Since the concept of left-handed medium (LHM) was proposed, the causality has been a big concern in the understanding of LHM. Through an exact analysis of a 1D transient current source radiating in a LHM, the causality in the propagation of electromagnetic waves is investigated where three cases are considered for different frequency dispersions in LHM. Numerical experiments have shown that the causality would be violated if the LHM were homogeneous and frequency nondispersive in the whole frequency range or in a certain frequency band. However, such a nondispersive LHM does not exist. For a realistic artificial LHM which is frequency dispersive [Science 292, 77 (2001)], we have shown that the causality is not violated at all.

From Maxwell’s equations and the Poynting theorem, the time-domain electric and magnetic energy densities are generally defined in the frequency-dispersive media based on the conservation of energy. As a consequence, a general definition of electric and magnetic energy is proposed. Comparing with existing formulations of electric and magnetic energy in frequency-dispersive media, the new definition is more reasonable and is valid in any case. Using the new definition and staring from the equation of motion, we have shown rigorously that the total energy density and the individual electric and magnetic energy densities are always positive in a realistic artificial left-handed medium (LHM) [R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001)], which obeys actually the Lorentz medium model, although such a LHM has negative permittivity and negative permeability simultaneously in a certain frequency range. We have also shown that the conservation of energy is not violated in LHM. The earlier conclusions can be easily extended to the Drude medium model and the cold plasma medium model. Through an exact analysis of a one-dimensional transient current source radiating in LHM, numerical results are given to demonstrate that the work done by source, the power flowing outwards a surface, and the electric and magnetic energy stored in a volume are all positive in the time domain.

Artificial left-handed (LH) materials have been realized recently using a two-dimensional array of repeated unit cells of conducting rods and split ring resonators. As a consequence, part of electromagnetic energy is stored in the structure, making the equivalent LH material lossy. In this Letter, the propagation of electromagnetic waves in lossy LH materials is investigated. By introducing a small loss, we easily show that the propagating constant in LH materials is negative, and furthermore, the index of refraction is negative. Then the reflection and transmission of a Gaussian beam in a lossy LH half space and a dielectric slab are investigated, where the lossy effect on propagating and evanescent waves has been intensively studied. For the case of LH half space, it is shown that the evanescent waves have been greatly amplified when the loss is small, and can be amplified to infinity when the LH material is lossless. This is a very interesting physical phenomenon where the lossless passive LH half space is an infinite amplifier, producing a physical singularity. In a lossless LH slab, however, the physical singularity is naturally cancelled, and hence such a slab can make a perfect image [Phys. Rev. Lett. 85 (2000) 3966]. For the case of lossy LH slab, a nearly-perfect image can still be obtained when the loss is small due to the amplification of evanescent waves. Numerical simulations are presented to support the above conclusions.

It is known that the extended Born approximation (ExBorn) is much faster than the method of moments (MoM) in the study of electromagnetic scattering by three-dimensional (3-D) dielectric objects, while it is much more accurate than the Born approximation at low frequencies. Hence, it is more applicable in the low-frequency numerical simulation tools. However, the conventional ExBorn is still too slow to solve large-scale problems because it requires (2) computational load, where is the number of unknowns. In this paper, a fast ExBorn algorithm is proposed for the numerical simulation of 3-D dielectric objects buried in a lossy earth. When the buried objects are discretized with uniform rectangular mesh and the Green's functions are extended appropriately, the computational load can be reduced to (log) using the cyclic convolution, cyclic correlation, and fast Fourier transform (FFT). Numerical analysis shows that the fast ExBorn provides good approximations if the buried target has a small or moderate contrast. If the contrast is large, however, ExBorn will be less accurate. In this case, a preconditioned conjugate-gradient FFT (CG-FFT) algorithm is developed, where the solution of the fast ExBorn is chosen as the initial guess and the preconditioner. Numerical results are given to test the validity and efficiency of the fast algorithms.

The very early time electromagnetic system (VETEM) is an efficient tool for the detection of buried objects in very lossy earth, which allows a deeper penetration depth compared to the ground-penetrating radar. In this paper, the inversion of VETEM data is investigated using three-dimensional (3-D) inverse scattering techniques, where multiple frequencies are applied in the frequency range from 0-5MHz. For small and moderately sized problems, the Born approximation and/or the Born iterative method have been used with the aid of the singular value decomposition and/or the conjugate gradient method in solving the linearized integral equations. For large-scale problems, a localized 3-D inversion method based on the Born approximation has been proposed for the inversion of VETEM data over a large measurement domain. Ways to process and to calibrate the experimental VETEM data are discussed to capture the real physics of buried objects. Reconstruction examples using synthesized VETEM data and real-world VETEM data are given to test the validity and efficiency of the proposed approach.

Transmission lines with rectangular cross sections are usually used in integrated circuit (IC) and computer chip problems. In this paper, a full-wave method is proposed based on an efficient wire model to analyze transmission-line circuits, where the cross sections of wires can be arbitrary. Comparing the existing wire models in the method of moments, it has been shown that the best performance occurs when the current is assumed to flow along the electrical axis of a wire and the testing is on the whole surface if two wires are very close. The physical significance of such modeling implies that the surface current on a wire is equivalent to a current filament along the electrical axis. For a single round wire, the electrical axis is exactly the same as its geometrical axis. For two parallel round wires, the electrical axis of each wire is located at the image position of the other wire. In this paper, a general wire model is proposed to determine electrical axes of wires with arbitrary cross sections by solving a static problem. Then, full-wave formulations are derived for wire structures with rectangular cross sections, which are the most important for IC and computer-chip problems. Numerical simulations are given to test the validity and accuracy of the proposed method.

An efficient multiregion model has been proposed for the fast implementation of the electromagnetic scattering by perfectly electrical conducting (PEC) targets and the radiation of point sources or wire antennas near PEC targets. In the multiregion model, the PEC target under consideration is divided by multiple regions depending on the position of point source/antenna or the incident direction of plane waves. Then the method of moments (MoM) is used on the first region, which is close to the source or is the illuminated region, to obtain the accurate electric current. The mutual coupling between different regions are considered approximately based on the magnetic-field integral equation, from which closed-form approximations for electric currents on other regions are derived. Because MoM is only performed on the first region, the number of unknowns in the new model is much fewer than that in the full MoM analysis, making the new model much more efficient. Compared with the published hybrid methods, the multiregion model gives a more reasonable physical explanation, and provides a better accuracy in both currents and scattered fields. Numerical simulations for two-dimensional (2-D) problems (transverse-magnetic/transverse-electric) and 3-D problems are given to test the validity and efficiency of the proposed modeling.

It has been observed that super resolution is possible in the electromagnetic imaging. In the first part of the paper, the possible resolution of image is investigated in the inversion of farfield data using the diffraction tomographic (DT) algorithm, where two cases are considered when the object is in a homogeneous space and in an air-earth half space. The study shows that the resolution of image for inversion of far-field data has been limited theoretically to 0.3536-0.5 wavelength using the DT algorithm in homogeneous-space problems, and it is even worse in half-space problems. If the transmitters and receivers are located in the near-field regime, however, the image resolution is less than 0.25 wavelength, which is the super-resolution phenomenon. In the second part of the paper, the physical reason for the super-resolution phenomenon is investigated using different electromagnetic inverse scattering methods. The study has demonstrated that the information of evanescent waves in the measurement data and its involvement in inversion algorithms is the main reason for the super resolution. Four inversion algorithms are considered for half-space problems: the DT algorithm, the spatial-domain Born approximation (BA), the Born iterative method (BIM), and the distorted BIM (DBIM). The first two belong to linear inverse scattering, while the last two belong to nonlinear inverse scattering. Further analysis shows that DBIM provides a better super resolution than BIM, and BIM provides a better super resolution than BA. Numerical simulations validate the above conclusions.

The extended Born approximation (ExBorn) has been shown an efficient formulation in the electromagnetic (EM) scattering by dielectric objects in both free-space and air-earth half-space problems. In most cases, ExBorn is much more accurate than the conventional Born approximation at low frequencies. When the frequency is high or the contrast of dielectric objects is large, however, the ExBorn approximation becomes inaccurate. In this paper, new approximations are proposed for the EM scattering by dielectric objects buried in a lossy earth, which are also suitable for the case of free space. It has been shown that the zeroth-order form of new approximations is completely equivalent to ExBorn. Hence, high-order approximations can be regarded as high-order ExBorn. Closed-form formulations are derived for the new approximations. Using the fast Fourier transform (FFT), these formulations can be implemented efficiently at a cost of log, where is the number of unknowns and is a small number. Numerical simulations show that high-order ExBorn approximations are much more accurate than the ExBorn approximation.

Based on the addition theorem, the principle of a multilevel ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) has been demonstrated for three-dimensional (3-D) electromagnetic scattering problems. From a rigorous mathematical derivation, the relation among RPFMA, FAFFA, and a conventional multilevel fast multipole algorithm (MLFMA) has been clearly stated. For very large-scale problems, the translation between groups in the conventional MLFMA is expensive because the translator is defined on an Ewald sphere with many sampling K directions. When two groups are well separated, the translation can be simplified using RPFMA, where only a few sampling K directions are required within a cone zone on the Ewald sphere. When two groups are in the far-field region, the translation can be further simplified by using FAFFA where only a single K is involved in the translator along the ray-propagation direction. Combining RPFMA and FAFFA with MLFMA, three algorithms RPFMA-MLFMA, FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, which are more efficient than the conventional MLFMA in 3-D electromagnetic scattering and radiation for very large structures. Numerical results are given to verify the efficiency of the algorithms.