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.

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 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.

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.

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.