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.

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.

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.

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.