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.