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TOC Alert for Publication# 8 2017May 22<![CDATA[Table of contents]]>655C12143232<![CDATA[IEEE Transactions on Antennas and Propagation]]>655C2C269<![CDATA[A Dual-Polarization $X$ -Band Traveling-Wave Antenna Panel for Small-Satellite Synthetic Aperture Radar]]>$X$ -band traveling-wave antenna for application in synthetic aperture radar (SAR) on a small-satellite platform. A rectangular slotted parallel-plate antenna panel capable of radiating dual polarization over the same physical aperture was selected for this purpose. The design procedure, which provides for an optimal antenna pattern in a SAR application, is described. A meta-heuristic multiobjective optimization algorithm was applied to synthesize an appropriate far-field pattern, which enhances the quality of the SAR image. Subsequently, the optimization results were used to build a more realistic model of the antenna panel in electromagnetic simulation software. An antenna panel was fabricated, and its electrical characteristics were measured. The fabricated prototype weighed 1310 g and measurements showed nearly 50% aperture efficiency for both circular polarizations [34.6-dBic right-hand circular polarized (RHCP), 34.5-dBic left-hand circular polarized (LHCP), and peak gain at 9.65 GHz], with low side-lobes. A beam shift of 2.1° was observed between the RHCP and LHCP beams at the design center frequency and was later analyzed to be the result of an error in the modeling of the adhesive layer.]]>655214421563613<![CDATA[Wideband Glass and Liquid Cylindrical Dielectric Resonator Antenna for Pattern Reconfigurable Design]]>$varepsilon _{r} = 6.85$ ) and the outer zone is filled with a dielectric liquid—ethyl acetate ($varepsilon _{r} = 7.1$ ). Both of them are put into a cylindrical container fabricated by 3-D printing technology and excited by a single coaxial probe. The inner glass DRA is excited in its broadside HEM$_{mathrm {11delta }}$ mode when the ethyl acetate is pumped out, while the conical TM$_{mathrm {01delta }}$ mode is excited in the reconstituted cylindrical DRA when the ethyl acetate is pumped in. Consequently, a mechanical reconfiguration of broadside and conical radiation patterns can be achieved over a wide impedance bandwidth of 35.5% from 3.75 to 5.37 GHz. For demonstration, the reconfigurable DRA was fabricated and measured. The measured results of the standing wave ratio, radiation pattern, gain, and efficiency are discussed. Reasonable agreement between the measured and simulated results is observed.]]>655215721641830<![CDATA[Characteristic Mode Analysis of Plasmonic Nanoantennas]]>655216521723455<![CDATA[Compact Folded Dipole With Embedded Matching Loop for Universal Tag Applications]]>$0.095lambda )$ and low in profile (1.6 mm). It is composed of a matching loop, which is encircled by two patch-shaped radiating arms, forming an embedded structure that has high compactness. Slots are etched in the radiators for fine-tuning the resonant frequency. An equivalent circuit has also been obtained for analyzing the impedance characteristics of the tag antenna across the frequency range, and it is found that the radiating element itself is capacitive and inclusion of the matching loop is essential for making the tag antenna inductive for achieving good matching with the chip. Simulation and experiment have been conducted to study the charateristics of the proposed tag antenna. When tested in free space with an Effective Isotropic Radiated Power (EIRP) input power of 3.28 W, the tag antenna is able to reach a maximum read range of 5.2 m, but it reduces to 1.8 m when placed on metal. Also, the resonant frequency of the proposed tag antenna is found to be stable and not affected much by its backing object.]]>655217321812629<![CDATA[A Low-Profile Reconfigurable Cavity-Backed Slot Antenna With Frequency, Polarization, and Radiation Pattern Agility]]>655218221892787<![CDATA[Design of Printed Chipless-RFID Tags With QR-Code Appearance Based on Genetic Algorithm]]>$times $ 30 mm and consist of a grid of small metallic elements arranged arbitrarily over a $60 times 60$ element array creating a variety of new structures. The frequency signature of the GA-based tags is optimized to fit with a frequency-shift keying-based coding methodology and a capacity of 8 b is achieved. The performance of the resultant tags is experimentally verified. Optimal tag samples are fabricated using silver-ink, low-cost flexible substrates, and by screen printing, which is a mass-compatible production technique. The feasibility of this optimization technique for the design of chipless-RFID tags is corroborated.]]>655219021951347<![CDATA[Pattern Reconfigurable Antenna Based on Morphing Bistable Composite Laminates]]>655219622073011<![CDATA[5:1 Bandwidth Dielectric Rod Antenna Using a Novel Feed Structure]]>$r = 2.53$ ) and measured performance is compared with simulation results, illustrating the effectiveness of the new feed structure in providing 5:1 bandwidth with stable radiation patterns within the entire band.]]>655220822141983<![CDATA[Slot Antenna Miniaturization Using Slit, Strip, and Loop Loading Techniques]]>655221522211750<![CDATA[Morphing Origami Conical Spiral Antenna Based on the Nojima Wrap]]>655222222324583<![CDATA[Frequency-Dependent Directive Radiation of Monopole-Dielectric Resonator Antenna Using a Conformal Frequency Selective Surface]]>655223322393158<![CDATA[A Low-Profile Omnidirectional Circularly Polarized Antenna Using Planar Sector-Shaped Endfire Elements]]>$0.62lambda _{0}$ and a low profile of $0.029lambda _{0}$ was fabricated. Experimental results show that the designed antenna has a usable bandwidth from 5.68 to 5.91 GHz (the common overlapped bandwidth limited by the −10 dB $vert S_{11}vert $ and the 3-dB axial ratio). Within the operation band, good omnidirectivity and a wide coverage can be obtained.]]>655224022472175<![CDATA[A Wideband Differentially Fed Dual-Polarized Antenna with Stable Radiation Pattern for Base Stations]]>$approx 8$ dBi) and a stable radiation pattern with 3-dB beamwidth of 65° ±5° were also found over the operating frequencies. Moreover, the proposed antenna can be easily built by using printed circuit board fabrication technique due to its compact and planar structure.]]>655224822552605<![CDATA[Bespoke Lenses Based on Quasi-Conformal Transformation Optics Technique]]>655225622643708<![CDATA[Miniaturized Transparent Metallodielectric Resonator Antennas Integrated With Amorphous Silicon Solar Cells]]>$0.18lambda $ and multimode operation with realized gain higher than 6 dBi.]]>655226522752703<![CDATA[Theory of Impedance Loaded Loop Antennas and Nanorings From RF to Optical Wavelengths]]>655227622811885<![CDATA[A Physically Reconfigurable Structurally Embedded Vascular Antenna]]>655228222882155<![CDATA[Single-Port Reconfigurable Magneto-Electric Dipole Antenna With Quad-Polarization Diversity]]>$x$ -direction, LP in $y$ -direction, left-hand circular polarization (CP), and right-hand CP. Under each of the two LP states, the reconfigurable ME dipole can be further tuned to work in two adjacent frequency ranges (i.e., a relatively higher band and a lower band). The uniqueness of this design arises from the fact that all the polarization and frequency agilities can be realized with a single port and without complicate feeding network, thus eliminating the insertion loss and considerably increased design complexity associated with a reconfigurable feeding network. Other advantages that make the proposed design attractive comparing with conventional reconfigurable microstrip antennas include the comparatively stable and high gain, nearly the same gain for both linear and CPs, symmetrical radiation pattern, and low back radiation level at the operating frequencies.]]>655228922962313<![CDATA[Compact Multimode Monopole Antenna for Metal-Rimmed Mobile Phones]]>$60 times 5 times 5$ mm$^{3}$ on a $120 times 60$ mm$^{2}$ system board, which has a narrow ground clearance and a low profile. A prototype is fabricated and measured to validate the proposed design. Measured results show that the proposed antenna has two impedance bands with $S_{11}$ less than −6 dB, i.e., 23% for the low band (0.76–0.96 GHz) and 57% for the high band (1.51–2.72 GHz). The proposed monopole antenna is capable of covering the GSM/DCS/PCS/UMTS and LTE2300/2500 bands for modern metal-rimmed mobile phone applications.]]>655229723042293<![CDATA[Maximum Achievable Power Conversion Efficiency Obtained Through an Optimized Rectenna Structure for RF Energy Harvesting]]>655230523173018<![CDATA[Ultrawideband In-Ground Multiport Antenna for Small Cell Applications]]>$4times 4$ multiple-input and multiple-output (MIMO) systems. The isolation between different ports exceed 28 dB over the commercial long term evolution bands 3 and 7. The multiport matching bandwidth of the antenna (>-0.3 dB) extends over 1700–3000 MHz range. The antenna is mechanically robust and can withstand a weight of 40 ton. MIMO performance of this antenna is verified by virtue of field measurements. A comparative study between the proposed antenna and a classic half-wavelength dipole antenna is presented highlighting the advantages of the proposed antenna. Finally, its compliance with the exposure limits for nonionizing radiation is also demonstrated.]]>655231823274869<![CDATA[Compact UHF Three-Element Sequential Rotation Array Antenna for Satcom Applications]]>$0.216lambda _{0}$ ), low cost, easy fabrication, and good performance is realized. A prototype is fabricated and measured, and the results prove the good performance of the proposed design.]]>655232823384158<![CDATA[Experimental Study of Electrically Compact Retrodirective Monopole Antenna Arrays]]>655233923471916<![CDATA[Multiobjective Beampattern Optimization in Collaborative Beamforming via NSGA-II With Selective Distance]]>655234823572454<![CDATA[An Effective Method for Synthesizing Multiple-Pattern Linear Arrays With a Reduced Number of Antenna Elements]]>655235823661736<![CDATA[High-Gain and Wide-Bandwidth Filtering Planar Antenna Array-Based Solely on Resonators]]>$4 times 4$ planar antenna arrays utilizing rectangular waveguide cavity resonators operated at X-band frequencies. The first topology is seventh order and based on 39 resonators configured in two waveguide-layers; that is one layer for the feed resonators and one layer for the radiating resonators. The second topology is fourth order based on 25 resonators configured only in a single waveguide-layer. Fabrication and measurements have been performed, showing very good agreement with the simulations.]]>655236723752333<![CDATA[Frequency Selective Surface Structure Miniaturization Using Interconnected Array Elements on Orthogonal Layers]]>$ll lambda )$ . The element can also have a low profile since the cross-layer capacitance is stronger with a thinner substrate. The sensitivity to the incident angle of the proposed structure is comparable with traditional ones. A theoretical equivalent circuit model is developed to characterize the structure, based on the analysis of the geometrical configuration of the FSS structure and the electric field distribution on it. The theory was verified by the experimental results.]]>655237623852980<![CDATA[Polarization-Independent Backscattering Enhancement of Cylinders Based on Conformal Gradient Metasurfaces]]>655238623962494<![CDATA[Analysis of Metasurfaces at Oblique Incidence]]>65523972404663<![CDATA[Miniaturization of Frequency Selective Surfaces Using 2.5-D Knitted Structures: Design and Synthesis]]>$lambda _{0}/p = 16$ , where $lambda _{0}$ is the free-space wavelength of resonant frequency and $p$ is the periodicity of unit element. In addition, the frequency response of this miniaturized FSS is also stable for various incident angles and polarizations. Furthermore, a general equivalent circuit model (ECM) is developed for 2.5-D SL-FSS by combining the prevailing electrical models of planar square loop and through-silicon vias. A wide set of parametric simulations for various element sizes, substrate thicknesses, and via counts are carried out with this ECM. Then, its performance is assessed on the basis of root-mean-square error (RMSE) criteria by comparing the results with appropriate electromagnetic simulations. The findings suggest that the ECM has sufficient accuracy for estimating the resonant frequency of 2.5-D SL-FSS with the RMSE values close to 3%. Moreover, the proposed concept of knitting is further validated by measuring two physical prototypes of the 2.5-D SL-FSS and the experimental results show a good consistency with full-wave simulations.]]>655240524123716<![CDATA[Finite-Element Modeling of Metasurfaces With Generalized Sheet Transition Conditions]]>655241324201336<![CDATA[On the Incident Power on a Receiving Slender Antenna and the Optical Theorem in the Near Field]]>655242124271447<![CDATA[Feasibility Study of Using Electrically Conductive Concrete for Electromagnetic Shielding Applications as a Substitute for Carbon-Laced Polyurethane Absorbers in Anechoic Chambers]]>655242824352140<![CDATA[Fast and Efficient Analysis of Radome-Enclosed Antennas in Receiving Mode by an Iterative-Based Hybrid Integral Equation/Modified Surface Integration Method]]>655243624451669<![CDATA[A Dynamic $p$ -Adaptive DGTD Algorithm for Electromagnetic and Multiphysics Simulations]]>$p$ -refinement. However, a global and static $p$ -refinement will increase the computational cost significantly. In this paper, a dynamic $p$ -adaptation algorithm is proposed based on the discontinuous Galerkin time-domain method, which is able to determine and adjust the basis order in a given discretization element in real time of the simulation. Based on the relation between the nodal and modal approximations defined on unstructured tetrahedral elements, an error estimator, which is very cheap to compute, is developed to determine the proper basis order to achieve a desired numerical accuracy. The dynamic $p$ -adaptation algorithm proposed in this paper is able to capture the fast varying physics by changing the order of basis functions wherever and whenever needed. Several numerical examples adopted from multiple physical disciplines are presented to demonstrate the accuracy, efficiency, and flexibility of the proposed algorithm in the simulation of electromagnetic and multiphysics problems.]]>655244624598651<![CDATA[Rotated Nonuniform Subgrids in the FDTD Method With Application to a Hemispherical Antenna Array]]>655246024662295<![CDATA[Efficient Scalable Parallel Higher Order Direct MoM-SIE Method With Hierarchically Semiseparable Structures for 3-D Scattering]]>655246724782637<![CDATA[Evaluation of 4-D Reaction Integrals in the Method of Moments: Coplanar Element Case]]>$R$ singularities, we apply the surface divergence theorem twice to obtain a novel formula for 4-D reaction integrals, generalizing earlier schemes while retaining their benefits and without distorting the original configuration space. Numerical results illustrate the method’s efficiency, which is improved by employing appropriate transformations to further smooth the resulting integrands and hence accelerate their convergence. The reaction integral formula can be extended to noncoplanar elements.]]>655247924932802<![CDATA[Versatile and Accurate Schemes of Discretization in the Scattering Analysis of 2-D Composite Objects With Penetrable or Perfectly Conducting Regions]]>655249425062765<![CDATA[Multiple-Frequency DBIM-TwIST Algorithm for Microwave Breast Imaging]]>$L^{1}$ norm and the Pareto curve. We present reconstruction examples which illustrate the benefits of these optimization strategies, which have resulted in a DBIM algorithm that outperforms our previous implementations for microwave breast imaging.]]>655250725162327<![CDATA[Interpolation of Ewald-Accelerated Periodic Green’s Function Representations for Homogeneous or Layered Media]]>655251725251700<![CDATA[Evaluation of Potential and Impedance Integrals in Analysis of Axially Symmetric Metallic Structures to Prescribed Accuracy Up To Machine Precision]]>655252625393121<![CDATA[Efficient Complex Root Tracing Algorithm for Propagation and Radiation Problems]]>$mathbb {C}times mathbb {R}$ space. Moreover, an engagement of the tracing process with a global root finding algorithm recently presented in the literature is performed. In order to confirm a validity and efficiency of the proposed technique, a few different types of structures have been analyzed.]]>655254025461178<![CDATA[An Alternative Direction Decomposition Scheme and Error Analysis for Parabolic Equation Model]]>655254725574474<![CDATA[Optimized (2, 4) Stencil Runge–Kutta ADE-ADI FDTD With Application to Plasma]]>655255825651382<![CDATA[Finite-Difference Modeling of Broadband Huygens’ Metasurfaces Based on Generalized Sheet Transition Conditions]]>655256625772352<![CDATA[Convex Space Building Discretization for Ray-Tracing]]>655257825912413<![CDATA[Cross-Correlated Contrast Source Inversion]]>655259226038289<![CDATA[Attributed Scattering Center Extraction Algorithm Based on Sparse Representation With Dictionary Refinement]]>655260426142890<![CDATA[On Unified Numerical Algorithm for 3-D Scattering From Dielectric and PEC Random Rough Surfaces]]>2) to O(N). The orthogonality and Riesz basis of the Coiflets generate well-conditioned impedance matrix, with rapid convergence for the conjugate gradient solver. In addition, a semianalytical expression of the tapered-wave carried power is derived, which speeds up computations of the normalization factor of scattering coefficients. Numerical results demonstrate that the reduced PEC model does not suffer from ill-posed problems, namely, matrix condition numbers are kept small and solutions are stable under extremely large loss tangent, where normal components of $H$ -field and tangential $E$ -field have vanished. Compared with the previous publications and laboratory measurements, good agreement is observed.]]>655261526231741<![CDATA[Ray Tracing and Modal Methods for Modeling Radio Propagation in Tunnels With Rough Walls]]>655262426341160<![CDATA[Analysis of Subchannel Correlation in Dual-Polarised MIMO Systems via a Polarisation Diversity Scheme]]>655263526442008<![CDATA[Design of a Novel Wideband and Dual-Polarized MagnetoElectric Dipole Antenna]]>655264526491556<![CDATA[A Miniature Feeding Network for Aperture-Coupled Wearable Antennas]]>$0.073 times 0.061~lambda _{0}^{2}$ at 2.45 GHz, realized on a PCB substrate of $10 times 10$ mm^{2} ($0.0817 times 0.0817~lambda _{0}^{2}$ at 2.45 GHz). The demonstration antenna incorporating the new feeding network has a realized gain of 5.6 dBi, a total efficiency of 47%, a low cross-polarization, and a high front-to-back ratio. Simulations and experiments agree well, proving the validity of the new concept.]]>655265026541093<![CDATA[Reconfiguring the Frequency and Directive Behavior of a Printed V–Shaped Structure]]>655265526601530<![CDATA[A Nonbalancing End-Fire Microstrip Dipole With Periodic-Offset DSPSL Substrate]]>655266126652489<![CDATA[Design of a Near-Field Nonperiodic Zero Phase Shift-Line Loop Antenna With a Full Dispersion Characterization]]>655266626701044<![CDATA[Design of a Wideband Antenna With Stable Omnidirectional Radiation Pattern Using the Theory of Characteristic Modes]]>$vert {text{S}_{11}}vert < -10$ dB (1.85–2.9 GHz) and stable radiation patterns at both E-plane and H-plane were achieved over the operating frequency band.]]>655267126761692<![CDATA[Low-Cost, Direct-Fed Slot Antenna Built in Metal Cover of Notebook Computer for 2.4-/5.2-/5.8-GHz WLAN Operation]]>655267726822368<![CDATA[A Triband Low-Profile High-Gain Planar Antenna Using Fabry–Perot Cavity]]>655268326881777<![CDATA[Leaky-Wave Antenna Array With a Power-Recycling Feeding Network for Radiation Efficiency Improvement]]>$m=0$ ) wave and radiates in the forward direction. The other one is designed to work on the −1th ($m = -1$ ) spatial harmonic and radiates in the backward direction. The nonradiated power at the end of one kind of the LWA is directly fed into the other (adjacent) kind of the LWA in reverse direction. Therefore, the reversed feeding can compensate the opposite radiation direction of the two kinds of LWAs, and result in a superposition of radiation. So, both the gain and radiation efficiency of the antenna can be significantly improved, while the array maintains a compact size as those of traditional planar arrays. Simulation results are compared with measurement results to validate the proposed concept of integrating different leaky-wave structures into one array.]]>655268926942276<![CDATA[Accurate Equivalent-Circuit Descriptions of Thin Glide-Symmetric Corrugated Metasurfaces]]>65526952700869<![CDATA[Diversity Study of a Frequency Selective Surface Transponder for Wearable Applications]]>65527012706885<![CDATA[Electromagnetic Fields Generated Above a Shallow Sea by a Submerged Horizontal Electric Dipole]]>655270727121098<![CDATA[A Broadband Reflectarray Antenna Using Triple Gapped Rings With Attached Phase-Delay Lines]]>655271327171828<![CDATA[Electromagnetic Performance Analysis of Graded Dielectric Inhomogeneous Streamlined Airborne Radome]]>655271827231536<![CDATA[A Triple Band Frequency Selective Surface Design for GSM Systems by Utilizing a Novel Synthetic Resonator]]>655272427271136<![CDATA[Efficient Implementation for the AH FDTD Method With Iterative Procedure and CFS-PML]]>655272827332459<![CDATA[An Upgraded ACA Algorithm in Complex Field and Its Statistical Analysis]]>65527342739977<![CDATA[An Efficient Semianalytical Method for Hypersingularity Treatment Over Curved Patches]]>65527402744548<![CDATA[Finite-Difference Time-Domain Technique for Gyroelectric Material Structure Simulation Using Recursive Convolutions in Polarization]]>65527452747277<![CDATA[A Source-Model Technique for Analysis of Waveguiding Across an Array of Arbitrary Smooth Cylinders Partially Buried in a Penetrable Substrate]]>65527482753961<![CDATA[Plane Wave Scattering by a Conducting Cylinder Located Near an Interface Between Two Dielectric Half-Spaces: A Perturbation Method]]>655275427581159<![CDATA[A Comparison Between Natural Resonances and Characteristic Mode Resonances of an Infinite Circular Cylinder]]>$ka$ values. Furthermore, by linking the standard and the generalized eigenvalue problems, a relation between natural resonances and characteristic mode eigenvalues is shown. Finally, the thesis stating that external CMR does not imply maximum field scattering is also demonstrated.]]>65527592763596<![CDATA[Human Activity Classification With Transmission and Reflection Coefficients of On-Body Antennas Through Deep Convolutional Neural Networks]]>$S_{21}$ ) and reflection coefficient ($S_{11}$ ) of on-body antennas with deep convolutional neural networks (DCNNs). It is shown that spectrograms of $S_{21}$ and $S_{11}$ exhibit unique time-varying signatures for different body motion activities that can be used for classification purposes. DCNN, a deep learning approach, is applied to spectrograms to learn the necessary features and classification boundaries. It is found that DCNN can achieve classification accuracies of 98.8% using $S_{21}$ and 97.1% using $S_{11}$ . The effects of operating frequency and antenna location on the accuracy have been investigated.]]>655276427681397<![CDATA[Full-Sphere Angle of Arrival Detection using CMRCLEAN]]>65527692772428<![CDATA[Corrections to “Lower Bounds on Q for Finite Size Antennas of Arbitrary Shape” [Jan 16 146-154]]]>[1, Appendix B] should, respectively, read as begin{align*}&hspace {-2pc}int nolimits _{V_infty }-(nabla G_{1}) G_{2}^{*} - {hat {boldsymbol {r}}} jkfrac {e^{jk( {boldsymbol {r}}_{1}- {boldsymbol {r}}_{2})cdot {hat {boldsymbol {r}}} }}{16pi ^{2}| {boldsymbol {r}}|^{2}} {dV} =-frac { {boldsymbol {r}}_{12}}{| {boldsymbol {r}}_{12}|}frac {cos (k| {boldsymbol {r}}_{12}|)}{8pi } notag \&-, jfrac {2 {boldsymbol {r}}_{1}}{8pi k^{2}}left ({ frac {sin (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{3}}-frac {kcos (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{2}} }right )notag \&-, jfrac {| {boldsymbol {r}}_{1}|^{2}-| {boldsymbol {r}}_{2}|^{2}}{8pi k^{2}}frac { {boldsymbol {r}}_{12}}{| {boldsymbol {r}}_{12}|^{2}}notag \× left ({ frac {k^{2}sin (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|}- 3left ({frac {sin (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{3}}-frac {kcos (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{2}} }right )}right ) end{align*} and begin{align*}&hspace {-2pc}int nolimits _{V_infty } j(nabla G_{1}) G_{2}^{*} - {hat {boldsymbol {r}}} kfrac {e^{jk( {boldsymbol {r}}_{1}- {boldsymbol {r}}_{2})cdot {hat {boldsymbol {r}}} }}{16pi ^{2}| {boldsymbol {r}}|^{2}} {dV} =jfrac { {boldsymbol {r}}_{12}}{| {boldsymbol {r}}_{12}|}frac {cos (k| {boldsymbol {r}}_{12}|)}{8pi } \&{-} frac { {boldsymbol {r}}_{12}}{8pi k^{2}}left ({ frac {sin (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{3}}-frac {kcos (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{2}} }right ) \&{-} frac { {boldsymbol {r}}_{1}+ {boldsymbol {r}}_{2}}{8pi k^{2}}left ({ frac {sin (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{3}}-frac {kcos (k| {boldsymb-
l {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{2}} }right ) \&{-} frac {| {boldsymbol {r}}_{1}|^{2}-| {boldsymbol {r}}_{2}|^{2}}{8pi k^{2}}frac { {boldsymbol {r}}_{12}}{| {boldsymbol {r}}_{12}|^{2}} \× left ({ frac {k^{2}sin (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|}-3left ({frac {sin (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{3}}-frac {kcos (k| {boldsymbol {r}}_{12}|)}{| {boldsymbol {r}}_{12}|^{2}} }right )}right ) \=&jfrac { {boldsymbol {r}}_{12}}{2} text {Re}{G_{12}}-frac {1}{2 k^{2}} text {Im}{nabla _{1} G_{12}} \&{-}frac { {boldsymbol {r}}_{1}+ {boldsymbol {r}}_{2}}{2 k^{2}} text {Im}left {{nabla _{1} G_{12}cdot frac { {boldsymbol {r}}_{12}}{| {boldsymbol {r}}_{12}|^{2}}}right } \&{+}frac {| {boldsymbol {r}}_{1}|^{2}-| {boldsymbol {r}}_{2}|^{2}}{2k^{2}| {boldsymbol {r}}_{12}|^{2}} text {Im}{ {boldsymbol {r}}_{12}k^{2}G_{12}+3nabla _{1} G_{12}}. end{align*} ]]>6552773277378<![CDATA[Introducing IEEE Collabratec]]>655277427742169<![CDATA[Fuel Your Imagination]]>655277527751635<![CDATA[Member Get-A-Member (MGM) Program]]>655277627763474<![CDATA[IEEE Transactions on Antennas and Propagation]]>655C3C359<![CDATA[Institutional Listings]]>655C4C4425