calibration of the TECP. In addition, substantial characterization of the instrument has been conducted to identify behavioral characteristics that might affect landed surface operations. The greatest potential issue identified in characterization tests is the extraordinary sensitivity of the TECP to placement. Small gaps alter the contact between the TECP and regolith, complicating data interpretation. Testing with the Phoenix Robotic Arm identified mitigation techniques that will be implemented during flight. A flight model of the instrument was also field tested in the Antarctic Dry Valleys during the 2007-2008 International Polar year. 2

Zent, Aaron P.↗