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Two different supervised learning algorithms, support vector machine (SVM) and neural networks (NN), are applied in classifying metallic objects according to size using the expansion coefficients of their magneto-quasistatic response in the spheroidal coordinate system. The classified objects include homogeneous spheroids and composite metallic assemblages meant to resemble unexploded ordnance. An analytical model is used to generate the necessary training data for each learning method. SVM and NN are shown to be successful in classifying three different types of objects on the basis of size. They are capable of fast classification, making them suitable for real-time application. Furthermore, both methods are robust and have a good tolerance of 20-dB SNR additive Gaussian noise. SVM shows promise in dealing with noise due to uncertainty in the object's position and orientation. Index Terms--Neural network (NN), spheroidal modes, supervised learning, support vector machine (SVM), unexploded ordnance (UXO).

We propose a spheroidal mode approach to characterize the electromagnetic induction (EMI) response of buried objects, assumed to be much more conductive than their environment. Both the excitation and the response are formulated as the linear superpositions of basic spheroidal modes. The scattering coefficients characterize objects, regardless of their geometrical complexity and material inhomogeneity, due to the orthogonality of the spheroidal modes. The ill-conditioning encountered in retrieving the scattering coefficients is dealt with by mode truncation and Tikhonov regularization. The approach is tested for both simulated and measured data, and the retrieval results show encouragingly that only few excitation and response modes effectively represent the EMI response of the objects. The proposed approach is therefore promising in the detection and classification of buried objects. Index Terms--Electromagnetic induction (EMI), inversion, spheroid, subsurface sensing, unexploded ordnance (UXO).

Electromagnetic induction (EMI) is a popular technique to detect and discriminate buried unexploded ordnance (UXO). However, modeling of the EMI response from many types of UXO is difficult due to the small skin depth of the interior fields. In grid-based numerical methods, meshing the target volume or surface to resolve the skin depth is often highly impractical, yet a failure to do so yields inaccurate results. This paper addresses the problem with a time-domain hybrid technique based on thin-skin approximation (TSA) that is very accurate for small skin depths. The TSA method is applied to axisymmetric problems and is shown to be both fast and accurate when the skin depth is small. The method is compared with analytical results, and excellent agreement is obtained. For magnetic materials (such as steel), the TSA method is accurate for the complete time-domain EMI response. In such cases, the TSA method provides an improved accuracy along with an order-of-magnitude reduction in CPU time compared to a dense-mesh finite-element method (FEM). For nonmagnetic materials, the TSA loses accuracy as time progresses and must be combined with a coarse-mesh FEM. In such cases, the combined method still provides greater accuracy with comparable CPU time. Index Terms--Buried object detection, electromagnetic induction (EMI), finite-element method (FEM), method of moments (MoM).

A fast method of moments is presented to calculate electromagnetic wave scattering from layered one-dimensional rough surfaces. The formulation is provided for M stratified homogeneous regions, separated by M - 1 rough surfaces, and solved using point matching and pulse basis functions. Compared to the single surface case, the solution of scattering from M - 1 surfaces requires significantly more memory and computational time. To facilitate the solution, the forward-backward method with spectral acceleration is applied. As an example, a dielectric layer on a perfect electric conductor surface is studied. The numerical results are compared with the analytical solution for layered flat surfaces to partly validate the formulation. The accuracy, efficiency, and convergence of the method are then studied for various rough surfaces and layer permittivities. Index Terms--Forward-backward (FB) method, layered surfaces, method of moments, novel spectral acceleration (SA), rough surfaces, stratified surfaces.

Four properties related to left-handed metamaterials are studied numerically: transmission within a stop-band, backward phase, negative refraction, and partial focusing. The unit cell of the metamaterial under study is composed of a rod and a ring originally proposed at infrared frequencies and redesigned here at microwave frequencies. We show that this ring, because of its symmetry, exhibits a better transmission in a parallel-plate waveguide than the original concentric split-ring resonator. Negative refraction is studied from a prism-shaped metamaterial, while all of the other properties are studied from a slab-shaped metamaterial. In particular, transmission and backward phase are studied on a slab where rings naturally couple with the incident wave, while partial focusing is studied on a slab of rings perpendicular to the direction of propagation. The numerical simulations are based on a two-dimensional periodic method of moments, whose Green's function is computed via Ewald's method, and a three-dimensional finite-difference time-domain technique. Index Terms--Focusing, left-handed (LH) metamaterial, method of moments (MoM), negative index of refraction, phase measurements, prism measurements.

A mode-expansion method that needs less than 6% the number of unknowns required by conventional method of moments is introduced in calculating two-dimensional electromagnetic wave scattering from perfectly conducting objects on rough ocean surfaces. Modes are selected for dominant propagation waves so that the number of unknowns in the matrix equation are minimized. In the numerical examples, ocean surfaces are modeled as perfectly conducting rough surfaces described by the Pierson--Moskowitz power spectrum. Bistatic radar cross-sections (RCS) of various objects, such as ship-like and low-observable targets, are calculated for a 1-GHz incident plane wave and are validated for accuracy against an iterative MoM solution. Index Terms--Electromagnetic wave scattering, method of moments (MoM), mode-expansion method (MEM), rough surface.

We present the experimental realization of a one-dimensional left-handed/right-handed resonator. The left-handed (LH) part of the resonator is formed by a solid-state-like metamaterial composed of [OMEGA] metallic structures, while the right-handed part is just air. The resonant behavior is successfully observed and an acceptable Q value is obtained. Through phase measurement, we verify that the LH metamaterial layer acts as a phase compensator. Further proof is given by varying the thicknesses of both layers simultaneously to achieve the same resonant frequency under the limitation of total phase difference less than 2 [pi], which is a criterion dramatically different from traditional cavity resonators. Index Terms--Left-handed metamaterials (LHMs), resonator.

The refraction of phase and power at the interface between free space and anisotropic media is studied. Under a TE incidence (electric field along [??]) and [k.sub.y] = 0 incidence (where [k.sub.y] is the [??] component of the wave vector), a closed-form generalization of Snell's laws is proposed. The two relations (one for the phase and one for the power) are expressed in terms of the incident angle, the constitutive parameters of the anisotropic medium (which can take negative values), and the tilting angle of the dispersion relation. In addition, both positive and negative dispersions are discussed, making the formulas directly usable for the design of left-handed metamaterials. The validation is done by two methods. First, the electromagnetic fields in layered anisotropic media are computed analytically. The angle of refraction of the wave vector is thus directly obtained, while that of the power is obtained by computing the time-average Poynting power. Second, numerical simulations are performed using HFSS to record the deflection of the power by a prism characterized by positive or negative constitutive parameters. For the specific prism experiment, in which the incident angle is equal to the tilting angle of the dispersion relation, we show that the refraction laws reduce to a simple Snell's law form. Index Terms--Anisotropic media, left-handed metamaterials (LHMs), refraction laws.

We use a hybrid model including asymptotic expressions of the spheroidal wave functions (SWFs) to obtain a reliable broadband solution for the electromagnetic induction (EMI) response from a conducting and permeable spheroid. We obtain this broadband response, valid in the magnetoquasistatic regime from zero to hundreds of kilohertz, by combining three different techniques, each applicable over a different frequency range. At low frequencies, the exact analytical solution is used. At midrange frequencies, asymptotic expressions for the angular and radial SWFs ate incorporated into the exact solution in order to maintain a stable solution for the induced magnetic field. At higher frequencies, a small penetration approximation (SPA) solution is used when the SPA solution approaches the asymptotically assisted solution to within some predefined tolerance. Validation of this combined technique is accomplished through the comparison of the induced magnetic field predicted by our model to both a finite element/boundary integral (FE-BI) numerical solution and experimental data from various spheroids taken by an ultrawideband EMI instrument. Index Terms--Asymptotic expansion, electromagnetic induction (EMI), small penetration approximation (SPA), spheroidal wave functions (SWFs).

This paper exposes an efficient way of evaluating Green's functions arising in planar stratified media. In the spectral domain, the components are split into a singular and a regular part. The latter is expressed in terms of exactly four boundary coefficients, which computation is extracted from the numerical kernel of the method, and the former is evaluated analytically via Sommerfeld identity. The spatial counterparts are then evaluated by a method which combines the advantages of the complex image method (CIM) and the direct numerical evaluation of Sommerfeld integral, while trying to avoid their respective drawbacks. The result is an efficient technique to treat horizontal and vertical metallizations embedded in multilayered media. Results for a three-dimensional (3-D) planar inverted 'F' antenna are obtained with this technique and successfully compared to measurements. Index Terms--Green functions, integral equations, microstrip antennas, moment methods, nonhomogeneous media.

In the presence of normal substrates, it is well known that there exists strong transverse magnetic (TM) surface wave coupling between antenna ports on a shared ground plane. Through the analysis of surface wave propagation, such coupling is proposed to be substantially decreased via the use of magnetic metamaterials. The design and the characterization of the metamaterials are presented, and it is shown that within a certain frequency band, the material behaves as an anisotropic magnetic plasma, suppressing the propagation of a TM surface wave. Experimental measurements further confirm such a suppression, and an isolation improvement of 15 dB between an aperture spaced 9.2 cm apart is observed, in agreement with numerical simulations. [ABSTRACT FROM AUTHOR]

A general equivalent circuit model to calculate the effective permeability of various configurations of split-ring resonators (SRRs) is presented. In the proposed model, each column of the SRR units along the axis of the rings is modeled as a quasisolenoid under magnetic induction. The inductance per ring of the infinite column of these rings is calculated, assuming all the rings in this column support the same current. The electromagnetic coupling between these individual columns of the rings is integrated into this circuit model, which is then applied to a two dimensional cross embedded split-ring resonator. The agreement between the predicted results and numerical simulations shows the efficiency of the model in predicting the frequency band of negative permeability. [ABSTRACT FROM AUTHOR]

The measurement of the negative effective permittivity and permeability of a material is a direct way to verify its left-handed properties. In this paper, a transmission experiment for a left-handed material (LHM) sample is performed in a parallel plate waveguide. The effective frequency dispersive permittivity and permeability are retrieved from the experimental scattering data and found to be simultaneously negative in a specific frequency range. The simulation results also show that the misalignments of the metallic inclusions of the LHM introduce some dips to the retrieved curves, which prevent us from obtaining ideal curves following the Lorentz or Drude model. [ABSTRACT FROM AUTHOR]

A generalized analytical formulation for analyzing the Goos-Hänchen (GH) lateral shift direction is provided, from which we show that the phenomenon of both positive and negative GH shifts at different incident angles can be observed with left-handed material (LHM) slabs. The formulation also reveals that this unique phenomenon is related to the relative amplitudes of the growing and decaying evanescent waves inside the LHM slabs. The energy flux patterns with LHM slabs are further studied to show the influence of the evanescent waves on the GH shift direction change. [ABSTRACT FROM AUTHOR]

In this article, we report experimental results on the shift of a beam that propagates through a slab of metamaterial, known to exhibit left-handed properties. A similar experiment with a Teflon sample of similar size is also carried out for comparison. The results show the existence of a frequency band over which the shift experienced by the beam exceeds the theoretical limit above which the material is left handed. This demonstrates the effectiveness of using a beam shift experiment to characterize the left-handed properties of metamaterial. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Demonstrates the left-handed property of a metamaterial by measuring the power at the output of a T-junction waveguide loaded with a metamaterial having one edge cut at 45 degrees with respect to the waveguide axis. Use of a periodic arrangement of wires and split-ring resonators; Conditions which suggest a negative index of refraction.

The article discusses the design and characterization of the magnetic metamaterials, which are found to be responsible for the suppression of surface waves propagation in antenna systems. The anisotropic magnetic plasma behavior of the materials is found to be the main reason behind the suppression.

A generalized analytical formulation for analyzing the Goos-Hanchen (GH) lateral shift direction is provided from which the phenomenon of both positive and negative GH shifts at different incident angles with left-handed material (LHM) slabs is shown. The formulation reveals that this unique phenomenon is related to the relative amplitudes of the growing and decaying evanescent waves inside the LHM slabs.

The guidance conditions of modes with both real and imaginary transverse wave numbers inside a dielectric slab with negative permittivity and permeability are discussed. In particular, propagation of guided waves inside less dense negative media is discussed.

We present experimental measurements at microwave frequencies of a double band left-handed metamaterial. The sample of metamaterial is composed of an extended version of the S-shaped resonators that exhibit simultaneously a negative permittivity and a negative permeability response at comparable frequencies. The experimental results clearly show that there exist two frequency bands where the refraction index is negative. The double left-handed passbands are due to the multiple capacitances and inductances induced in the structure, which can be further tuned to realize a metamaterial with multiple (more than two) left-handed frequency bands. [ABSTRACT FROM AUTHOR]

The guidance conditions of modes with both real and imaginary transverse wave numbers inside a dielectric slab with negative permittivity and permeability are solved. We show that for real transverse wave numbers, cutoffs exist for all modes, unlike in conventional media where the first even mode is always propagating. In addition, we also show that guided modes exist for imaginary transverse wave numbers, with the power concentrated at the interfaces instead of having maxima inside the slab. A graphical method of determining the imaginary transverse wave numbers of the guided modes is introduced which clearly identifies the different conditions of propagation depending on the properties of the slab. In particular, propagation of guided waves inside less dense negative media is shown to be possible. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]