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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Electromagnetic scattering by coated convex surfaces and wedges simulated by approximate boundary conditions

Asymptotic/high-frequency solutions are developed for analyzing the non-specular scattering mechanisms associated with coated convex surfaces and edges simulated by approximate boundary conditions. In particular, the standard impedance boundary conditions (SIBC's) and the second order generalized impedance boundary conditions (GIBC's) are employed for a characterization of the edge diffraction, creeping wave, and surface diffracted wave contributions. To study the creeping wave and surface diffracted wave mechanisms, rigorous UTD (uniform geometrical theory of diffraction) diffraction coefficients are developed for a convex coated cylinder simulated with SIBC's and GIBC's. The ray solutions obtained remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficient for a convex cylinder are obtained via a generalization of the corresponding ones of the circular cylinder. To validate the asymptotic/high-frequency solution, integral equations are derived for both E and H-polarization and solved numerically using the method of moments. Results are presented for a single and three layered coated convex cylinder. Some insights are also provided on the accuracy of the employed GIBC's versus SIBC's for application to curved surfaces. To characterize the scattering by impedance wedges illuminated at skew incidence, diffraction coefficients are derived from an approximate solution of the governing functional difference equations. This solution exactly recovers the known ones for an impedance half plane or an arbitrary wedge at normal incidence, and to validate it for other wedge angles, a moment method code was used. Finally, to test the usefulness of the approximate skew incidence impedance wedge diffraction coefficient for three dimensional structures, equivalent currents are derived in the context of the physical theory of diffraction (PTD) for a finite length impedance wedge of arbitrary internal angles. These are incorporated in a standard general purpose PTD code and results are presented for a number of different impedance structures.

Syed, H. H.↗
NASA NTRS1990

Electromagnetic scattering from two-dimensional thick material junctions

The problem of the plane wave diffraction is examined by an arbitrary symmetric two dimensional junction, where Generalized Impedance Boundary Conditions (GIBCs) and Generalized Sheet Transition Conditions (GSTCs) are employed to simulate the slabs. GIBCs and GSTCs are constructed for multilayer planar slabs of arbitrary thickness and the resulting GIBC/GSTC reflection coefficients are compared with exact counterparts to evaluate the GIBCs/GSTCs. The plane wave diffraction by a multilayer material slab recessed in a perfectly conducting ground plane is formulated and solved via the Generalized Scattering Matrix Formulation (GDMF) in conjunction with the dual integral equation approach. Various scattering patterns are computed and validated with exact results where possible. The diffraction by a material discontinuity in a thick dielectric/ferrite slab is considered by modelling the constituent slabs with GSTCs. A non-unique solution in terms of unknown constants is obtained, and these constants are evaluated for the recessed slab geometry by comparison with the solution obtained therein. Several other simplified cases are also presented and discussed. An eigenfunction expansion method is introduced to determine the unknown solution constants in the general case. This procedure is applied to the non-unique solution in terms of unknown constants; and scattering patterns are presented for various slab junctions and compared with alternative results where possible.

Ricoy, M. A.↗
NASA NTRS1985

Numerical simulation of transient inviscid gas flows in a shock tube

Time-dependent upwind high resolution schemes for solving the Euler equations were developed and applied to simulate 1-D and 2-D transient inviscid gas flows in a shock tube. Using obstacles of different geometries, a series of calculations were carried out to investigate the transient complex shock-wave diffraction phenomena. Shock-wave and objects interactions with shock Mach-number Ms ranging from 2 to 20 were considered. Comparison with analytical and available experimental results indicate good agreement. Display of detailed flow structures including multiple Mach shocks, slip surfaces, and vortex are also given.

Yang, J. Y.↗
NASA NTRS1992

On the convergence of the coupled-wave approach for lamellar diffraction gratings

Among the many existing rigorous methods for analyzing diffraction of electromagnetic waves by diffraction gratings, the coupled-wave approach stands out because of its versatility and simplicity. It can be applied to volume gratings and surface relief gratings, and its numerical implementation is much simpler than others. In addition, its predictions were experimentally validated in several cases. These facts explain the popularity of the coupled-wave approach among many optical engineers in the field of diffractive optics. However, a comprehensive analysis of the convergence of the model predictions has never been presented, although several authors have recently reported convergence difficulties with the model when it is used for metallic gratings in TM polarization. Herein, three points are made: (1) in the TM case, the coupled-wave approach converges much slower than the modal approach of Botten et al; (2) the slow convergence is caused by the use of Fourier expansions for the permittivity and the fields in the grating region; and (3) is manifested by the slow convergence of the eigenvalues and the associated modal fields. The reader is assumed to be familiar with the mathematical formulations of the coupled-wave approach and the modal approach.

Li, Lifeng↗
NASA NTRS1978

Aircraft noise propagation

Sound diffraction experiments conducted at NASA Langley Research Center to study the acoustical implications of the engine over wing configuration (noise-shielding by wing) and to provide a data base for assessing various theoretical approaches to the problem of aircraft noise reduction are described. Topics explored include the theory of sound diffraction around screens and wedges; the scattering of spherical waves by rectangular patches; plane wave diffraction by a wedge with finite impedence; and the effects of ambient flow and distribution sources.

Hadden, W. J.↗
NASA NTRS1978

Application of normal mode theory to seismic source and structure problems: Seismic investigations of upper mantle lateral heterogeneity

The theory of the normal modes of the earth is investigated and used to build synthetic seismograms in order to solve source and structural problems. A study is made of the physical properties of spheroidal modes leading to a rational classification. Two problems addressed are the observability of deep isotropic seismic sources and the investigation of the physical properties of the earth in the neighborhood of the Core-Mantle boundary, using SH waves diffracted at the core's surface. Data sets of seismic body and surface waves are used in a search for possible deep lateral heterogeneities in the mantle. In both cases, it is found that seismic data do not require structural differences between oceans and continents to extend deeper than 250 km. In general, differences between oceans and continents are found to be on the same order of magnitude as the intrinsic lateral heterogeneity in the oceanic plate brought about by the aging of the oceanic lithosphere.

Okal, E. A.↗
NASA NTRS1975

The scattering of electromagnetic pulses by a slit in a conducting screen

A direct method for calculating the impulse response of a slit in a conducting screen is presented which is derived specifically for the analysis of transient scattering by two-dimensional objects illuminated by a plane incident wave. The impulse response is obtained by assuming that the total response is composed of two sequences of diffracted waves. The solution is determined for the first two waves in one sequence by using Green's functions and the equivalence principle, for additional waves in the sequence by iteration, and for the other sequence by a transformation of coordinates. The cases of E-polarization and H-polarization are considered.

Ackerknecht, W. E., III↗
NASA NTRS2004

Improved Phase-Mask Fabrication of Fiber Bragg Gratings

An improved method of fabrication of Bragg gratings in optical fibers combines the best features of two prior methods: one that involves the use of a phase mask and one that involves interference between the two coherent laser beams. The improved method affords flexibility for tailoring Bragg wavelengths and bandwidths over wide ranges. A Bragg grating in an optical fiber is a periodic longitudinal variation in the index of refraction of the fiber core. The spatial period (Bragg wavelength) is chosen to obtain enhanced reflection of light of a given wavelength that would otherwise propagate relatively unimpeded along the core. Optionally, the spatial period of the index modulation can be made to vary gradually along the grating (such a grating is said to be chirped ) in order to obtain enhanced reflection across a wavelength band, the width of which is determined by the difference between the maximum and minimum Bragg wavelengths. In the present method as in both prior methods, a Bragg grating is formed by exposing an optical fiber to an ultraviolet-light interference field. The Bragg grating coincides with the pattern of exposure of the fiber core to ultraviolet light; in other words, the Bragg grating coincides with the interference fringes. Hence, the problem of tailoring the Bragg wavelength and bandwidth is largely one of tailoring the interference pattern and the placement of the fiber in the interference pattern. In the prior two-beam interferometric method, a single laser beam is split into two beams, which are subsequently recombined to produce an interference pattern at the location of an optical fiber. In the prior phase-mask method, a phase mask is used to diffract a laser beam mainly into two first orders, the interference between which creates the pattern to which an optical fiber is exposed. The prior two-beam interferometric method offers the advantage that the period of the interference pattern can be adjusted to produce gratings over a wide range of Bragg wavelengths, but offers the disadvantage that success depends on precise alignment and high mechanical stability. The prior phase-mask method affords the advantages of compactness of equipment and relative insensitivity to both misalignment and vibration, but does not afford adjustability of the Bragg wavelength. The present method affords both the flexibility of the prior two-beam interferometric method and the compactness and stability of the prior phase-mask method. In this method (see figure), a laser beam propagating along the x axis is normally incident on a phase mask that lies in the (y,z) plane. The phase of light propagating through the mask is modulated with a spatial periodicity, p, along the y axis chosen to diffract the laser light primarily to first order at the angle . (The zero-order laser light propagating along the x axis can be used for alignment and thereafter suppressed during exposure of the fiber.) The diffracted light passes through a concave cylindrical lens, which converts the flat diffracted wave fronts to cylindrical ones, as though the light emanated from a line source. Then two parallel flat mirrors recombine the diffracted beams to form an interference field equivalent to that of two coherent line sources at positions A and B (virtual sources). The interference pattern is a known function of the parameters of the apparatus and of position (x,y) in the interference field. Hence, the tilt, wavelength, and chirp of the Bragg grating can be chosen through suitable adjustments of the apparatus and/or of the position and orientation of the optical fiber. In particular, the Bragg wavelength can be adjusted by moving the fiber along the x axis, and the bandwidth can be modified over a wide range by changing the fiber tilt angle or by moving the phase mask and/or the fiber. Alignment is easy because the zero-order beam defines the x axis. The interference is relatively stable and insensitive to the mechanical vibration because of the gh symmetry and compactness of the apparatus, the fixed positions of the mirrors and lens, and the consequent fixed positions of the two virtual line sources, which are independent of the translations of the phase mask and the laser relative to the lens.

Grant, Joseph↗