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Showing papers on "Near and far field published in 2012"


Journal ArticleDOI
TL;DR: It is shown that for moderate and large light scattering near field calculations the computer time required is reduced in comparison to some of the other methods.
Abstract: A near-field calculation of light electric field intensity inside and in the vicinity of a scattering particle is discussed in the discrete dipole approximation. A fast algorithm is presented for gridded data. This algorithm is based on one matrix times vector multiplication performed with the three dimensional fast Fourier transform. It is shown that for moderate and large light scattering near field calculations the computer time required is reduced in comparison to some of the other methods.

236 citations


Journal ArticleDOI
TL;DR: This work derives near field extensions of the Kerker conditions in order to determine the conditions that strongly reduce scattering in either the forward or backward directions and designs a lossless dielectric collector element whose directivity is boosted by the coherent scattering of both electric and magnetic dipoles.
Abstract: Dielectric particles supporting both magnetic and electric Mie resonances are shown to be able to either reflect or collect the light emitted by a single photon source. An analytical model accurately predicts the scattering behavior of a single dielectric particle electromagnetically coupled to the electric dipole transition moment of a quantum emitter. We derive near field extensions of the Kerker conditions in order to determine the conditions that strongly reduce scattering in either the forward or backward directions. This concept is then employed to design a lossless dielectric collector element whose directivity is boosted by the coherent scattering of both electric and magnetic dipoles.

203 citations


Journal ArticleDOI
TL;DR: The results provide a basis for intrinsic and extrinsic resonant manipulation of optical forces, control of nanoscale radiative heat transfer with optical antennas, and use of this new technique of thermal infrared near-field spectroscopy for broadband chemical nanospectroscopy.
Abstract: Despite the seminal contributions of Kirchhoff and Planck describing far-field thermal emission, fundamentally distinct spectral characteristics of the electromagnetic thermal near-field have been ...

198 citations


Patent
27 Nov 2012
TL;DR: In this paper, an antenna and a wireless mobile communication device incorporating the antenna are provided, which includes a first conductor section electrically coupled to a first feeding point, a second conductor section and a diffuser to diffuse near-field radiation generated by the second conductor sections into a plurality of directions.
Abstract: An antenna and a wireless mobile communication device incorporating the antenna are provided. The antenna includes a first conductor section electrically coupled to a first feeding point, a second conductor section electrically coupled to a second feeding point, and a near-field radiation control structure adapted to control characteristics of near-field radiation generated by the antenna. Near-field radiation control structures include a parasitic element positioned adjacent the first conductor section and configured to control characteristics of near-field radiation generated by the first conductor section, and a diffuser in the second conductor section configured to diffuse near-field radiation generated by the second conductor section into a plurality of directions.

185 citations


Journal ArticleDOI
TL;DR: In this article, the authors apply the plasmonic cloaking technique based on scattering cancellation to suppress microwave scattering from a finite-length dielectric cylinder, and verify that scattering suppression is obtained all around the object in the near and far-field and for different incidence angles, validating their measurements with analytical results and full-wave simulations.
Abstract: We report the experimental verification of metamaterial cloaking for a 3D object in free space. We apply the plasmonic cloaking technique, based on scattering cancellation, to suppress microwave scattering from a finite-length dielectric cylinder. We verify that scattering suppression is obtained all around the object in the near- and far-field and for different incidence angles, validating our measurements with analytical results and full-wave simulations. Our near- field and far-field measurements confirm that realistic and robust plasmonic metamaterial cloaks may be realized for elongated 3D objects with moderate transverse cross-section at microwave frequencies.

161 citations



Journal ArticleDOI
TL;DR: This work shows experimentally that the phase transition of VO2 entails a change of surface polariton states that significantly affects radiative heat transfer in near field, and indicates that heat flow contrasts can be realized inNear field that can be larger than those obtained in far field.
Abstract: The control of heat flow is a formidable challenge due to lack of good thermal insulators. Promising new opportunities for heat flow control were recently theoretically discovered for radiative heat flow in near field, where large heat flow contrasts may be achieved by tuning electronic excitations on surfaces. Here we show experimentally that the phase transition of ${\mathrm{VO}}_{2}$ entails a change of surface polariton states that significantly affects radiative heat transfer in near field. In all cases the Derjaguin approximation correctly predicted radiative heat transfer in near field, but it underestimated the far field limit. Our results indicate that heat flow contrasts can be realized in near field that can be larger than those obtained in far field.

129 citations


Journal ArticleDOI
TL;DR: In this paper, the optical properties of metal-dielectric-metal structures with patterned top metallic surfaces, in the THz frequency range, were studied and a detailed analysis of the physical mechanisms which give rise to these photonic modes were provided.
Abstract: We present an experimental and theoretical study of the optical properties of metal-dielectric-metal structures with patterned top metallic surfaces, in the THz frequency range. When the thickness of the dielectric slab is very small with respect to the wavelength, these structures are able to support strongly localized electromagnetic modes, concentrated in the subwavelength metal-metal regions. We provide a detailed analysis of the physical mechanisms which give rise to these photonic modes. Furthermore, our model quantitatively predicts the resonance positions and their coupling to free space photons. We demonstrate that these structures provide an efficient and controllable way to convert the energy of far field propagating waves into near field energy.

115 citations


Journal ArticleDOI
TL;DR: In this paper, the near field solution for the scattering of a plane monochromatic electromagnetic wave by an ensemble of parallel infinite dielectric cylinders at perpendicular incidence is presented.
Abstract: The near field solution for the scattering of a plane monochromatic electromagnetic wave by an ensemble of parallel infinite dielectric cylinders at perpendicular incidence is presented in this paper. The solution is given for the calculation of the electric and magnetic near fields and the Poynting vector. A MATLAB program has been developed to solve the near field formulas which is introduced and validated. The near to far field transition as well as formation and transport of photonic nanojets have been calculated for multiple cylinder scattering.

112 citations


Journal ArticleDOI
TL;DR: It is demonstrated that by using nanostructured electromagnetic fields, the selection rules of absorption spectroscopy could be fundamentally manipulated and forbidden transitions between discrete quantum levels in a semiconductor nanorod structure are allowed within the near-field of a noble metal nanoparticle.
Abstract: In conventional spectroscopy, transitions between electronic levels are governed by the electric dipole selection rule because electric quadrupole, magnetic dipole, and coupled electric dipole-magnetic dipole transitions are forbidden in a far field. We demonstrated that by using nanostructured electromagnetic fields, the selection rules of absorption spectroscopy could be fundamentally manipulated. We also show that forbidden transitions between discrete quantum levels in a semiconductor nanorod structure are allowed within the near-field of a noble metal nanoparticle. Atomistic simulations analyzed by an effective mass model reveal the breakdown of the dipolar selection rules where quadrupole and octupole transitions are allowed. Our demonstration could be generalized to the use of nanostructured near-fields for enhancing light-matter interactions that are typically weak or forbidden.

96 citations


Journal ArticleDOI
TL;DR: The excitation of plasmonic resonances in arrays of periodically arranged gold nanoparticles placed in a uniform refractive index environment is examined and possibilities for electric field enhancement in the region between the nanoparticles are explored.
Abstract: We examine the excitation of plasmonic resonances in arrays of periodically arranged gold nanoparticles placed in a uniform refractive index environment. Under a proper periodicity of the nanoparticle lattice, such nanoantenna arrays are known to exhibit narrow resonances with asymmetric Fano-type spectral line shape in transmission and reflection spectra having much better resonance quality compared to the single nanoparticle case. Using numerical simulations, we first identify two distinct regimes of lattice response, associated with two-characteristic states of the spectra: Rayleigh anomaly and lattice plasmon mode. The evolution of the electric field pattern is rigorously studied for these two states revealing different configurations of optical forces: the first regime is characterized by the concentration of electric field between the nanoparticles, yielding to almost complete transparency of the array, whereas the second regime is characterized by the concentration of electric field on the nanoparticles and a strong plasmon-related absorption/scattering. We present electric field distributions for different spectral positions of Rayleigh anomaly with respect to the single nanoparticle resonance and optimize lattice parameters in order to maximize the enhancement of electric field on the nanoparticles. Finally, by employing collective plasmon excitations, we explore possibilities for electric field enhancement in the region between the nanoparticles. The presented results are of importance for the field enhanced spectroscopy as well as for plasmonic bio and chemical sensing.


Journal ArticleDOI
TL;DR: In this article, the equivalence principle was used to cancel the electromagnetic scattering of an object by using an array of sources by superimposing magnetic and electric surface current densities at the boundary of the object.
Abstract: Electromagnetic cloaking refers to the ability to prevent an object from scattering an incident electromagnetic field This has been accomplished in recent works by specially designed materials Another way of cloaking using sources has been known in the acoustics community In this letter, we introduce a prescription for canceling the electromagnetic scattering of an object by using an array of sources By using the equivalence principle, we show that by superimposing magnetic and electric surface current densities at the boundary of an object, the scattered fields from that object can be canceled These magnetic and electric surface currents can be discretized into electric and magnetic dipoles that are physically implementable by straight and loop wire antennas Finally, we confirm our results using numerical simulations

Journal ArticleDOI
TL;DR: To the authors' knowledge, this is the first time that both far- and near-field spectroscopy are carried out for identical individual nanostructures interacting via a subnanometer gap.
Abstract: Strongly coupled plasmons in a system of individual gold nanoparticles placed at subnanometer distance to a gold film (nanoparticle-on-plane, NPOP) are investigated using two complementary single particle spectroscopy techniques. Optical scattering spectroscopy exclusively detects plasmon modes that couple to the far field via their dipole moment (bright modes). By using photoemission electron microscopy (PEEM), we detect in the identical NPOPs near-field modes that do not couple to the scattered far field (dark modes) and are characterized by a strongly enhanced nonlinear electron emission process. To our knowledge, this is the first time that both far- and near-field spectroscopy are carried out for identical individual nanostructures interacting via a subnanometer gap. Strongly resonant electron emission occurs at excitation wavelengths far off-resonant in the scattering spectra.

Journal ArticleDOI
TL;DR: In this paper, spectrally resolved near and far field measurements were performed for a diode laser with 50 µm stripe width, and it was shown that current-induced thermal lensing dominates the lateral waveguiding, in spite of the presence of both strong built-in index guiding and gain guiding.
Abstract: For maximum fibre-coupled power, high power broad area diode lasers must operate with small lateral far field angles at high continuous wave (CW) powers. However, these structures are laterally multi-moded, with low beam quality and wide emission angles. In order to experimentally determine the origin of the low beam quality, spectrally resolved near and far field measurements were performed for a diode laser with 50 µm stripe width. Within the range measured (CW optical output powers to 1.5 W) the laser is shown to operate in just six stable lateral modes, with spatially periodic profiles. Comparisons of the measured profiles with the results of two-dimensional modal simulation demonstrate that current-induced thermal lensing dominates the lateral waveguiding, in spite of the presence of both strong built-in index guiding and gain guiding. No evidence is seen for filamentation. Building on the diagnosis, proposals are presented for improvements to beam quality.

01 Jan 2012
TL;DR: In this paper, it was shown that stored energy defined from the difference between the energy density and the far field energy equals the energy expressions proposed by Vandenbosch for many but not all cases.
Abstract: Decomposition of the electromagnetic energy into its stored and radiated parts is instrumental in the evaluation of antenna Q and the corresponding fundamental limitations on antennas. This decomposition is not unique and there are several proposals in the literature. Here, it is shown that stored energy defined from the difference between the energy density and the far field energy equals the energy expressions proposed by Vandenbosch for many but not all cases. This also explains the observed cases with negative stored energy and suggests a possible remedy to them. The results are compared with the classical explicit expressions for spherical regions where the results only differ by the electrical size ka that is interpreted as the far-field energy in the interior of the sphere.

Journal ArticleDOI
TL;DR: In this article, a near field power transfer equation for an inductively coupled near field system, analogous to the Friis transmission equation for far field communications, is derived based on the equivalent circuit model of the coupled resonant loops.
Abstract: A near field power transfer equation for an inductively coupled near field system, analogous to Friis transmission equation for far field communications, is derived based on the equivalent circuit model of the coupled resonant loops. Experimental results show the proposed near field coupling equation is trustworthy as it correctly predicts the transferred power versus distance relationship for different values of loaded quality factors at the transmitter and the receiver. Capacity performance of near field communication (NFC) links are analyzed based on information theory, respectively for noise limited and interference limited scenarios. The analytical results provide guidelines for power and capacity budget in inductively coupled antenna systems. Examples of inductively coupled VLF NFC links are evaluated for different operating scenarios, demonstrating the efficacy and importance of the proposed method for near field link budget.

Journal ArticleDOI
TL;DR: In this paper, a cylindrical cloak is designed to control the bending waves propagating in isotropic thin plates, which is achieved through homogenization of a multiply perforated coating of homogeneous elastic material, which greatly simplifies the design of the multilayered cloak.
Abstract: A cylindrical cloak is designed to control the bending waves propagating in isotropic thin plates. This is achieved through homogenization of a multiply perforated coating of isotropic homogeneous elastic material, which greatly simplifies the design of the multilayered cloak we proposed [Phys. Rev. Lett. 103, 024301 (2009)]. We first derive the homogenized biharmonic equation, which involves an anisotropic Young's modulus and an isotropic mass density. We then numerically show that a clamped obstacle is cloaked over a finite range of frequencies for an acoustic source located a couple of wavelengths away from its surrounding cloak. The reduced backward and forward scattering is confirmed by both the profile of the total field computed along a line passing through the source and the center of the cloak (near field confirmation), and the computation of the scattered far field.

Journal ArticleDOI
TL;DR: In this article, a conformal metamaterial-inspired Egyptian axe dipole antenna is introduced, and its performance characteristics are presented, where a combination of metastructures is used to achieve high directivity, electrically small, low profile, linear (LP) and circularly polarized (CP) near-field resonant parasitic (NFRP) antennas.
Abstract: A combination of metastructures is used to achieve high directivity, electrically small, low-profile, linear (LP) and circularly polarized (CP) near-field resonant parasitic (NFRP) antennas. A conformal metamaterial-inspired Egyptian axe dipole antenna is introduced, and its performance characteristics are presented. The electrically small, low-profile LP and CP high-directivity systems are achieved by amalgamating this NFRP antenna with an electromagnetic band-gap (EBG) structure, which acts as an artificial magnetic conductor (AMC) ground plane. As with all of the nonconformal metamaterial-inspired antennas, the designs of the driven and parasitic elements of these low-profile antennas are tailored to achieve nearly complete matching of the entire system to a 50- source without any matching network and to yield high radiation efficiencies.

Journal ArticleDOI
TL;DR: In this article, the optical properties of metallic nanoparticles (MNP) have been controlled by nanolithography techniques, including the geometrical parameters of the MNPs (size, shape, and gap), the LSP characteristics (near field decay length and resonance position), and the excitation parameters (excitation wavelength and associated electric field polarization).
Abstract: Major improvements in fabrication techniques at the nanoscale during the last two decades enable us to exploit and control nanoscale phenomena such as the localized surface plasmons (LSP) provided by metallic nanoparticles (MNP). The large enhancement of the electromagnetic field due to plasmonic effects increases drastically the response of any analyte located close to or adsorbed on MNPs, which opens ways for detection of very low concentration of analytes and sensor miniaturization. However, the efficiency of such nanosensors requires a precise control of the optical properties of the MNPs since it strongly depends on their geometrical properties. Such precision can be reached by nanolithography techniques. The parameters that govern the near field enhancement include the geometrical parameters of the MNPs (size, shape, and gap), the LSP characteristics (near field decay length and resonance position) and the excitation parameters (excitation wavelength and associated electric field polarization). Nanolithography techniques used for surface nanostructuring include optical, focused electron and ion beams, nanoimprint and nanosphere lithographies. Nanosensor fabricated lithographically exploit localized surface plasmon resonance, surface enhanced Raman scattering, and surface enhanced fluorescence.

Journal ArticleDOI
TL;DR: A novel broadband antenna for ultrahigh-frequency (UHF) near-field radio frequency identification (RFID) applications is presented and demonstrates good performance of tag identification with inductive coupling for near- field RFID applications.
Abstract: A novel broadband antenna for ultrahigh-frequency (UHF) near-field radio frequency identification (RFID) applications is presented. The antenna is composed of a grounded coplanar waveguide (GCPW), a coplanar stripline (CPS), a lumped balun, multiple resistors, and a finite-sized ground plane. The load impedance is equal to the characteristic impedance of the CPS, hence traveling wave can transmit along the CPS. The proposed antenna structure can produce large currents along the CPS so that a strong and uniform magnetic field distribution is excited in the adjacent region around the antenna. The antenna geometry, design concept, simulated, and measured results are carefully discussed throughout the paper. Measurements show that the antenna operating with a commercial reader demonstrates good performance of tag identification with inductive coupling for near-field RFID applications. In addition, the parametric study is conducted to facilitate the design and optimization processes for engineers.

Journal ArticleDOI
TL;DR: In this paper, a super-directive array composed of closely spaced electrically small resonant magnetic dipole elements is presented, which can exhibit a maximum directivity of 11.5 dBi, 15.2 dBi and 17.8 dBi for 2, 3, and 4 magnetic dipoles, respectively.
Abstract: The theory as well as numerical and experimental results are presented for a superdirective array composed of closely spaced electrically small resonant magnetic dipole elements. The array operates on a metal ground plane and can exhibit a maximum directivity of 11.5 dBi, 15.2 dBi, and 17.8 dBi (including 3 dB due to the ground plane), for 2, 3, and 4 magnetic dipoles, respectively. The array is self-resonant and is directly excited by a 50-ohm coaxial cable through the ground plane. The array radiates essentially the |μ| = 1 spherical modes, which, despite a narrow bandwidth, makes it an excellent first-order probe for spherical near-field antenna measurements at low frequencies.

Journal ArticleDOI
TL;DR: In this paper, the optical properties of dense spatially ordered two-dimensional arrays of 50 nm gold nanoparticles are investigated in this aim, and the experimental findings are then compared with calculations based on the discrete dipole approximation.
Abstract: Understanding the plasmon coupling between metal nanoparticles under light irradiation remains a challenging issue for optimizing plasmonic devices for chemical and biological sensing. Here, the optical properties of dense spatially ordered two-dimensional arrays of 50 nm gold nanoparticles are investigated in this aim. Microspectrophotometry experiments are carried out on square arrays and parallel chains, elaborated by electron beam lithography, having different periodicities ranging from 80 to 170 nm. The wavelength, width, and amplitude of the localized surface plasmon resonance (SPR) are quantitatively monitored as a function of both the incident light polarization and the interparticle distance. The experimental findings are then compared with calculations based on the discrete dipole approximation. They match remarkably well these numerical results, not only for the spectral location and the width of the SPR but also for the absolute value of the extinction cross section of the nanoparticles that i...

Journal ArticleDOI
TL;DR: In this article, a near-field plate that can generate an evanescent Bessel beam is presented, which consists of nonperiodic concentric corrugations that surround a coaxially fed aperture.
Abstract: We present a near-field plate that can generate an evanescent Bessel beam. The metallic plate consists of nonperiodic concentric corrugations that surround a coaxially fed aperture. The design procedure for such a device is outlined. The designed plate is simulated using a full-wave electromagnetic solver and is shown to produce an evanescent Bessel beam, thereby verifying its design and operation. The performance of the near-field plate is contrasted against a coaxial probe and a near-field plate designed to produce an Airy focal pattern with the same beamwidth. Such a device, capable of producing evanescent Bessel beams, will find applications in near-field probing/imaging systems, data storage, and biomedical devices.

Journal ArticleDOI
TL;DR: An integrated microparticle passive sorting system based on the near-field optical forces exerted by a 3-dB optical splitter that consists of a slot waveguide and a conventional channel waveguide is demonstrated and provides a new technique for sorting sub-micron particles.
Abstract: We demonstrate an integrated microparticle passive sorting system based on the near-field optical forces exerted by a 3-dB optical splitter that consists of a slot waveguide and a conventional channel waveguide. We show that 320 nm and 2 µm polystyrene particles brought into the splitter are sorted so that they exit along the slot waveguide and channel waveguide, respectively. Electromagnetic simulations and precise position tracking experiments are carried out to investigate the sorting mechanism. As the waveguides are separated by 200 nm, they provide two potential wells for the smaller particles, but only one broad potential well for the larger particles, since their diameters exceed the distance between the two field maxima. A structural perturbation consisting of a stuck bead transfers the smaller particles to the second well associated with the slot waveguide, while the larger particles are brought to the region between the two waveguides and eventually follow the channel waveguide, as it is associated with a deeper potential well. This label-free passive particle sorting system requires low guided power (20 mW in these experiments), and provides a new technique for sorting sub-micron particles.

Journal ArticleDOI
TL;DR: This work presents a theoretical approach to analyze solar cell performance by allowing rigorous electromagnetic calculations of the emission rate using the fluctuation-dissipation theorem and shows the direct quantification of the voltage, current, and efficiency of low-dimensional solar cells.
Abstract: Current methods for evaluating solar cell efficiencies cannot be applied to low-dimensional structures where phenomena from the realm of near-field optics prevail. We present a theoretical approach to analyze solar cell performance by allowing rigorous electromagnetic calculations of the emission rate using the fluctuation-dissipation theorem. Our approach shows the direct quantification of the voltage, current, and efficiency of low-dimensional solar cells. This approach is demonstrated by calculating the voltage and the efficiency of a GaAs slab solar cell for thicknesses from several microns down to a few nanometers. This example highlights the ability of the proposed approach to capture the role of optical near-field effects in solar cell performance.

Patent
03 Apr 2012
TL;DR: In this paper, a near field transducer comprising a conductive metal film and an optical waveguide for illumination of the near-field transducers is described, where a light guiding core layer of the waveguide is spaced from the transducers by less than about 100 nanometers and greater than 0 nanometers.
Abstract: An apparatus according to one embodiment includes a near field transducer comprising a conductive metal film; and an optical waveguide for illumination of the near field transducer, a light guiding core layer of the optical waveguide being spaced from the near field transducer by less than about 100 nanometers and greater than 0 nanometers, wherein a longitudinal axis of the optical waveguide is substantially perpendicular to an air bearing surface.

Journal ArticleDOI
TL;DR: The results show that surface waves corrupt the received signals over the longest transmission distances across the measurement array, however, the surface wave effects can be eliminated provided the feed line lengths are sufficiently long independently of the distance of the transmitting/receiving antenna tips from the imaging tank floor.
Abstract: Microwave imaging techniques are prone to signal corruption from unwanted multipath signals. Near-field systems are especially vulnerable because signals can scatter and reflect from structural objects within or on the boundary of the imaging zone. These issues are further exacerbated when surface waves are generated with the potential of propagating along the transmitting and receiving antenna feed lines and other low-loss paths. In this paper, we analyze the contributions ofmulti-path signals arising from surface wave effects. Specifically, experiments were conducted with a near-field microwave imaging array positioned at variable heights from the floor of a coupling fluid tank. Antenna arrays with different feed line lengths in the fluid were also evaluated. The results show that surface waves corrupt the received signals over the longest transmission distances across the measurement array. However, the surface wave effects can be eliminated provided the feed line lengths are sufficiently long independently of the distance of the transmitting/receiving antenna tips from the imaging tank floor. Theoretical predictions confirm the experimental observations.

Journal ArticleDOI
TL;DR: In this paper, the authors presented a passive UHF printed loop antenna with left-handed loading, which can work at near and far-field operation within the European UHF (865-868 MHz) band.
Abstract: This letter presents a passive UHF printed loop antenna with left-handed loading. The RFID reader antenna can work at near- and far-field operation within the European UHF (865-868 MHz) band. The operation frequency and radiation properties can be modified by employing varactor diodes. Also, the antenna can work in the near-field region having a flat magnetic distribution in the interrogation zone. A comparative study with other passive RFID reader conventional antennas shows that the left-handed loop achieves stronger near H-field with good impedance matching. Design details, simulated results, and a fabricated prototype are presented. The concept significantly extends the design degrees of freedom for RFID antennas.

Journal ArticleDOI
TL;DR: In this paper, the authors present an analysis of the near fields of antenna arrays using an alternative approach taking into account field variations due to mutual coupling. But their method does not require solving Maxwell's equations under the customary boundary condition, but is based instead on searching for equivalent dipole models that are capable of reproducing the same radiated fields of the actual array (ideally obtained through accurate measurement).
Abstract: This paper presents an analysis of the near fields of antenna arrays using an alternative approach taking into account field variations due to mutual coupling. The method does not require solving Maxwell's equations under the customary boundary condition, but is based instead on searching for equivalent dipole models that are capable of reproducing the same radiated fields of the actual array (ideally obtained through accurate measurement.) We treat mutual coupling between array elements as essentially a multiple scattering effect and propose a method to calculate the near field of arbitrary linear arrays with significant electromagnetic coupling. It is found that a single (analytical) dipole model obtained under certain circumstances, which are detailed in the paper, can be used to predict correctly the near field radiated by arbitrary-size antenna arrays. The paper ends by developing an application of the equivalent dipole method by expanding the near fields into a sum of propagating and nonpropagating parts. It is shown that the 3-D spatial Fourier transform required in this expansion can be eliminated when the dipole model is used in computing the near field in the domain of the validity of the model.