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(omega)=mu(omega)=-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.
A theory for a complete far-field transmit-receive system characterization of short-pulse antennas is derived in the time domain. The transmit-receive antenna system is characterized by a set of cascaded operators, which traPnsform the source waveform and power into similar quantities at the receiving antenna terminals. Two such sets are defined. The first one is phrased in terms of the wave-type "time-dependent effectiveheight" operator, while the second one is defined in terms of the energy-type "gain operator." Both definitions fit within a complete transmit-receive system description, the latter being equivalent to the frequency-domain Friis equation. However, these operators are derived entirely in the context of the timedomain field equation. The starting point in the time-domain analysis of the effective height is the slant stack transform (SST) of the time-dependent current distribution in a manner equivalent to the spatial Fourier transform used in the frequency domain. The vector autocorrelation of the transmitting effective height is then used to define the time-dependent gain operator under impulsive source excitation. Time-domain reciprocity leads to the definitions of antenna parameters under receiving conditions and the corresponding equivalent circuit. The parameters defined in this way fit within a consistent transmit-receive convolution operator, operating on the autocorrelation of the input signal. This independent time-domain representation is thus similar to the frequency-domain representation. However, unlike the conventional frequency-domain circuit parameters, which relate voltage and current amplitudes, the time-domain circuit representation is based on incident and reflected wave-type constituents. In addition, the use of appropriate norms facilitates the transformation of our operators to stand-alone figures of merits. The general concepts developed herein are demonstrated for the example of the short dipole antenna.
Paraxial Gaussian beams (GB's) are collimated wave objects that have found wide application in optical system analysis and design. A GB propagates in physical space according to well-established quasi-geometric-optical rules that can accommodate weakly inhomogeneous media as well as reflection from and transmission through curved interfaces and thin-lens configurations. We examine the GB concept from a broad perspective in the frequency domain (FD) and the short-pulse time domain (TD) and within as well as arbitrarily beyond the paraxial constraint. For the formal analysis, which is followed by physics-matched high-frequency asymptotics, we use a (space-time)-(wavenumber-frequency) phase-space format to discuss the exact complex-source-point method and the associated asymptotic beam tracking by means of complex rays, the TD pulsed-beam (PB) ultrawideband wave-packet counterpart of the FD GB, GB's and PB's as basis functions for representing arbitrary fields, GB and PB diffraction, and FD-TD radiation from extended continuous aperture distributions in which the GB and the PB bases, installed through windowed transforms, yield numerically compact physics-matched a priori localization in the plane-wave-based nonwindowed spectral representations.
Pulsed beam (PS) are highly localized space-time wavepackets solutions of the time-dependent wave equation that propagate al ong ray trajectories . Because they have these properties, PB ma.y be useful in various applications including mode li ng of highly focused energy t ransfer or ulLra wide bandwidth Radar beams, local interrogation of the propagation environment and computational electromagnetics. Several classes of wave packet solutions of the homogeneous wave-equation in free space have bee n introduced rec ently [1-9]. The present paper is concerned with PB fields in inhomogeneous medium. Utilizing the fact that these fields are high ly locali zed in spacetime we derive an approximate form of the time-dependent wave equation withi n a moving space-time window that bracket the PB. ·We then construct exact PB solution of this equation. This is done for both PB in free space and for PB in smoothly varying medium. Utilizing loc ality we also show how these PB are reflected and transmitted at a curved dielectric interface.Of particular importance in the present context are the complex source pulsed beam (CSPB) [7-9]' These are exact solutions of the time-dependent wave equation that can be modeled in terms of radiation from a. pulsed source located at a co mplex coo rd inate point. Physically, the CSPB are generated in te rms of radiation from a real time-dependent source distribution of finite Support [B ,9]j the complex source model is therefore a mathematical trick to derive simple exp ressions for the field radiated by this distribution. Near thei r propagation axis, the globally exact CSPB are similar to t he present paraxial PB solutions. The present solutions, however , have a more general form as they admit wavepacket astigmatism.An important feature of the CSPB is that they furnish exact closed-form solutions for scattering and diffraction by canonical configurations. Because of t he local nature of the PB, it is then possible to derive local scattering models that may be applied for non-canonical configurations that possess the same local characteristics in the pe rtinent space-time window. Following this route we analyzed the canonical problems of PB interaction with planar dielect ric inte rface [10,11] and with a perfectly conducting wedge {12]. These exact solutions validate the present paraxial models. The results are aJso important in diffract ion theory and in inverse scattering since by aiming the incident PB at specific regions and directions one may selectively excite local diffraction mec hanisms a.nd explore the sca.tter's local chara.cte ristics,The P B solut ions int roduced here can also be described by an ultra wide spect rum of time-harmonic Gaussian beams that have the same (i.e. frequency independent) waist plane and collimation length. This implies that t hei r beamwidth is proportional -593-to w-1 / 2 • Propagation of Gaussian beam in smoothJ y inhomogeneous med ium has been thoroughly inves tigated in [13). Reflection and transmission at curved interfaces have been described by ...
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