Wave propagation in a double negative (DNG) medium, i.e., a medium having negative permittivity and negative permeability, is studied both analytically and numerically. The choices of the square root that leads to the index of refraction and the wave impedance in a DNG medium are determined by imposing analyticity in the complex frequency domain, and the corresponding wave properties associated with each choice are presented. These monochromatic concepts are then tested critically via a one-dimensional finite difference time domain (FDTD) simulation of the propagation of a causal, pulsed plane wave in a matched, lossy Drude model DNG medium. The causal responses of different spectral regimes of the medium with positive or negative refractive indices are studied by varying the carrier frequency of narrowband pulse excitations. The smooth transition of the phenomena associated with a DNG medium from its early-time nondispersive behavior to its late-time monochromatic response is explored with wideband pulse excitations. These FDTD results show conclusively that the square root choice leading to a negative index of refraction and positive wave impedance is the correct one, and that this choice is consistent with the overall causality of the response. An analytical, exact frequency domain solution to the scattering of a wave from a DNG slab is also given and is used to characterize several physical effects. This solution is independent of the choice of the square roots for the index of refraction and the wave impedance, and thus avoids any controversy that may arise in connection with the signs of these constituents. The DNG slab solution is used to critically examine the perfect lens concept suggested recently by Pendry. It is shown that the perfect lens effect exists only under the special case of a DNG medium with $\epsilon \left(\omega \right)=\mu \left(\omega \right)=-1$ that is both lossless and nondispersive. Otherwise, the closed form solutions for the field structure reveal that the DNG slab converts an incident spherical wave into a localized beam field whose parameters depend on the values of $\epsilon$ and $\mu .$ This beam field is characterized with a paraxial approximation of the exact DNG slab solution. These monochromatic concepts are again explored numerically via a causal two-dimensional FDTD simulation of the scattering of a pulsed cylindrical wave by a matched, lossy Drude model DNG slab. These FDTD results demonstrate conclusively that the monochromatic electromagnetic power flow through the DNG slab is channeled into beams rather then being focused and, hence, the Pendry perfect lens effect is not realizable with any realistic metamaterial.

The design, fabrication, and testing of several metamaterials that exhibit double negative (DNG) medium properties at X band frequencies are reported. DNG media are materials in which the permittivity and permeability are both negative. Simulation and experimental results are given that demonstrate the realization of DNG metamaterials matched to free-space. The extraction of the effective permittivity and permeability for these metamaterials from reflection and transmission data at normal incidence is treated. It is shown that the metamaterials studied exhibit DNG properties in the frequency range of interest.

Planar metamaterials that exhibit a zero index of refraction have been realized experimentally by several research groups. Their existence stimulated the present investigation, which details the properties of a passive, dispersive metamaterial that is matched to free space and has an index of refraction equal to zero. Thus, unlike previous zero-index investigations, both the permittivity and permeability are zero here at a specified frequency. One-, two-, and three-dimensional source problems are treated analytically. The one- and two-dimensional source problem results are confirmed numerically with finite difference time domain (FDTD) simulations. The FDTD simulator is also used to treat the corresponding one- and two-dimensional scattering problems. It is shown that in both the source and scattering configurations the electromagnetic fields in a matched zero-index medium take on a static character in space, yet remain dynamic in time, in such a manner that the underlying physics remains associated with propagating fields. Zero phase variation at various points in the zero-index medium is demonstrated once steady-state conditions are obtained. These behaviors are used to illustrate why a zero-index metamaterial, such as a zero-index electromagnetic band-gap structured medium, significantly narrows the far-field pattern associated with an antenna located within it. They are also used to show how a matched zero-index slab could be used to transform curved wave fronts into planar ones.

A metamaterial paradigm for achieving an efficient, electrically small antenna is introduced. Spherical shells of homogenous, isotropic negative permittivity (ENG) material are designed to create electrically small resonant systems for several antennas: an infinitesimal electric dipole, a very short center-fed cylindrical electric dipole, and a very short coaxially-fed electric monopole over an infinite ground plane. Analytical and numerical models demonstrate that a properly designed ENG shell provides a distributed inductive element resonantly matched to these highly capacitive electrically small antennas, i.e., an ENG shell can be designed to produce an electrically small system with a zero input reactance and an input resistance that is matched to a specified source resistance leading to overall efficiencies approaching unity. Losses and dispersion characteristics of the ENG materials are also included in the analytical models. Finite element numerical models of the various antenna-ENG shell systems are developed and used to predict their input impedances. These electrically small antenna-ENG shell systems with idealized dispersionless ENG material properties are shown to be very efficient and to have fractional bandwidths above the values associated with the Chu limit for the quality factor without any degradation in the radiation patterns of the antennas. Introducing dispersion and losses into the analytical models, the resulting bandwidths are shown to be reduced significantly, but remain slightly above (below) the corresponding Chu-based value for an energy-based limiting (Drude) dispersion model of the permittivity of the ENG shell.

Planar two-dimensional (2D) and volumetric three-dimensional (3D) metamaterial-inspired efficient electrically-small antennas that are easy to design; are easy and inexpensive to build; and are easy to test; are reported, i.e., the EZ antenna systems. The proposed 2D and 3D electrical- and magnetic-based EZ antennas are shown to be naturally matched to a 50 source, i.e., without the introduction of a matching network. It is demonstrated numerically that these EZ antennas have high radiation efficiencies with very good impedance matching between the source and the antenna and, hence, that they have high overall efficiencies. The reported 2D and 3D EZ antenna designs are linearly scalable to a wide range of frequencies and yet maintain their easy-to-build characteristics. Several versions of the 2D EZ antennas were fabricated and tested. The measurement results confirm the performance predictions. The EZ antennas systems may provide attractive alternatives to existing electrically-small antennas.

The effect of surrounding an electrically small dipole antenna with a shell of double negative (DNG) material (/spl epsiv//sub r/<0 and /spl mu//sub r/<0) has been investigated both analytically and numerically. The problem of an infinitesimal electric dipole embedded in a homogeneous DNG medium is treated; its analytical solution shows that this electrically small antenna acts inductively rather than capacitively as it would in free space. It is then shown that a properly designed dipole-DNG shell combination increases the real power radiated by more than an order of magnitude over the corresponding free space case. The reactance of the antenna is shown to have a corresponding decrease. Analysis of the reactive power within this dipole-DNG shell system indicates that the DNG shell acts as a natural matching network for the dipole. An equivalent circuit model is introduced that confirms this explanation. Several cases are presented to illustrate these results. The difficult problem of interpreting the energy stored in this dipole-DNG shell system when the DNG medium is frequency independent and, hence, of calculating the radiation Q is discussed from several points of view.