Wave propagation in media having negative permittivity and permeability - art. no. 056625

Wave propagation in a double negative (DNG) medium. i.e., a medium having n egative permittivity and negative permeability. is studied both analyticall y and numerically. The choices of the square root that leads to the index o f refraction and the wave impedance in a DNG medium are determined by impos ing 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 d ifferent spectral regimes of the medium with positive or negative refractiv e indices are studied by varying the carrier frequency of narrowband pulse excitations. The smooth transition of the phenomena associated with a DNG m edium from its early-time nondispersive behavior to its late-time monochrom atic response is explored with wideband pulse excitations. These FDTD resul ts show conclusively that the square root choice leading to a negative inde x of refraction and positive wave impedance is the correct one, and that th is choice is consistent with the overall causality of the response. An anal ytical, 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 in dex of refraction and the wave impedance. and thus avoids any controversy t hat may arise in connection with the signs of these constituents. The DNG s lab solution is used to critically examine the perfect lens concept suggest ed recently by Pendry. It is shown that the perfect lens effect exists only under the special case of a DNG medium with epsilon(omega) = mu(omega) = - 1 that is both lossless and nondispersive. Otherwise. the closed form solut ions for the field structure reveal that the DNG slab converts an incident spherical wave into a localized beam field whose parameters depend on the v alues of epsilon and mu. This beam field is characterized with a paraxial a pproximation of the exact DNG slab solution. These monochromatic concepts a re again explored numerically via a causal two-dimensional FDTD simulation of the scattering of a pulsed cylindrical wave by a matched, loss Drude mod el DNG slab. These FDTD results demonstrate conclusively that the monochrom atic electromagnetic power flow through the DNG slab is channeled into beam s rather then being focused and, hence, the Pendry perfect lens effect is n ot realizable with any realistic metamaterial.