Spatiotemporal Visualization of THz Near-Fields in Metamaterial Arrays

We present an experimental approach to record the spatiotemporal electric field distribution of coherent broadband THz pulses propagating through planar metamaterial arrays. The electric field can be measured with sub-wavelength precision within a volume that is several wavelengths in size, thus, having the potential to map the near-field to far-field transition of the resonant structures constituting the metamaterial. To demonstrate the potential we present measurements of THz pulses propagating through a planar array of double split-ring resonators and their inverse analogues.     

A near-field to far-field transformation for spheroidal geometry utilizing an eigenfunction expansion

This work presents a near-field to far-field (NF-FF) transformation for antenna and scatterer radiation evaluation. The transformation allows practical computation by making use of a sampling surface in the near-field that is spheroidal in shape: namely a prolate or oblate spheroid. The resulting vector wave equation does not support orthogonal vector solutions in spheroidal coordinates and instead rectangular field components are solved for using the scalar wave equation in spheroidal coordinates. The new transformation only requires knowledge of the completely-specified near-field electric field along the spheroidal transformation surface and does not need any information associated with the corresponding magnetic field. The benefit of using a spheroidal near-field geometry is its ability to closely conform to both linear and planar radiating structures while still permitting evaluation of the full far-field radiation pattern. Our approach makes use of an eigenfunction expansion of spheroidal wave-harmonics to develop two distinct, yet closely related, NF-FF transformation algorithms for each type of spheroidal surface. The spheroidal NF-FF transformation is validated and performance assessed using a well-characterized radiation structure. By applying the prolate and oblate algorithms to a radiating structure with known analytical near- and far-field electric fields, viz., a filament dipole with sinusoidal current distribution, we are able to setup and conduct multiple numerical tests that serve as a proof-of-concept for the spheroidal NF-FF transformation.     

基于Gerchberg-Papoulis算法的平面近场截断误差修正方法研究

在平面近场天线测量中,有限扫描面截断是影响测量精度的主要误差源之一,找到解决截断误差的方法是天线测量的研究重点之一.文中将平面近场天线测量中由有限区域内的场求平面波谱的过程抽象为带限函数外推的数学模型,从实际测量中的近远场变换理论出发,论证了GP（Gerchberg-Papoulis）算法应用在平面近场测量中在理论上是切实可行的.将GP算法应用在平面近场天线测量中,并分析了不同迭代次数算法的修正情况.结果表明,随着算法迭代次数的增多,可信角域外计算方向图与理论方向图差别明显减小.因此,本文的方法能够明显减小平面近场测量中截断误差的影响.除此以外,还分析了误差对算法收敛性的影响,结果表明,误差对算法修正效果影响较大.     

减小平面近场测量中多次反射误差的新方法

本文给出了用平面近场技术测量超低副瓣天线时,平面近场测量总误差与天线远场方向图副瓣电平的误差方程,并进行了计算机仿真;提出了减小平面近场测量中探头天线与待测天线间多次反射误差和微波暗室电特性误差对超低副瓣天线所引入的测量误差的"自校准法",实验结果说明该方法是解决平面近场测量中多次反射和微波暗室电特性误差较为理想的方法.     

Planar near-field to far-field transformation using an array ofdipole probes

A method is presented for computing far-field antenna patterns from measured near-field data measured by an array of planar dipole probes. The method utilizes the near-field data to determine some equivalent magnetic current sources over a fictitious planar surface which encompasses the antenna. These currents are then used to find the far fields. The near-field measurement is carried out by terminating each dipole with 50 Ω load impedances and measuring the complex voltages across the loads. An electric field integral equation (EFIE) is developed to relate the measured complex voltages to the equivalent magnetic currents. The mutual coupling between the array of probes and the test antenna modeled by magnetic dipoles is taken into account. The method of moments with Galerkin's type solution procedure is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient-fast Fourier transformation (CG-FFT) method exploiting the block Toeplitz structure of the matrix. Numerical results are presented for several antenna configurations to show the validity of the method     

A plane-polar approach for far-field construction from near-field measurements

It is well-known that the far field of an arbitrary antenna may be calculated from near-field measurements. Among various possible nearfield scan geometries, the planar configuration has attracted considerable attention. In the past the planar configuration has been used with a probe scanning a rectangular geometry in the near field, and computation of the far field has been made with a two-dimensional fast Fourier transform (FFT). The applicability of the planar configuration with a probe scanning a polar geometry is investigated. The measurement process is represented as a convolution derivable from the reciprocity theorem. The concept of probe compensation as a deconvolution is then discussed with numerical results presented to verify the accuracy of the method. The far field is constructed using the Jacobi-Bessel series expansion and its utility relative to the FFT in polar geometry is examined. Finally, the far-field pattern of the Viking high gain antenna is constructed from the plane-polar near-field measured data and compared with the previously measured far-field pattern. Some unique mechanical and electrical advantages of the plane-polar configuration for determining the far-field pattern of large and gravitationally sensitive space antennas are discussed. The time convention exp (j omega r) is used but is suppressed in the formulations.     

Planar near-field to far-field transformation using an equivalentmagnetic current approach

An alternative method is presented for computing far-field antenna patterns from near-field measurements. The method utilizes the near-field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna, and these currents are used to ascertain the far fields. Under certain approximations, the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near-field measurements are made. An electric field integral equation (EFIE) is developed to relate the near fields to the equivalent magnetic currents. The method of moments is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient method, and in the case of a rectangular matrix, a least-squares solution for the currents is found without explicitly computing the normal form of the equation. Near-field to far-field transformation for planar scanning may be efficiently performed under certain conditions. Numerical results are presented for several antenna configurations     

Synthesis of near-field patterns of arrays

A new technique of synthesis of near-field (NF) amplitude and phase patterns of linear, planar, of volume arrays of finite size or arrays located on a planar contour of finite size is presented. The array could consist of point dipoles or directive elements. The criterion for prescribing the NF (amplitude and phase) pattern information in the synthesis problem for unique determination of array excitation currents is also stated. The proposed near-field synthesis technique is based on the potential integral solution of source currents, Nyquist sampling of the near-field data and the technique of linear least square approximation (LLSA). The NF pattern synthesis technique is illustrated to synthesize a variety of NF patterns with a number of array configurations. Application of the proposed NF pattern synthesis technique to minimize distortion in far-field patterns of arrays mounted on a conducting platform and to realize array antennas with low sidelobes in the near and far field is also presented.     

Quantitative microwave imaging with a 2.45-GHz planar microwavecamera

This paper presents microwave tomographic reconstructions of the complex permittivity of lossy dielectric objects immersed in water from experimental multiview near-field data obtained with a 2.35-GHz planar active microwave camera. An iterative reconstruction algorithm based on the Levenberg-Marquardt method was used to solve the nonlinear matrix equation which results when applying a moment method to the electric field integral representation. The effects of uncertainties in experimental parameters such as the exterior medium complex permittivity the imaging system geometry and the incident field at the object location are illustrated by means of reconstructions from synthetic data. It appears that the uncertainties in the incident field have the strongest impact on the reconstructions. A receiver calibration procedure has been implemented and some ways: to access to the incident field at the object location have been assessed     

On the induced electric field gradients in the human body for magnetic stimulation by gradient coils in MRI

Prior theoretical studies indicate that the negative spatial derivative of the electric field induced by magnetic stimulation may be one of the main factors contributing to depolarization of the nerve fiber. This paper studies this parameter for peripheral nerve stimulation (PNS) induced by time-varying gradient fields during MRI scans. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic human, full-body model. Whole-body cylindrical and planar gradient sets in MRI systems and various input signals have been explored. The spatial distributions of the induced electric field and their gradients are calculated and attempts are made to correlate these areas with reported experimental stimulation data. The induced electrical field pattern is similar for both the planar coils and cylindrical coils. This study provides some insight into the spatial characteristics of the induced field gradients for PNS in MRI, which may be used to further evaluate the sites where magnetic stimulation is likely to occur and to optimize gradient coil design.     

基于傅立叶变换频移特性的平面近场测试方法

为了满足快速和无相测试现场天线的需求,文中提出了一种基于傅立叶变换频移特性的平面近场测 试方法。该方法采用多探头技术,利用各个通道的移相,达到天线角域的移动,实现了任意指向角信号的采集,具有 测试快速、使用便捷的特点,特别适用于天线的大规模生产测试和现场测试等。对一个标准喇叭天线进行了平面近 场扫描测量,对比了用传统近场数据处理插值方式得到的和用频移性质得到的天线远场方向图(E 面)。实验显示, 该方法具有与传统近场测试方法相同的效果,能有效地测试天线方向图。     

A full-wave model for EMI prediction in planar microstrip circuitsexcited in the near-field of a short electric dipole

A full-wave model to evaluate the interference induced in planar microstrip lines of arbitrary shape exposed to the near-field of an elementary electric dipole is presented. The analysis of the line response, consisting in the evaluation of the surface current excited along the microstrip line, is based on the electric dyadic Green's function method. The surface current induced on the metal strip which, for the sake of generality, is considered as embedded in the dielectric substrate, is obtained solving by means of the spectral-domain approach (SDA) the electric integral equation, which enforces the boundary condition of zero tangential electric field on the surface of the strip. The induced current is computed for different line geometries and loads, and for various positions (inside or outside the dielectric substrate) and orientations of the dipolar source. Indications towards reducing the level of the signal induced on the loads of the line are inferred     

Planar near-field scanning in the time domain .2. Sampling theoremsand computation schemes

For part 1 see ibid. vol.47, no.9, p.1280 (1994). Two computation schemes for calculating the far-field pattern in the time domain from sampled near-field data are developed and applied. The sampled near-field data consists of the values of the field on the scan plane measured at discrete times and at discrete points on the scan plane. The first computation scheme is based on a frequency-domain near-field to far-field formula and applies frequency-domain sampling theorems to the computed frequency-domain near field. The second computation scheme is based on a time-domain near-field to far-field formula and computes the time-domain far field directly from the time-domain near field. A time-domain sampling theorem is derived to determine the spacing between sample points on the scan plane. The computer time for each of the two schemes is determined and numerical examples illustrate the use and the general properties of the schemes. For large antennas the frequency-domain computation scheme takes less time to compute the full far field than the time-domain computation scheme. However, the time-domain computation scheme is simpler, more direct, and easier to program. It is also found that planar time-domain near-field antenna measurements, unlike single-frequency near-field measurements, have the capability of eliminating the error caused by the finite scan plane, and thus can be applied to broadbeam antennas     

Near-field probe used as a diagnostic tool to locate defectiveelements in an array antenna

Results of an experimental study are presented in which the near-field probe was used as a diagnostic tool to locate the defective elements in a planar array. The near-field data were processed not only to obtain the far-field patterns of the array under the test, but also to reconstruct the aperture field for diagnostic purposes. The backward transform enables the near-field probe to identify accurately aperture faults at a distance, free of interactions and couplings with the array elements. In practice, to recover the aperture field properly from the near-field distribution, the evanescent components in the computed far-field spectrum must be excluded from the inverse process with fast-Fourier-transform (FFT) techniques. For low-gain array antennas, a correction on the far-field spectrum is required to remove the contribution of the probe and the element factor before the inverse transform, strongly enhancing the resolution     

Near-field to near/far-field transformation for arbitrarynear-field geometry utilizing an equivalent electric current andMoM

Presented here is a method for computing near- and far-field patterns of an antenna from its near-field measurements taken over an arbitrarily shaped geometry. This method utilizes near-field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna. This electric current, once determined, can be used to ascertain the near and the far field. This method demonstrates the concept of analytic continuity, i.e., once the value of the electric field is known for one region in space, from a theoretical perspective, its value for any other region can be extrapolated. It is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near-field measurements are made. In this approach, the measured data need not satisfy the Nyquist sampling criteria. An electric field integral equation is developed to relate the near field to the equivalent electric current. A moment method procedure is employed to solve the integral equation by transforming it into a matrix equation. A least-squares solution via singular value decomposition is used to solve the matrix equation. Computations with both synthetic and experimental data, where the near field of several antenna configurations are measured over various geometrical surfaces, illustrate the accuracy of this method     

An overview of near-field antenna measurements

After a brief history of near-field antenna measurements with and without probe correction, the theory of near-field antenna measurements is outlined beginning with ideal probes scanning on arbitrary surfaces and ending with arbitrary probes scanning on planar, cylindrical, and spherical surfaces. Probe correction is introduced for all three measurement geometries as a slight modification to the ideal probe expressions. Sampling theorems are applied to determine the required data-point spacing, and efficient computational methods along with their computer run times are discussed. The major sources of experimental error defining the accuracy of typical planar near-field measurement facilities are reviewed, and present limitations of planar, cylindrical, and spherical near-field scanning are identified.     

Surface accuracy measurement of a deployable mesh reflector byplanar near-field scanning

Using a near-field antenna measurement facility, it is possible to simultaneously evaluate the surface accuracy of a reflector antenna as well as the far-field pattern of the antenna for a short time. The surface errors of a 2-m deployable mesh reflector for satellite use were measured by a planar near-field system. As a result, the influence of periodic structures, due to the antenna ribs, is clearly observed. Also, the surface accuracy obtained with the near field scanning technique coincides well with that obtained by an optical measurement technique     

Extrapolation of near-field RCS measurements to the far zone

An algorithmic procedure for extrapolating near-field radar cross-section (RCS) measurements to the far zone has been derived, coded, and experimentally validated. The deviation of the extrapolation algorithm uses an optical model to estimate the surface currents induced on the scattering body by the incident field, and a specially weighted version of the Fourier transform to calculate the near-field scattering amplitudes associated with such surface currents. The extrapolation entails three steps. First, near-field measurements of the scattered electric and/or magnetic field are used to infer the monostatic vector potential. Next, the inverse Fourier transform of the inferred vector potential is multiplied by a special weighting function to estimate an equivalent obliquity factor. Finally, the far-field scattering pattern is estimated by taking the Fourier transform of the reweighted obliquity factor. This extrapolation procedure has been validated using anechoic-chamber data taken on a right-circular aluminium cylinder 25 λ high and 2.5 λ in radius at near-field range of 19% of 2 D²/λ where D is the nominal target diameter and λ the radiation wavelength. The extrapolated RCS pattern for this target was compared with an analytical estimate of its far-zone pattern and good amplitude and phase agreement was observed over a 20° cone of scattering angles     

一种宽频带,近场馈电的机械扫描平面（圆盘）反射器天线

本文分析了一种宽频带，近场喇叭馈电的平面圆盘反射器机械扫描天线。天线的组成见图1。平面圆盘被处在近场区域中的喇叭照射．并绕着喇叭轴旋转使圆盘散射场形成的波瓣在水平面内扫描。采用矢量Kirchhoff公式计算由喇叭照射在圆盘表面引起的磁场，并应用物理光学方法计算圆盘产生的散射场，即圆盘的散射波瓣，其中还包括喇叭的直接辐射场。计算结果基本上与实测结果吻合。因此本文的方法可用于宽频带，机械扫描平面反射器天线的设计。