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The transient properties of short-pulsed elliptically/ circularly polarized antennas, namely, the transmitting and receiving effective heights, are introduced. Due to the pulsed temporal dependence of the radiation pattern, an instantaneous axial ratio is introduced as a quality measure of the polarization performance. For these antennas, it is shown that the trace of the tip of the electric-field polarization vector in time depends on the pulse-width (bandwidth) regime of the excitation signal. Only for quasi-monochromatic or narrow-band excitations is a 'pure' elliptical/circular trace achieved (i.e., axial ratio approaching unity for circular polarization). For short-pulsed excitations, a deformation of the elliptical/circular polarization vector trace is obtained due to a Hilbert-transform dependence in the antenna's effective heights and the finite duration pulsed-envelope. A remedy for that deformation, for circular polarization, is obtained by using an array of sequentially rotated circularly polarized antenna elements, which extends the temporal duration for which an instantaneous axial ratio lower than some prescribed value is obtained beyond that of a single antenna. Index Terms--Circular polarization, time-domain (TD) antennas, time-domain (TD) reciprocity, true time delay.

A fast multilevel algorithm with reduced memory requirements for the evaluation of transient near-field to far-field transforms is presented. The computational scheme is based on a hierarchical decomposition of an arbitrary shaped enclosing surface over which the near-fields of an antenna or a scatterer are given. For surface subdomains at the highest decomposition level, the angular-temporal far-field patterns are calculated directly from the known near fields over a sparse angular grid of directions and a short temporal duration. The multilevel computation comprises angular and temporal interpolations thus increasing angular resolution and temporal duration of radiation patterns while aggregating the subdomain contributions between successive decomposition levels. These steps are repeated until obtaining the transient far-field response of the whole enclosing surface. The computational complexity of the proposed algorithm is substantially lower than that of the direct evaluation. Reduction in memory requirements is obtained by formulating the algorithm as a marching-on-in-time windowed scheme. This approach allows for embedding of the accelerated transforms within existing near-field modeling tools. Index Terms--Antenna transient analysis, computation time, finite-difference (FD) methods, finite-volume (FV) methods, near-field far-field (NF-FF) transformation.

The author talks about a frame-based approach, which is used for the ultra-wideband correlation-inversion and imaging of an unknown weak and lossless scatterer embedded in a known background medium. The forward-backward propagation functions are shown to form a frame set in a finite Hilbert space in the ultra wideband domain.

A multilevel algorithm for the computation of the transient radiation patterns of true time delay (TTD) conformal arrays over a range of observation and beam steering directions is presented. The multilevel algorithm is based on hierarchical decomposition of the array into smaller sub-arrays of elements. At the finest level of decomposition, the angular-temporal radiation patterns of single-element sub-arrays are obtained over a sparse angular grid of directions and short temporal duration, by either measurement or calculation. Subsequent steps of the algorithm comprise multilevel aggregation of delayed sub-array contributions. This process continues until the transient radiation pattern of the whole array is obtained. At each level, the radiation pattern is interpolated to a finer angular grid of observations and steering directions followed by temporal delay compensation. The multilevel array decomposition algorithm attains a computational complexity substantially lower than that of the direct evaluation. Furthermore, the algorithm is particularly efficient for large arrays with large numbers of elements. Index Terms--Antenna transient analysis, computation time, domain decomposition, time-delay arrays, ultrawideband (UWB) antennas.

A new time domain (TD) representation for radiation from apertures, wherein the field is expanded in a discrete lattice of shifted, tilted, and retarded pulsed beam (PB) propagators is proposed. The PB representation provides a uniformly accurate systematic framework for ray-based tracking of ultrawide-band transient fields in complex configurations, e.g., slowly or abruptly varying inhomogeneous media. The excitation coefficients of the PBs are extracted from the aperture source distribution via a new 'discretized local slant stack transform.' The formulation is structured upon a new class of frames, termed windowed Radon transform frames. The sets of expansion and analysis functions are shown to be dual frames, thus, facilitating representation of arbitrary bandlimited source fields. Explicit expressions for the processing windows (the analysis frame set) and for the PB propagators (the expansion set) are provided for the class of isodiffracting PBs. Accuracy of the PB expansion technique is demonstrated for a focusing aperture case, that tends to fail the conventional ray shooting schemes. Index Terms--Beam summation representations, frame theory, phase space, pulsed beams (PBs), time domain (TD) radiation theory, ultrawide-band (UWB), windowed Fourier transform (WFT), windowed Radon transform (WRT).

The ultrawide-band (UWB) beam summation representation introduced in Part I of this two-part sequence, is extended here to make it more efficient for excitations with bandwidths that are larger than one octave. The main features of the basic formulation in Part I were: 1) utilization of overcomplete windowed Fourier transform (WFT) frames to construct the beam lattice (or skeleton) that is independent of the frequency; 2) the use of isodiffracting Gaussian beams (ID-GBs) provides the snuggest frame representation, and thus stable and localized expansion coefficients, for all frequencies; 3) the ID-GBs can readily be tracked in the ambient medium and, due to the ID property, their propagation parameters are calculated only once and then can be used for all frequencies. Although the basic formulation can accommodate large bandwidths, it becomes increasingly less efficient at the low end of the frequency spectrum where the overcompleteness increases. The self-consistent multiband beam-summation scheme presented here extends and generalizes the basic formulation of Part I by dividing the excitation band into one-octave sub-bands and applying the UWB beam expansion of Part I in each band. This is done, though, via a novel self-consistent scheme wherein the beam sets at the lower bands are decimated subsets of those at the highest band, so that only the set of beam-propagators at the highest band needs to be traced, while for the lower bands one uses properly decimated subsets. This approach requires less beam elements at the lower frequency bands and thus keeps the overcompleteness (oversampling) in all the bands below a given level. As in Part I, we provide the guidelines for choosing the expansion parameters and then demonstrate the effectiveness of the new scheme via a numerical example of UWB focused aperture whose frequency band spans several octaves. Index Terms--Beam summation representations, frame theory, Gaussian beams (GB), isodiffracting (ID), phase space, ultrawide-band (UWB), windowed Fourier transform (WFT).

A new discrete phase space Gaussian beam (GB) summation representation for ultrawide-band (UWB) radiation from an aperture source distribution is presented. The formulation is based on the theory of the windowed Fourier transform (WFT) frames, wherein we introduce a novel relation between the frequency and the frame overcompleteness. With this procedure, the discrete lattice of beams that are emitted by the aperture satisfies the main requirement of being frequency independent, so that only a single set of beams needs to be traced through the medium for all the frequencies in the band. It is also shown that a properly tuned class of iso-diffracting (ID) Gaussian-windows provides the 'snuggest' frame representation for all frequencies, thus generating stable and localized expansion coefficients. Furthermore, due to the ID property, the resulting GBs propagators are fully described by frequency independent matrices whose calculation in the ambient environment need to be done only once for all frequencies. Consequently, the theory may also be expressed directly in the time-domain as will be presented elsewhere. The localization implied by the new formulation is demonstrated numerically for an UWB focused aperture. It is shown that the algorithm extracts the local radiation properties of the aperture source and enhances only those beams that conform with these properties, i.e., those residing near the phase space Lagrange manifold. Further localization is due to the fact the algorithm accounts only for beams that pass within a few beamwidths vicinity of the observation point. It is thus shown that the total number of beams is much smaller than the Landau Pollak bound on the aperture's degrees of freedom. Index Terms--Beam summation representations, frame theory, Gaussian beams (GBs), phase space, ultrawide-band (UWB), windowed Fourier transform (WFT).

The radiation from a time-dependent source distribution in free-space is analyzed using time-domain (TD) spherical wave (multipole) expansion. The multipole moment functions are calculated from the time-dependent source distribution. The series convergence rate in the near and far zone and the bounds on the near-zone reactive field are determined as functions of the source support and of the pulse length. The formulation involves a spherical transmission line representation that can be extended to more general spherical configurations. This formulation also describes the field and energy transmission mechanisms in a physically transparent fashion that will be used in a companion paper to define and explore fundamental concepts such as TD reactive energy and Q and to derive bounds on the antenna properties. Finally, the concepts discussed above are demonstrated numerically for pulsed radiation by a circular current disk. Index Terms - Antenna theory, near field, short-pulse electromagnetics, time-domain analysis.

The time-domain (TD) multipole expansion, developed in the first part of this two-part sequence, is extended here to analyze the power-flow and energy balance in the vicinity of a pulsed antenna. Using the spherical transmission line formulation, we derive expressions for the pulsed power-flow and energy and identify the radiative and the reactive constituents. For time-harmonic fields, the reactive concepts are well understood in terms of the stored energy, but this interpretation is not applicable for short-pulse fields where there is no stored energy. By considering the TD energy balance, we clarify the transition of the near-zone pulsed reactive energy to the radiation power and show that the pulsed reactive energy discharges back to the source once the pulse has been radiated. We thus introduce a TD Q factor that quantifies the radiation efficiency. In particular, we show that super resolution using short-pulse fields involves large TD reactive energies and Q and is, therefore, not feasible. The general TD concepts discussed are demonstrated through a numerical example of radiation from a circular disk carrying a pulsed current distribution. Index Terms - Antenna theory, near field, Q factor, short-pulse electromagnetics, time-domain analysis.

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 effective-height' 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 time-domain 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. Index Terms - Antennas, transient analysis.