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Showing papers on "Near and far field published in 1991"


Journal ArticleDOI
TL;DR: In this article, an efficient time-domain near-zone-to-far-zone transformation for FDTD (finitedifference-time-domain) computations is presented, which is based on keeping a running accumulation of the far-zone timedomain vector potentials due to the tangential electric and magnetic fields on a closed surface surrounding the scatterer at each time step.
Abstract: An efficient time-domain near-zone-to-far-zone transformation for FDTD (finite-difference-time-domain) computations is presented. The approach is to keep a running accumulation of the far-zone time-domain vector potentials due to the tangential electric and magnetic fields on a closed surface surrounding the scatterer at each time step. At the end of the computation, these vector potentials are converted to time-domain far-zone fields. Many far-zone bistatic directions can be included efficiently during one FDTD computational run. Frequency domain results can be obtained via fast Fourier transform. Wideband results for scattering from a perfectly conducting plate were obtained from a single FDTD computation transformed to the frequency domain, and compared with moment method results. This approach is significantly more efficient than computing many FDTD results using sinusoidally varying excitation if a wide frequency band is of interest. Coupled with recent advances in computing FDTD results for frequency-dependent materials, wideband results for far-zone scattering from targets including frequency-dependent materials can be obtained efficiently. >

294 citations


Book
01 Jan 1991
TL;DR: In this paper, the authors present a near-field measurement error analysis for microwave interferometer coordinate measurements and machining of small near field measurement systems robotic systems design operations, and a list of acronyms.
Abstract: Near-field measurement concepts near-field measurements microwave interferometer coordinate measurements and machining small near-field measurement systems robotic systems design operations near-field measurement error analysis. List of acronyms. List of symbols.

204 citations


Journal ArticleDOI
TL;DR: The Lax-Wendroff explicit scheme is used to solve the discrete Maxwell's equations and as a result, second-order accuracy is achieved in both time and space.

151 citations


Patent
05 Aug 1991
TL;DR: An antenna for transmitting electromagnetic energy for deactivating a resonant tag circuit of an electronic article surveillance tag without regard to the orientation of the tag while minimizing far field radiation was proposed in this paper.
Abstract: An antenna for transmitting electromagnetic energy for deactivating a resonant tag circuit of an electronic article surveillance tag without regard to the orientation of the tag while minimizing far field radiation. The antenna includes a substantially planar dielectric substrate having a first side and a second side. The antenna also includes four substantially coplanar conductive loops on the first side of the dielectric substrate. The conductive loops are arranged in a two-by-two sequence and connected in series such that current flowing through any one of the conductive loops is out of phase with respect to current flowing in each adjacent conductive loop. The antenna also includes a ground trace on the second side of the substrate.

138 citations


Journal ArticleDOI
TL;DR: In this article, Cauchy's technique for interpolating a rational function from samples of frequency responses and/or their derivatives is investigated, which can be used to speed up the numerical computations of parameters, including input impedance and RCS of any linear time-invariant electromagnetic system.
Abstract: Cauchy's technique for interpolating a rational function from samples of frequency responses and/or their derivatives is investigated. This technique can be used to speed up the numerical computations of parameters, including input impedance and RCS of any linear time-invariant electromagnetic system. This technique is utilized to find the far field of a slit conducting cylinder (TM incidence) over a bandwidth utilizing the information about the current and its derivatives at a few sample points. The numerical results are presented are in good agreement with exact computational data. This technique is a true interpolation/extrapolation technique as it provides the same defective result as the original electric field integral equation at a frequency which corresponds to the internal resonance of the closed structure. >

115 citations


Journal ArticleDOI
01 Nov 1991-Nature
TL;DR: In this article, the authors present a technique that creates a point of sub-wavelength light without associated evanescent losses in its excitation while achieving the advantage of the exponential increase in intensity that occurs within the near-field.
Abstract: NEAR-field optics involves scanning a spot of light, of dimensions smaller than a wavelength, across the surface of a sample at a distance small enough (a few hundred angstroms) that far-field diffraction effects do not occur1,2. In principle this method should generate an image with a resolution determined principally by the dimensions of the spot of light and not limited by the wavelength3. Although near-field imaging was first proposed in 19284,5, efficient implementations that overcome the problem of large evanescent losses in passing light through a sub-wavelength aperture have not been previously realized. Here we present a technique that creates a point of sub-wavelength light without associated evanescent losses in its excitation while achieving the advantage of the exponential increase in intensity that occurs within the near-field3. The sub-wavelength light source is provided by a micropipette coated with a metal and filled with a fluorescent dye embedded in a plastic matrix. The instrument we describe combines the potential for near-field microscopy with the characteristics of a conventional far-field light microscope. Images with overlapping resolutions can be obtained having magnifications that range from a few hundred with the conventional microscope to magnifications, in the near-field mode, of tens of thousands that are of the order normally associated with scanning electron microscopy. Such imaging with light can be achieved even with fluorescence, under ambient conditions and without the destructive sample preparation and beam damage that is characteristic of electron microscopy.

105 citations


Journal ArticleDOI
TL;DR: In this article, the lateral modes of an ideal broad area laser, including the nonlinear interaction between the carriers and the optical field, were calculated and the results showed that unsaturable losses are higher and quantum efficiencies are lower than those determined from plane-wave approximations.
Abstract: Calculations of the lateral modes of an ideal broad area laser, including the nonlinear interaction between the carriers and the optical field, are made. The results include periodically modulated near fields and single- and double-lobed far fields similar to those previously measured. The unsaturable losses are higher and quantum efficiencies are lower than those determined from plane-wave approximations. Broad area InGaAs-GaAlAs-GaAs quantum-well lasers were fabricated and measured and found to closely agree with the theory in near, far, and spectrally resolved near fields. An occultation experiment on the far field confirms previously predicted unstable resonatorlike modes with V-shaped fronts. >

88 citations


Journal ArticleDOI
TL;DR: In this paper, a finite-difference time-domain (FDTD) algorithm for the solution of electromagnetic scattering problems is formulated in numerically defined generalized coordinates in three dimensions and implemented in a code with the lowest order Bayliss-Turkel radiation boundary condition expressed in spherical coordinates.
Abstract: The finite-difference time-domain (FDTD) algorithm for the solution of electromagnetic scattering problems is formulated in numerically defined generalized coordinates in three dimensions and implemented in a code with the lowest order Bayliss-Turkel radiation boundary condition expressed in spherical coordinates. It is shown that the algorithm is capable of accurately tracking the progress of a pulse of electromagnetic radiation through the curvilinear mesh generated by a body of revolution, the only problems occurring in the vicinity of the rotation axis, which represents a coordinate singularity. A simple method to deal with this singular line is presented and discussed, and its is shown that, at least for the test problem, this approximation is sufficient. The algorithm discussed is useful for the solution of the exterior problem in the presence of conductors and dielectrics with complicated shapes and electrical compositions, and for near-field problems such as cavity penetration problems. The far fields are obtained by replacing the scatterer with a virtual surface enclosing all sources. >

83 citations


Patent
20 Jun 1991
TL;DR: An acoustic microscope assembly for atomic level inspection of a target object includes a cantilever arm with a sharp tip on its lower surface and a zinc oxide piezoelectric thin film on its upper surface.
Abstract: An acoustic microscope assembly for atomic level inspection of a target object includes a cantilever arm with a sharp tip on its lower surface and a zinc oxide piezoelectric thin film on its upper surface. High frequency excitation signals, having a frequency of at least 50 Megahertz, are applied to the piezoelectric thin film so as to generate high frequency acoustic signals that are transmitted through the sharp tip so as to impact on a target object. The assembly can either receive acoustic signals reflected by the target object, or it can receive acoustic signals that have propagated through the target object. One method of using this assembly is to apply a continuous wave signal to the piezoelectric thin film while scanning the target object, and measuring characteristics of the target object at various positions thereof by measuring the resonant frequency of the transmitted high frequency acoustic signals. Other methods include pulsed operation, and combining acoustic measurements with atomic force measurements and/or tunneling current measurements to characterize a target object. The acoustic microscope assembly can also be used for storing information on a substrate, by deforming the substrate at selected positions, and for reading such stored information by determining which positions on a substrate have been deformed.

81 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the coupling of electromagnetic energy into a conical waveguide through an electrically small hole near the cone tip and found that the values obtained for the energy transmitted through an aperture with a diameter significantly less than that of the radiation being used are small.
Abstract: The coupling of electromagnetic energy into a conical waveguide through an electrically small hole near the cone tip is considered. This problem is relevant to near‐field microscopy, where tapered metallic probes are used to either illuminate, or collect light from, the structure under investigation. The situation considered in detail here is simplified by assuming that the aperture is surrounded by a planar baffle, which approximates the flat ends of fabricated probes. An established formulation for small‐hole coupling into waveguides is used and the waveguide itself taken to be a truncated, perfectly conducting cone. As expected, the values obtained for the energy transmitted through an aperture with a diameter significantly less than that of the radiation being used are small. However, it is also found that the size of the waveguide at the hole position strongly affects the percentage of the incident energy transmitted.

67 citations


Journal ArticleDOI
TL;DR: In the complex source point technique, an omnidirectional source diffraction solution becomes that for a directive beam when the coordinates of the source position are given appropriate complex values.
Abstract: In the complex source point technique, an omnidirectional source diffraction solution becomes that for a directive beam when the coordinates of the source position are given appropriate complex values. This is applied to include feed directivity in reflector edge diffraction. Solutions and numerical examples for planar strip and parabolic cylinder reflectors are given, including an offset parabolic reflector. The main beams of parabolic reflectors are calculated by aperture integration and the edge diffracted fields by uniform diffraction theory. In both cases, a complex source point feed in the near or far field of the reflector may be used in the pattern calculation, with improvements in accuracy in the lateral and spillover pattern lobes. >

Journal ArticleDOI
TL;DR: In this paper, a self-consistent formalism is presented in order to determine the dispersion equation of the coupled electromagnetic modes between a dielectric probe tip of arbitrary shape and a rough surface.
Abstract: A self‐consistent formalism is presented in order to determine the dispersion equation of the coupled electromagnetic modes between a dielectric probe tip of arbitrary shape and a rough surface. A microscopic picture of the matter is used for describing the dielectric response of the tip, and the coupling with the substrate is introduced from a dynamical matrix expressed in terms of propagators. Retardation effects may be included without formal difficulty through an appropriate response function describing the surface of the solid (local or nonlocal). An advantage of such a calculation lies in the possibility of simulating dielectric tips of arbitrary shape without introducing boundary conditions at the surface of the probe. Connection with atomic force microscopy and near field detection by local probe will be discussed.

Journal ArticleDOI
TL;DR: In this paper, the extreme near-field behavior of the wire grid model of a conducting surface is examined, and it is verified that the best accuracy for the E-field is obtained when the wire satisfies the'same surface area' rule of thumb.
Abstract: The extreme near-field behavior of the wire grid model of a conducting surface is examined. Using a wire grid model of an infinite transverse magnetic circular cylinder, it is verified that the best accuracy for the E-field is obtained when the wire satisfies the 'same surface area' rule of thumb. Two excitations are considered: a uniform surface current and plane wave incidence. In the first case, although the boundary value match between the wires is poor the extreme near field is still quite accurate. In the second case, the near field is also accurate, however, the largest errors occur not between the wires, but in the interior of the scatterer. In both cases, the boundary match between the wires as a check on the accuracy of the solution is misleading. >

Journal ArticleDOI
TL;DR: In this paper, the authors apply the theory of Weidelt and Christensen describing the electromagnetic fields of a grounded electric dipole over a horizontally stratified earth to attack the problem of industrial interference in magnetotellurics.
Abstract: In order to attack the problem of industrial interference in magnetotellurics, we apply the general theory of Weidelt and Christensen describing the electromagnetic fields of a grounded electric dipole over a horizontally stratified earth. The impedance tensor for dipole fields is proven to be independent of the dipole orientation. Within the near field, the elements of the impedance tensor are real quantities, and are independent of period. Because of this, the logarithm of the apparent resistivity versus the logarithm of period rises with a slope of 45 degrees and the phase is zero. We study the inversion of the controlled-source impedance tensor to reveal earth structure at a given distance from the source, using a nonlinear least-squares technique. We present an interpretation of magnetotelluric data in the Tangshan area of China as a practical application of the technique. Sedimentary thicknesses of about 600 m are estimated and agree well with conventional Schlumberger soundings. The upper resistive crust (thickness about 13 km) overlies a more conductive lower crust whose resistivity is below a few hundred Omega . m.

Patent
16 Oct 1991
TL;DR: In this paper, the construction and theory of operation of such a coupling device for coupling RF energy into an antenna is disclosed. And the coupling device provides receiver sensitivity measurements and produces rectified pulses or DC levels for the purpose of measuring transmitter power.
Abstract: An RF coupler is used to measure transmitted power and receiver sensitivity of an avionics RF transceiving system (e.g., a secondary radar transponder). The coupler physically mates with (e.g., by conformally enveloping) an airborne type blade antenna mounted to the fuselage of an aircraft. The construction and theory of operation of such a coupling device for coupling RF energy into an antenna is disclosed. The coupling device provides receiver sensitivity measurements and produces rectified pulses or DC levels for the purpose of measuring transmitter power. The system measures such parameters in the extreme near-field (e.g., about 0.1 wavelength) to simplify the measurements and to isolate the measurements from errors due to standing waves and the presence of other nearby objects.

Journal ArticleDOI
TL;DR: In this paper, a spherical mode expansion with Cartesian vector coefficients is presented for the study of the radiation patterns of arbitrary wire antennas, and the length of the expansion is related to the precision specified for the pattern; i.e., more precision requires more terms.
Abstract: A spherical mode expansion with Cartesian vector coefficients is presented for the study of the radiation patterns of arbitrary wire antennas. Coefficients are obtained by using a spherical harmonic series for the free space Green's function in conjunction with the current distribution obtained with the method of moments. Transverse components of the far field are ultimately obtained yielding a compact pattern representation suitable for rapid retrieval and display. The length of the expansion is shown to be related to the precision specified for the pattern; i.e., more precision requires more terms. A useful truncation criterion is proposed and verified by comparing results obtained for several typical wire antennas. >

Journal ArticleDOI
01 Feb 1991
TL;DR: In this paper, the far field radiation patterns of wrap-around, circular disk and annular ring microstrip patch antennas mounted on a sphere are studied theoretically, where the patches are replaced by equivalent magnetic currents based on cavity model theory.
Abstract: The far field radiation patterns of wrap-around, circular disk and annular ring microstrip patch antennas mounted on a sphere are studied theoretically. The patches are replaced by equivalent magnetic currents based on cavity model theory. The radiation fields are then determined using the modal expansion technique in spherical co-ordinates. Results for a wraparound antenna of a half-wavelength in width, for the broadside TM11 mode of a circular disk antenna and for the TM11 and TM12 modes of an annular ring antenna are given. The accuracy of the simple theory is confirmed by a more rigorous but complicated theoretical approach based on electric surface current model.

Journal ArticleDOI
TL;DR: In this article, the effect of the gravitational field generated by a small rotating quadrupole on a graviational wave antenna was analyzed and the effect on the Explorer 2270 kg cryogenic gravitational wave antenna of the Rome group.
Abstract: We present a detailed analysis of the effect of the gravitational field generated by a small rotating quadrupole on a graviational wave antenna and we report on the preliminary measurement of this effect on the Explorer 2270 kg cryogenic gravitational wave antenna of the Rome group. The induced signal had an amplitude twenty times larger than the detector noise when the antenna was equipped with an FET amplifier and was easily detected without requiring integration in time. We remark that with this method we were able to make an absolute calibration of a gravitational wave antenna.

Journal ArticleDOI
TL;DR: In this paper, a spherical back-projection algorithm is proposed to reconstruct near-field microwave images of conducting objects, where an object is mounted on a rotating pedestal and its backscattered near field is measured at discrete-frequency steps.
Abstract: A spherical back-projection algorithm is proposed to reconstruct near-field microwave images of conducting objects. In this imaging scheme, the object is mounted on a rotating pedestal and its backscattered near field is measured at discrete-frequency steps. Implementation of the method consists of first estimating the spherical projection (or range profile) at each aspect by inverse Fourier transforming the range-corrected scattered near field, and then coherently spherically back-projecting the range profiles into the image plane. The images are interpreted and predicted based on the procedure of the spherical back-projection method, and numerical and experimental results are presented to verify the effectiveness of the proposed algorithm. >

Patent
16 Dec 1991
TL;DR: In this paper, the antenna is placed in near field relationship to the sample to direct microwave energy toward a first specimen surface, which provides a substantially more powerful microwave field than prior art systems, and the specimen comprises an impedance termination for the microwave path that includes the microwave generator and antenna.
Abstract: A contactless apparatus for measuring contaminants in a semiconductor specimen (24) includes a tunable microwave generator (26) coupled by a coaxial cable (36) to a tuned narrowband microstrip antenna (38) that defines a through hole (72). The antenna is placed in near field relationship to the specimen to direct microwave energy toward a first specimen surface (44). This proximity provides a substantially more powerful microwave field than prior art systems, and the specimen comprises an impedance termination for the microwave path that includes the microwave generator and antenna, thereby rendering system measurements substantially immune to mechanical vibration of the specimen. A pulsed laser (42) directs optical energy through the antenna through hole toward the first specimen surface (44). The optical energy generates minority carriers within the specimen that begin to recombine upon cessation of each pulse. Minority lifetime decay affects microwave energy reflecting from freed holes and electrons in the specimen, which energy is coupled from the antenna to a detector (46) and preferably a computer system (48) that controls the system and provides signal processing of the detector output.

Journal ArticleDOI
TL;DR: Comparison of the radiometric with experimental data points out quite a good agreement in the case of models made of water near 1.5 and 3 GHz, which can be used for medical applications, in which high-water-content tissues are often examined.
Abstract: A method is developed for computing the near field transmitted by a monomode rectangular waveguide aperture into a homogeneous lossy material. The principle of this method is discussed, and its results are verified by experiments both in an active process (when the antenna transmits a signal toward the material) and in a passive process (when the antenna receives the thermal noise transmitted by the different subvolumes of the material). The method has been applied to the computation of radiometric signals for both power and correlation radiometry. Comparison of the radiometric with experimental data points out quite a good agreement in the case of models made of water near 1.5 and 3 GHz. Consequently, this method of computing the radiometric signals can be used for medical applications, in which high-water-content tissues are often examined. >

Patent
17 Sep 1991
TL;DR: In this paper, the authors described a system for simulating electromagnetic environments to be encountered by a moving object such as a missile, which includes compact ranges in HIL simulating as projection system to provide a cost and space efficient way for testing the performance of missiles and other objects.
Abstract: Systems and methods for simulating electromagnetic environments to be encountered by a moving object such as a missile (14) are disclosed. The systems include compact ranges in 'hardware in the loop' ('HIL') simulating as projection system (10) to provide a cost- and space-efficient way for testing the performance of missiles and other objects. The systems disclosed may include mobile (62) or stationary (146, 150) compact ranges and may use lenses (70) or reflectors (186) in connection with an array (170) of one or more feed horns (66) to convert spherical or 'near field' wavefronts to plane waves within designated 'quiet zones'. If mobile ranges are employed, such ranges may be mounted on the flight tables (82) used for repositioning the missile seekers during the simulations. Also disclosed are systems for varying the amplitude and phase characteristics of the energy provided to an array of two or more feed horns in order to vary the apparent angle of received electromagnetic energy at electronic speeds. Typically, the number of feed horns used in varying the apparent angle of arrival is small (e.g. three). However, the small group may be part of a larger array in which switching is used to select one or more groups.

Journal ArticleDOI
TL;DR: In this paper, an antiguide laser diode array has been fabricated which radiates a predominantly single lobe far field with a full width at half-maximum of 1.5 times the diffraction limit at a continuous wave output power of 500 mW with a differential quantum efficiency of 50%.
Abstract: An antiguide laser diode array has been fabricated which radiates a predominantly single lobe far field with a full‐width at half‐maximum of 1.5 times the diffraction limit at a continuous wave output power of 500 mW with a differential quantum efficiency of 50%. By spectrally resolving the far field of the device at high operating powers it is shown that the two longitudinal modes correspond to adjacent lateral modes of the array. The operation of the second lateral mode is the result of spatial hole‐burning of the first optical mode.

Journal ArticleDOI
TL;DR: In this article, an analytical and numerical study of microwave diversity imaging of continuous and discrete conducting objects in the near-field region is presented, where the image of the scattering object can be reconstructed by Fourier inversion of the data acquired from the recorded scattered field using angular and frequency diversity techniques.
Abstract: Analytical and numerical studies of microwave diversity imaging of continuous and discrete conducting objects in the near-field region are presented. Analytical results show that the image of the scattering object can be reconstructed by Fourier inversion of the data acquired from the recorded scattered field using angular and frequency diversity techniques. Different feature information of the scattering object can be obtained using a polarization diversity technique. Various scattering arrangements are studied and compared on the basis of the reconstructed image quality and practical considerations. Numerical results show that the described frequency, angular, and polarization diversity techniques in the backward scattering arrangement can result in a cost-effective approach in near-field microwave imaging systems. >

Journal ArticleDOI
01 Apr 1991
TL;DR: In this article, the electromagnetic scattering from an impedance cylinder embedded in a nonconcentric dielectric cylinder is derived rigorously by using a boundary value approach, where the two cylinders are assumed to be infinite in length and of circular cross-section.
Abstract: The electromagnetic scattering from an impedance cylinder embedded in a nonconcentric dielectric cylinder is derived rigorously by using a boundary value approach. The two cylinders are assumed to be infinite in length and of circular cross-section. The incident electromagnetic field is in terms of an electric or a magnetic field component parallel to both cylinder axes. The problem is two dimensional and the solution to either types of polarisation (TM or TE) can be found independently. Plane wave and line source excitations are considered in this analysis. The effects of various geometrical and electrical parameters (such as the cylinder's radii, permittivity, surface impedance and eccentricity) on the near field distribution and the far scattered field pattern are examined. Bistatic and monostatic scattering cross-sections of the composite cylinder which minimise or maximise the radar cross-section are also investigated. >

Journal ArticleDOI
01 Jan 1991
TL;DR: In this article, the far field radiation pattern of a circular disk microstrip antenna mounted on a sphere is studied theoretically. But the spectral domain Green's function matrix is diagonal, and the results are verified by comparison with results obtained from the cavity model theory.
Abstract: The far field radiation patterns of a circular disk microstrip antenna mounted on a sphere are studied theoretically. The radiator is replaced by an assumed surface current distribution. The effects of the dielectric layer and the metallic sphere are rigorously taken into account by the spectral domain Green's function formulation. In the spectral domain represented by the vector Legendre series, the Green's function matrix is diagonal. The results are verified by comparison with results obtained from the cavity model theory. The cavity model agrees asymptotically with the present method for the case of a thin dielectric substrate.

Journal ArticleDOI
TL;DR: By expanding the incident, scattered, and transmitted electromagnetic fields in terms of appropriate vector spheroidal wave functions, an analytic solution is obtained to the problem of electromagnetic scattering by n dielectric spheroids of arbitrary orientation as discussed by the authors.

Journal ArticleDOI
01 Oct 1991
TL;DR: In this paper, the problem of electromagnetic scattering from a perfectly electrically conducting cylinder in the presence of a slot in a parallel-plate waveguide is considered, where a two-dimensional slot in one of the walls of the guide opens into a half-space in which the twodimensional conducting cylinder resides, and the excitation for this structure is an incident TEM wave from within the waveguide, and/or a magnetic line source which produces an incident TEy wave in the exterior half space.
Abstract: The problem of electromagnetic scattering from a perfectly electrically conducting cylinder in the presence of a slot in a parallel-plate waveguide is considered. A two-dimensional slot in one of the walls of the parallel-plate guide opens into a half-space in which the twodimensional conducting cylinder resides. The excitation for this structure is an incident TEM wave from within the waveguide, and/or a magnetic line source which produces an incident TEy wave in the exterior half-space. Coupled integral equations for the aperture electric field and the cylinder current are derived from first principles and are solved numerically for cylinders of various cross-section, size, and location relative to that of the slot aperture. From knowledge of the aperture electric field and cylinder current, all other quantities of interest may be determined. For TEM excitation from within the guide, the reflection coefficient and radiation pattern data are presented along with the aperture electric field and cylinder current. For external excitation, data are presented that illustrate how the cylinder serves as a shield for the aperture. From this data one can assess the effectiveness of a conducting shield placed over, but not in contact with, the guide aperture.

Journal ArticleDOI
TL;DR: An efficient numerical technique is presented for electromagnetic scattering in the near-field zone by three-dimensional permeable conducting objects excited by a loop antenna to illustrate the dependence of the scattered field on the physical characteristics of the scatterer and its location.
Abstract: An efficient numerical technique is presented for electromagnetic scattering in the near-field zone by three-dimensional permeable conducting objects excited by a loop antenna. The impedance boundary conditions are used to simplify the formulation and reduce the computation time and memory. Numerical results are presented to illustrate the dependence of the scattered field on the physical characteristics of the scatterer and its location. >