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.     

柱面波激励的超宽带口径辐射特性的研究

如何高效而又较少畸变地将信号辐射出去是超宽带天线的设计关键，本文利用FDTD方法研究了柱面波激励不同形状、尺寸口径时口径的辐射特性，并用空时方向图表征口径在主辐射面的辐射波形与口径尺寸、形状以及激励脉冲的脉宽在自由空间展布的宽度之间的关系。通过与平面波正投射时口径的辐射特性进行比较，得出在上述两种激励脉冲激励口径的情况下不同形状和尺寸的口径的辐射特性的差异。     

A radiation center representation of antenna radiation patterns ona complex platform

A sparse model of the antenna radiation pattern on a complex platform is presented. This representation is based on a point radiator model that describes the radiation pattern by a collection of radiation centers on the platform. The methodology for obtaining the radiation center model is presented. It entails first generating the three-dimensional (3-D) antenna synthetic aperture radar (ASAR) imagery of the platform and then parameterizing the resulting image by a collection of point radiators via the CLEAN algorithm. It is shown that once such a representation is obtained, we can reconstruct and extrapolate antenna radiation patterns over frequencies and aspects with good fidelity, thus achieving high data compression ratio. Furthermore, it is shown that the resulting radiation center information can be used to pinpoint cause-and-effect in platform scattering and provide important guidelines for reducing platform effects     

Narrow-waisted Gaussian beam discretization for short-pulseradiation from one-dimensional large apertures

We develop a Gabor-based Gaussian beam (GB) algorithm for representing two-dimensional (2-D) radiation from finite aperture distributions with short-pulse excitation in the time domain (TD). The work extends previous results using 2-D frequency-domain (FD) narrow-waisted Gaussian beams. The FD algorithm evolves from the rigorous Kirchhoff integration over the aperture distribution, which is then parameterized via the discrete Gabor basis and evaluated asymptotically for high frequencies to furnish the GB propagators to the observer. The TD results are obtained by Fourier inversion from the FD and yield pulsed beams (PB). We describe the resulting TD algorithm for several aperture distributions, ranging from simple linearly phased (linear delay) to arbitrary time delay profiles; the latter accommodate the important case of focusing TD aperture fields. For modulated pulses with Gaussian envelopes, we compute accurate closed form analytic solutions, which have been calibrated against numerical reference data. Our results confirm that the previously established utility of the Gabor-based narrow-waisted FD-GB algorithm for radiation from distributed apertures remains intact in the TD     

Gabor's expansion of an aperture field in exponential elementarybeams

Gabor's expansion of an aperture field in a discrete two-dimensional superposition of Gaussian elementary beams is extended to incorporate exponential beams. The resultant expansion scheme has an advantage over the commonly used Gaussian beam representation in situations involving an exponential aperture distribution such as the modal field in a thin slab laser amplifier     

Study of deployed and modular active phased-array multibeam satellite antenna

A deployed, self-cooled and modular (tile-based) active phased array for multibeam applications has recently been proposed in the literature. This novel antenna facilitates the implementation of large array antennas in space with many beams from the same aperture, offering a flexible payload with the potential for high traffic capacity. However, the configuration also raises some questions about degradation in antenna performance, due to constraints such as non-circular aperture, frame gap, uniform amplitude excitation, and a calibration boom deployed in front of the array. Methods dealing with these issues are discussed in this paper. It is shown that a phase-only optimization technique can effectively reduce interference between same-frequency spatially reused beams, and can compensate for EIRP and C/I degradation for tile-correlated errors and failures.     

Cross-shaped and four-ridge waveguide—Horn radiators: Internal and external characteristics

A mathematical model is developed for smooth-wall waveguide-horn radiators with an arbitrary cross section of the aperture. The exterior problem is solved in the Huygens-Kirchhoff approximation and the interior problem is solved with the use of a numerical algorithm constructed on the basis of the finite-element method. Internal (cutoff frequencies of modes, the field structure, attenuation coefficients, the wave impedance, and the maximum transmitted power of the fundamental mode) and external (radiation patterns, polarization characteristics, the aperture efficiency, and matching to free space) characteristics of dual-polarization waveguide-horn radiators with cross-shaped and four-ridge circular and square cross sections are investigated. Optimum relationships for cross-sectional dimensions that maximize the operating bandwidth, minimize the loss level, and maximize the power transmitted through the waveguides are found. It is shown that optimization of cross-sectional parameters can ensure a high degree of the axial symmetry of radiation patterns, a good matching to free space, and a low level of sidelobe radiation in the operating frequency band—characteristics which are better than those of similar radiators with square and circular cross sections. Numerical results are compared with experimental data.     

Simple state-space formulations of 2-D frequency transformation and double bilinear transformation

In this paper, an explicit relationship between the two-dimensional (2-D) frequency transformation and the theory of linear fractional transformation (LFT) representation is shown. Based on this relationship, a simple alternative state-space formulation of 2-D frequency transformation for 2-D digital filters is derived by utilizing the well-known Redheffer star product of LFT representations. The proposed formulation is then utilized to establish a simple relationship between the state-space representations of a 2-D continuous system and a 2-D discrete system which are related by the double bilinear transformation. Moreover, the inherent relations among the proposed formulations and the existing results are discussed. It turns out that all the existing results given in the literature can be unified as special or equivalent cases by the new state-space formulation of 2-D frequency transformation in a very concise and elegant form. Numerical examples are given to illustrate the effectiveness of the proposed formulations.     

Time-domain radiation from large two-dimensional apertures via narrow-waisted Gaussian beams

This paper deals with the short-pulse radiation of three-dimensional (3-D) vector electromagnetic fields from arbitrarily polarized large two-dimensional (2-D) truncated aperture distributions, which are parameterized in terms of narrow-waisted ray-like pulsed Gaussian basis beams centered on a discretized Gabor lattice in a four-dimensional (4-D) configuration-spectrum phase space. The study extends our previous Gabor-based investigation of time-domain (TD) short-pulse radiation of 2-D fields from 1-D large truncated apertures with nonphased, linearly phased (delayed) and nonlinearly phased focusing aperture field profiles . We begin with, and summarize, a Gabor-based frequency domain (FD) formulation of the 2-D aperture problem which has been presented and tested elsewhere, but we include additional numerical examples for validation and quality assessment. As done by Galdi, Felsen and Castanon (see ibid., vol 49, p. 1322-32, Sept. 2001) we access the time domain by Fourier inversion from the FD, starting from the initial 3-D space-time Kirchhoff formulation (whose numerical integration furnishes reference solutions), and then passing on to Gabor-parameterized field representations in terms of pulsed beam (PB) wavepackets which are launched by linearly and nonlinearly phase-delayed focusing aperture distributions. Example calculations and comparisons with numerically generated reference data serve to calibrate the Gabor-PB algorithms and assess their domains of validity.     

Certain considerations in aperture synthesis ofultrawideband/short-pulse radiation

The authors consider certain characteristics of the radiation from collimated, ultrawideband short-pulse aperture distributions. It is shown that an efficient radiation must account for the multifrequency nature of the field. Two alternative schemes for wideband aperture synthesis of an impulse-like radiation pattern are examined. The first, entitled the “iso-width aperture”, utilizes only temporal shaping of the excitation pulse. In the other, the “iso-diffracting aperture”, they suggest source shaping in space-time so that all the frequency components in the field have the same collimation distance. The “iso-diffracting” scheme yields higher directivity and more efficient pulsed radiation. Explicit examples for the pulsed source distribution and for the pulsed radiation patterns are presented, parametrized, and contrasted     

Theory on small radiating apertures in the outer sheath of a coaxial cable

An analytical expression for the aperture field is obtained from an integral equation formulation and a subsequent use of a quasistatic approach in which the dominant part of the solution can be extracted from canonical problems. Unlike the conventional approach of replacing the aperture field by equivalent dipoles, our method retains the basic features of the propagating mode in the coaxial region, and the radiation characteristic of the coaxial cylinder. An equivalent network representation of a small aperture is then derived. The network equivalence of a symmetrical aperture with its axes oriented in the direction of the incident field is shown to consist of a lumped shunt capacitanceC_{b}and a series impedanceZcomposed of an inductive elementL_{b}, a capacitive elementC_{T}and the input admittanceY_{binfty}of the external antenna, all in parallel.     

Natural-mode representation of transient scattered fields

Electromagnetic scattering from a perfectly conducting body of finite extent is considered from an integral equation point of view. It is shown that the operator inverse to the integral operator of the magnetic field formulation is an analytic operator-valued function in the complex frequency plane except at certain points (the natural frequencies) where it has poles. Furthermore, a representation of the inverse operator in terms of the natural frequencies and the nontrivial solutions of the homogeneous integral equation is given. Explicit expressions for the scattered field in terms of exponentially damped sinusoidal oscillations are given for the special case where the incident wave is a delta-function plane wave and the inverse operator has only simple poles.     

Systematic study of fields due to extended apertures by Gaussianbeam discretization

Gaussian beams are used as basis elements in field representations. To gain insight into how the choice of beam parameters affects the final representation, a systematic study for the simple test case of a one-dimensional linearly phased cosine-aperture distribution has been undertaken. By successively adding individual displaced and/or tilted beams with large, narrow, or matched waists, one can assess how the elements in various portions of the lattice contribute to the build-up of the actual field in the aperture, near zone, and far zone. Adding enough beams always guarantees homing in on the exact solution, as is verified here by independent comparison. Different beam choices imply different modeling of the radiation process. The understanding gained thereby is helpful for selecting beam parameters in subsequent applications where it is necessary to balance requirements of good convergence, ease of computation, and ability to track the beams through perturbing environments like a radome. Indications are that the narrow beams provide the most robust and versatile formulation to deal with these generalized conditions     

Computation of optical flow using basis functions

The issues governing the computation of optical flow in image sequences are addressed. The trade-off between accuracy versus computation cost is shown to be dependent on the redundancy of the image representation. This dependency is highlighted by reformulating Horn's (1986) algorithm, making explicit use of the approximations to the continuous basis functions underlying the discrete representation. The computation cost of estimating optical flow, for a fixed error tolerance, is shown to be a minimum for images resampled at twice the Nyquist rate. The issues of derivative calculation and multiresolution representation are also briefly discussed in terms of basis functions and information encoding. A multiresolution basis function formulation of Horn's algorithm is shown to lead to large improvements in dealing with high frequencies and large displacements.     

Gaussian beam analysis of propagation from an extended planeaperture distribution through dielectric layers. I. Plane layer

High-frequency propagation of electromagnetic wavefields from an extended planar aperture distribution through a complicated environment is addressed. Geometric optical ray tracing provides a versatile approximate approach to the class of problems, but it fails in transition regions surrounding shadow boundaries and caustics. The uniformity required there can be established by field tracking with Gaussian beams. The basic theory is summarized and applied to the two-dimensional test problem of transmission of radiation from a finite one-dimensional plane aperture through a planar dielectric layer. For a truncated uniform or focused aperture illumination, tracking the edge or caustic transition regions through the layer when it is located within the Fresnel zone of the aperture poses a problem of substantial complexity. It is shown that narrow-waisted beams, which can be propagated in their far zone as complex ray fields, reconstruct the correct transmitted field in these cases, as established independently by numerical evaluation of an exact spectral integral     

宽带平面直角双频单极天线

对于超宽带系统,需要具备可工作频率为3.1~10.6GHz的宽带天线。本文介绍了四种宽带平面单极天线,分别为圆形平面单极天线、平面直角单极天线、平面双频单极天线和平面直角双频单极天线。其中平面直角单极天线兼具宽频和全向特性,平面双频单极天线和平面直角双频单极天线在两个谐振点都具有宽带特性,平面直角双频单极天线在整个频带内水平面的辐射方向图几乎都可以达到全向。     

Discrete radiation from curved single-mode fibres: a comparison of theories

An apparent discrepancy between coupled-mode and `whispering-gallery? theories for the radiation of discrete beams from curved single-mode fibres is resolved. It is shown that the two formally different approaches are in very good agreement with each other in predicting the periodicity of the radiation.     

Discrete-time, discrete-frequency, time-frequency analysis

A formulation of a discrete-time, discrete-frequency Wigner distribution for analysis of discrete-time, periodic signals is given using an approach involving group representation theory. This approach is motivated by a well-known connection between group theory and the continuous Wigner distribution. The advantage of this approach is that the resulting discrete distribution satisfies mathematical properties analogous to those satisfied by the continuous distribution. After outlining the relationship between group representation theory and time-frequency analysis, we derive the discrete distribution and exhibit many of its mathematical properties. These include time and frequency marginals, the Weyl correspondence, and covariance. In particular, the interpretation of covariance for the discrete distribution is shown to be different than that for the continuous distribution. Finally, we note some unusual features of this discrete distribution, which are a consequence of the group-theoretic derivation     

硬边光阑光学计算方法的比较研究

对通过硬边光阑光学系统光束传输问题的直接数值积分法、复高斯函数展开法、矩阵法和光束模式展开法作了比较研究。研究表明,直接数值积分应用范围广泛,但随着光阑数的增加,它变得既烦琐又耗时。复高斯函数展开法为快速模拟硬边衍射光束在菲涅耳区和夫琅和费区的传输提供了一个有用方法,只是在很近的场存在着显著的计算误差。矩阵法能用于菲涅耳区和夫琅和费区,但只适用于旋转对称的光学系统与光束。光束模式展开法可用于近似计算远场的弱截断光束。     

二维信号Wigner分布的数值计算

Wigner分布函数作为一个同时表达空间 频率变量的函数 ,在光学领域中有着广泛的应用。提出了二维信号Wigner分布函数的数值计算方法 ,并模拟了一些二维实信号 (圆孔 ,圆环和方孔 )的Wigner分布函数