Amir Shlivinski

Time-domain near-field analysis of short-pulse antennas .I. Spherical wave (multipole) expansion

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.

Time-domain near-field analysis of short-pulse antennas .II. Reactive energy and the antenna Q

For pt. I see ibid., vol.47, no.2, p.271-79 (1999). 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.

A phase-space beam summation formulation for ultrawide-band radiation. II: a multiband scheme

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.

A Unified Kinematic Theory of Transient Arrays

We have present a unified framework for the kinematic analysis of transient arrays. In addition to the side-lobes (SL) and the grating-lobes (GL), which are due to phase-interference, we also identified cross-pulse-lobes (CPL) which are an intrinsic wideband phenomenon. It has been shown that the lobe structure is an interplay of several mechanisms and controlled by the problem parameters: the center frequency, the fractional bandwidth, the pulse repetition rate, the inter-element spacing and the total number of elements. It has been shown that the conventional frequency domain dense-array condition d<c/f where f is the frequency, which is used to avoid the formation of GL, is irrelevant in the UWB case and in fact the UWB signal spectrum does not have to satisfy this condition. Thus, under these conditions one may use sparse array (with inter-element spacing much larger than the wavelength for all frequencies in the band) without suffering from sever GL problems.

KINEMATIC PROPERTIES OF SHORT-PULSED SPARSE TRANSMITTING ARRAYS

The kinematic properties of an array of transmitting antennas that are transiently excited by a sequence of modulated pulses, with high repetition rate, are explored. The arrays parameterization is carried out via the energy radiation pattern. It is shown that the energy radiation pattern can be decomposed into a set of difierent types of beam contributions, deflned over a beam- skeleton, which is determined by the arrays physical and excitation parameters. The difierent types of beams are main beams, grating- lobe beams and cross-pulsed lobe beams, each corresponding to a difierent pulsed interference mechanism. While grating lobes are time- harmonic phenomena, cross-pulsed lobes are unique for excitation with a pulsed sequence. The difierent beam types set limits for array sparsity in terms of the arrays physical and excitation parameters. The arrays directivity is introduced as a flgure of merit of its performance and to demonstrate the resulting efiect of the time-domain excitation characteristics. The arrays parameterization can be used with any type of excitation | from extreme narrow band (time-harmonic) to extreme ultra-wideband (transient/short pulsed) excitation. For time- harmonic excitation, the resulting characterization matches that of the classical frequency domain antenna theory.

Time-Domain Circularly Polarized Antennas

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 ldquopurerdquo 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 antennas 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.

Back-Propagation and Correlation Imaging Using Phase-Space Gaussian-Beams Processing

We present a beam-based imaging scheme for targets in homogeneous medium whereby the fields of the source and receiver arrays are expanded using special phase-space bases of collimated beam fields, thus converting the physical data into a beam-domain data describing the scattering amplitudes seen (synthetically) by the receiver beams due to excitation by the source beams. The image is then formed by correlating the backpropagated beam data with the incident beams. The formulation utilizes the ultra-wideband phase-space beam-summation method where the beam bases consist of Gaussian beams that emerge from a discrete set of points and directions in the source and the receiver domains. An important feature of this method is that the beam-sets are frequency independent and hence are calculated once and then used for all frequencies. A closed form expression for the data-transformation matrix from the physical domain to the beam domain is derived, leading to sparse beam-domain data. The beam approach enables local imaging of any sub-domain of interest by retaining only the subset of source and receiver beams that pass through that domain, thus reducing the overall computation complexity. The method properties are explored via numerical simulations in a noisy environment.

Multilevel Surface Decomposition Algorithm for Rapid Evaluation of Transient Near-Field to Far-Field Transforms

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.

Time domain radiation by scalar sources: Plane wave to multipole transform

The radiation from a pulsed source distribution can be described by a spectrum of time-dependent plane waves or of spherical waves (multipoles). These two fundamental representations are based on the slant stack transform and on the time-dependent multipole moment, respectively. In this article, we present a direct transformation relating these two representations.

Characteristic Basis Functions of the Energy Radiation Pattern of a Sparse True Time Delay Array

A set of characteristic basis functions of the energy radiation pattern for a true-time-delay array of equi-spaced elements radiating a pulsed/transient wave-fleld was derived. This set is determined by the array layout and by the set of excitation waveforms that can be used to expand the actual excitation pulse. It is established that the characteristic basis function set spans the mapping of the square amplitudes of the discrete Fourier transform of the excitation coe-cients to the energy radiation pattern. This mapping is further used to analyze array performance and re-examine the term array sparsity. Additional use of this set can be found in synthesizing an array radiation pattern to meet prescribed requirements.