Incident Electromagnetic Field Research Articles

Analysis and Experimental Study of Radiative Microwave Pulses Effects on the Nonlinear Performance of a Low-Noise Amplifier

In this article, the performance of an unshielded low-noise amplifier (LNA), which is subjected to the incident high power microwave (HPM) pulse waves, is investigated analytically and experimentally. For this purpose, a time-domain algorithm is proposed, which uses the finite difference time domain (FDTD) method and a globally convergent iterative method to solve linear and nonlinear equations of the problem simultaneously. In particular, the effects of external incident electromagnetic (EM) field illumination with different types of waveforms, including HPM pulses and sinusoidal waves, on the nonlinear performance of a microwave LNA are investigated and discussed by this method. Furthermore, using a measurement setup comprised of a transverse EM (TEM) cell, the proposed method is validated by comparing with the measurement results in good agreement. The presented analysis would be useful in EM interference/compatibility (EMI/EMC) analysis, such as radiated susceptibility analysis of RF/microwave nonlinear circuits excited by the incident HPM pulse wave.

Electromigrated nanogaps: A review on the fabrications and applications

Electromigration—a critical failure mode of metal interconnects in integrated circuits—has been exploited for constructing nanometer-sized gaps (or nanogaps, less than a few nanometers) on metallic nanowires. Electromigrated nanogaps have been utilized extensively in the field of nanotechnology and have demonstrated to be an effective platform for electrically accessing small things such as molecules in a device fashion, establishing metal-molecule-metal junctions. These devices allow the study of the electronic transport phenomena through molecules and DNA. Furthermore, electromigrated nanogaps can read out incident electromagnetic fields as an antenna due to the plasmonic excitation on the surface, which is usually maximized in nanogaps. Moreover, structural changes caused by electromigration on metallic nanowires have been leveraged to create single-component resistive switching memories. In this review, we discuss the recent progress and challenges of electromigration methods for a nanogap creation as well as their applications for electronic devices (molecular/DNA devices and resistive switches), thermoelectric energy conversion devices, and photonic devices (nanoantennas).

Intelligent Surface-Aided Transmitter Architectures for Millimeter-Wave Ultra Massive MIMO Systems

In this paper, we study two novel massive multiple-input multiple-output (MIMO) transmitter architectures for millimeter wave (mmWave) communications which comprise few active antennas, each equipped with a dedicated radio frequency (RF) chain, that illuminate a nearby large intelligent reflecting/transmitting surface (IRS/ITS). The IRS (ITS) consists of a large number of low-cost and energy-efficient passive antenna elements which are able to reflect (transmit) a phase-shifted version of the incident electromagnetic field. Similar to lens array (LA) antennas, IRS/ITS-aided antenna architectures are energy efficient due to the almost lossless over-the-air connection between the active antennas and the intelligent surface. However, unlike for LA antennas, for which the number of active antennas has to linearly grow with the number of passive elements (i.e., the lens aperture) due to the non-reconfigurablility (i.e., non-intelligence) of the lens, for IRS/ITS-aided antennas, the reconfigurablility of the IRS/ITS facilitates scaling up the number of radiating passive elements without increasing the number of costly and bulky active antennas. We show that the constraints that the precoders for IRS/ITS-aided antennas have to meet differ from those of conventional MIMO architectures. Taking these constraints into account and exploiting the sparsity of mmWave channels, we design two efficient precoders; one based on maximizing the mutual information and one based on approximating the optimal unconstrained fully digital (FD) precoder via the orthogonal matching pursuit algorithm. Furthermore, we develop a power consumption model for IRS/ITS-aided antennas that takes into account the impacts of the IRS/ITS imperfections, namely the spillover loss, taper loss, aperture loss, and phase shifter loss.

Single-Conductor Transmission Line Model Incorporating Radiation Reaction

Increasing attention has been paid to the study of electromagnetic (EM) phenomena in complicated wire networks [e.g., metamaterials and EM compatibility (EMC)]. However, their lack of physical insights usually prevents systematic analysis of the phenomena. To address this, this article describes a transmission line (TL) model of a finite-length single conductor without a return current path to be applied as a fundamental physical model. The model includes radiation effects in a self-consistent way (i.e., its radiation reaction is included in an explicit way), and it is based on Sommerfeld principal wave propagation (strictly speaking, its behavior is asymptotic as the wire's conductivity approaches infinity). This formulation naturally leads to the consequence that the current flowing along a single conductor illuminated by an incident EM field is classified into three components, which are dominated by physically distinct principles, the principal wave itself (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> , the traveling wave), the one reinduced by the traveling wave radiation (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">re</sub> , the radiation reaction), and the one that directly scatters the incident field (I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sc</sub> , the scattering wave). The EM energies of the traveling wave and radiation reaction components are stored in the TL and propagate, while the scattering component indicates an instantaneous scattering process. These components reveal the dynamical characteristics of a single-conductor TL model that includes radiation phenomena.

Inverse design method of microscatterer array for realizing scattering field intensity shaping

It is a novel and interesting idea to inversely design the scattering structure with the desired scattering field intensity distribution in a given target area as the known information. The inverse design method proposed in this paper does not need to be optimized, and the spatial distribution and dielectric constant distribution of the micro-scatterer array can be quickly analytically calculated according to the desired scattering field intensity in the target area. First, based on the spatial Fourier transform and angular spectrum transformation, the plane wave sources required in all directions are inversely obtained from the electric field intensity distribution required in the target area. Then, based on the theory of induced source, a method of irradiating the array of all-dielectric micro-scatterers with incident electromagnetic field to generate the required plane wave source is proposed. The scattering fields generated by these micro-scatterers will be superimposed on the target area to achieve the desired scattering field strength intensity. Finally, according to the proposed inverse design theory model, a specific three-dimensional (3D) design is carried out. In the 3D example, we study the scattering field intensity distribution of the point-focused shape of the square surface target area, and show an all-dielectric micro-sphere distribution design. Its spatial distribution and permittivity distribution are both obtained through the rapid analytical calculation of the desired scattered field intensity shape in the target area. Finally, based on the principle of linear superposition, we quickly and easily generate the complex shapes of “I”, “T”, and “X” in the target area. The satisfactory results of full-wave simulation show that the proposed inverse design method is effective and feasible.

A high-speed programmable and scalable terahertz holographic metasurface based on tiled CMOS chips

Metasurfaces, which consist of arrays of subwavelength scatterers, can be used to precisely control incident electromagnetic fields, but are typically static once fabricated. A dynamically programmable array of terahertz meta-elements, in which each element can be individually reconfigured to allow controlled wavefront shaping, could be of value in terahertz applications such as wireless communication, sensing and imaging. Here, we show that large-scale programmable metasurfaces can be created using arrays of complementary metal–oxide–semiconductor (CMOS)-based chip tiles. We developed an aperture with a 2 × 2 array of tiled chips consisting of 576 meta-elements, each individually addressable and digitally programmable with 8 bits of control at GHz speed, and fabricated in a 65 nm industry-standard CMOS process. The active-circuit-coupled terahertz meta-element structure can be reconfigured, providing digitally programmable metasurfaces with amplitude and phase control, around 25 dB of amplitude modulation depth, dynamic beamforming across ±30°, multibeam formation and programmable holographic projections at 0.3 THz. The integration of active electronic systems and meta-elements using commercial silicon fabrication techniques can be used to create scalable and dynamically programmable terahertz metasurfaces.

Full wavefield simulation versus measurement of microwave scattering by a complex 3D-printed asteroid analogue

Context. The small bodies of the Solar System, and especially their internal structures, are still not well-known. Studies of the interior of comets and asteroids could provide important information about their formation and also about the early Solar System. Aims. In this paper, we investigate the possibility of obtaining information about their inner structure from their response to an incident electromagnetic field in preparation for future space radar missions. Our focus is on experimental measurements concerning two analog models with the shape of 25143 Itokawa, a small rubble pile asteroid monitored by the Japanese space agency’s (JAXA) Hayabusa mission in 2005. Methods. The analog models prepared for this study are based on the a priori knowledge of asteroid interiors of the time. The experimental data were obtained by performing microwave-range laboratory measurements. Two advanced in-house, full-wave modelling packages – one performing the calculations in the frequency domain and the other one in the time domain – were applied to calculate the wave interaction within the analog models. Results. The electric fields calculated via both the frequency and time domain approach are found to match the measurements appropriately. Conclusions. The present comparisons between the calculated results and laboratory measurements suggest that a high-enough correspondence between the measurement and numerical simulation can be achieved for the most significant part of the scattered signal, such that the inner structure of the analog can be observed based on these fields. Full-wave modeling that predicts direct and higher order scattering effects has been proven essential for this application.

Light-Induced Voltages in Catalysis by Plasmonic Nanostructures.

ConspectusPlasmonic nanostructures have garnered widescale scientific interest because of their strong light-matter interactions and the tunability of their absorption across the solar spectrum. At the heart of their superlative interaction with light is the resonant excitation of a collective oscillation of electrons in the nanostructure by the incident electromagnetic field. These resonant oscillations are known as localized surface plasmon resonances (LSPRs). In recent years, the community has uncovered intriguing photochemical attributes of noble metal nanostructures arising from their LSPRs. Chemical reactions that are otherwise unfavorable or sluggish in the dark are induced on the nanostructure surface upon photoexcitation of LSPRs. This phenomenon has led to the birth of plasmonic catalysis. The rates of a variety of kinetically challenging reactions are enhanced by plasmon-excited nanostructures. While the potential utility for solar energy harvesting and chemical production is clear, there is a natural curiosity about the precise origin(s) of plasmonic catalysis. One explanation is that the reactions are facilitated by the action of the intensely concentrated and confined electric fields generated on the nanostructure upon LSPR excitation. Another mechanism of activation involves hot carriers transiently produced in the metal nanostructure by damping of LSPRs.In this Account, we visit a phenomenon that has received less attention but has a key role to play in plasmonic catalysis and chemistry. Under common chemical scenarios, plasmonic excitation induces a potential or a voltage on a nanoparticle. This photopotential modifies the energetics of a chemical reaction on noble metal nanoparticles. In a range of cases studied by our laboratory and others, light-induced potentials underlie the plasmonic enhancement of reaction kinetics. The photopotential model does not replace other known mechanisms, but it complements them. There are multiple ways in which an electrostatic photopotential is produced by LSPR excitation, such as optical rectification, but one that is most relevant in chemical media is asymmetric charge transfer to solution-phase acceptors. Electrons and holes produced in a nanostructure by damping of LSPRs are not removed at the same rate. As a result, the slower carrier accumulates on the nanostructure, and a steady-state charge is built up on the nanostructure, leading to a photopotential. Potentials of up to a few hundred millivolts have been measured by our laboratory and others. A photocharged nanoparticle is a source of carriers of a higher potential than an uncharged one. As a result, redox chemical reactions on noble metal nanoparticles exhibit lower activation barriers under photoexcitation. In electrochemical reactions on noble metal nanoparticles, the photopotential supplements the applied potential. In a diverse set of reactions, the photopotential model explains the photoenhancement of rates as well as the trends as a function of light intensity and photon energy. With further gains, light-induced potentials may be used as a knob for controlling the activities and selectivities of noble metal nanoparticle catalysts.

Backward Scattering of Electrically Large Standard Objects Illuminated by OAM Beams

To evaluate the interaction between the orbital angular momentum (OAM) beams and the electrically large standard objects, the backward scattering characteristics of the perfect electrical conductor (PEC) sphere and PEC cone are studied. First, the incident vortex electromagnetic field carrying OAM is generated by Hertizian dipole arrays. Subsequently, the backward-scattered field is calculated by the physical optics algorithm. The phase profiles and OAM spectra are analyzed in detail, which indicates that the scattered field for axial symmetric objects still keeps the main characters of the vortex field due to the angular momentum conservation. Finally, the radar cross section for PEC sphere and cone are calculated, respectively. The backward scattering features show significant differences when OAM beams change their topological charges. Consequently, given a specific propagation direction, compared to plane waves, more information will be offered by the OAM beams for object detection and recognition.

Silver Double Nanorings with Circular Hot Zone.

Silver double nanorings with circular intra-nanogaps between two nanorings of different diameters were synthesized without a linker molecule to confine an incident electromagnetic field in a single entity. We used on-demand, rational, and systematic multi-stepwise reactions consisting of (1) selective etching of gold, (2) rim-on deposition of platinum, (3) eccentric growth of gold, and (4) concentric growth of silver. The resulting silver double nanorings exhibited a high degree of homogeneity in both shape and size, with strongly coupled circular hot zones (or "hot halos", referring to the circular intra-nanogaps capable of focusing the near electromagnetic field) resulting from strong surface plasmon coupling between the inner and outer nanorings. Remarkably, these silver double nanorings exhibited strong, stable, and reproducible single-particle surface-enhanced Raman scattering signals without blinking. The signals appeared independently of polarization directions, which is a unique feature of a circular hot halo. The estimated enhancement factor was between 2 × 108 and 7 × 108. The measured limit of detection was 10-7 M in bulk concentration, and the signal appeared 570 s after sample exposure.

Fiber Lithography: A Facile Lithography Platform Based on Electromagnetic Phase Modulation Using a Highly Birefringent Electrospun Fiber.

Lithography plays a key role in advancing manufacturing as well as the semiconductor industry. However, the currently available state-of-the-art lithography methods still require access to expensive tools and facilities. Herein, we suggest a novel lithography method based on electromagnetic phase modulation of ultraviolet using a highly birefringent electrospun fiber to overcome such limitations. The optical birefringent effect, by which the phase of incident ultraviolet electromagnetic fields is retarded when passing through optically anisotropic media, is combined with semicrystalline poly(ethylene oxide) (PEO)-poly(ethylene glycol) (PEG) polymeric microfibers patterned in a programmable form using near-field electrospinning. By positioning the mask between two linear polarizers that are perpendicular to each other, only the UV waves that are passing through the fibers can be selectively utilized to exhibit lithographic property. Therefore, the UV intensity on the photoresist (PR) surface follows the shape of the fiber pattern, enabling precisely controlled patterning of the photoresist. Zero- to two-dimensional key features of lithography are achieved, including straight, curved, array, and isolated patterns. Facile optical alignments without using dedicated alignment marks are successfully demonstrated, as well as various applications including micro- to macroscale serpentine, tree, and antenna circuit patterns on a flexible substrate. The presented approach, packed in a table-top scale, is expected to provide a practical and affordable lithography solution by leveraging the direct-writing capability and tunable optical functionality of polymers, scalability, and the simple optical alignment method.

Infrared dielectric metamaterials from high refractive index chalcogenides

High-index dielectric materials are in great demand for nanophotonic devices and applications, from ultrathin optical elements to metal-free sub-diffraction light confinement and waveguiding. Here we show that chalcogenide topological insulators are particularly apt candidates for dielectric nanophotonics architectures in the infrared spectral range, by reporting metamaterial resonances in chalcogenide crystals sustained well inside the mid-infrared, choosing Bi2Te3 as case study within this family of materials. Strong resonant modulation of the incident electromagnetic field is achieved thanks to the exceptionally high refractive index ranging between 7 and 8 throughout the 2–10 μm region. Analysis of the complex mode structure in the metamaterial allude to the excitation of circular surface currents which could open pathways for enhanced light-matter interaction and low-loss plasmonic configurations by coupling to the spin-polarized topological surface carriers, thereby providing new opportunities to combine dielectric, plasmonic and magnetic metamaterials in a single platform.

Can second order nonlinear spectroscopies selectively probe optically "dark" surface states in small semiconductor nanocrystals?

Second order nonlinear responses such as sum frequency and second harmonic generation arise from the response of a material system to the second power of an incident electromagnetic field through the material's first hyperpolarizability or second-order optical susceptibility. These quantities are nonzero only for noncentrosymmetric systems, but different length scales of the noncentrosymmetry give rise to second harmonic or sum frequency radiation with different spatial and coherence characteristics. This perspective discusses the possible contributions to the second-order signal from films of small semiconductor quantum dots and addresses whether such experiments are expected to selectively enhance transitions to surface defects or trap states in such systems. It points out how "surface" and "bulk" contributions to the sum frequency or the second harmonic signal should be distinguishable through their angular dependence in a scattering geometry. It also explores possible mechanisms whereby second order spectroscopies might provide access to surface states that are very weak or absent in other forms of optical spectroscopy.

Time-Domain Procedures for Lightning-Induced Voltage Calculation in Electromagnetic Transient Simulators

In this paper, two time-domain procedures are proposed for the calculation of lightning-induced voltages using lossy transmission line models available in electromagnetic transient simulators. In both procedures, the influence of the incident electromagnetic field is represented in the form of current sources that are connected externally at the ends of the illuminated line. One of the procedures is formulated directly in the phase-domain and is compatible with the universal line model (ULM). The second procedure is formulated in the modal domain and is compatible with the transmission line model proposed by Marti. Both procedures are validated taking as reference a first order FDTD solution of telegrapher's equations considering the presence of external electromagnetic fields. It is shown that the proposed procedures can be efficiently and accurately used for the calculation of lightning-induced voltages on overhead lines.

Phase-matched frequency conversion in waveguides by means of transverse wavevector projections

We present a versatile technique for modal phase-matched second-harmonic generation in a waveguide, which relies on the incident electromagnetic field having transverse wavevector components on the input facet of the waveguide. Such a requirement is satisfied by using an angular-coupling arrangement, which allows for the excitation of modes having an odd spatial distribution that contribute to modal phase-matched second-harmonic generation. The strength of the second-harmonic signal is directly related to the angle at which the incident field is coupled into these modes. This is critical for on-chip nonlinear frequency conversion processes in the areas of optical communication, optical computing, and quantum computing.

Tailoring the surface plasmon resonance energy of Au nanowire arrays by defect management and thermal treatment

Abstract We present a novel route to tune and adapt the energy of surface plasmon resonances (SPR) of 3-dimensional (3D) Au nanowire arrays. Based on an annealing and defect management of anodic aluminum oxide (AAO) we demonstrate a tuning of the longitudinal resonance mode (L mode) of plasmons towards higher energies. Here we present an experimental fabrication as well as a modeling of optical absorption spectra. As a result, the combination of tunable optical properties of AAO and controllable nanowire structures has been realized. The L mode energy is found to shift with a modification of the average dielectric constant of the host porous alumina by an annealing process. We find that in a 3D Au nanowire array system, a plasmon interaction between neighboring wires exists. It proves a complex nonlinear relationship between SPR energy, wire aspect ratio and surrounding medium of the dielectric constant. In our modeling we consider the quasistatic limit of electromagnetic fields in a nanowire array and the respective angle of the incident electromagnetic field.

Polymer Nanoparticle Identification and Concentration Measurement Using Fiber-Enhanced Raman Spectroscopy

We present a measurement technique for chemical identification and concentration measurement of polymer nanoparticles in aqueous solution, which is achieved using Raman spectroscopy. This work delivers an improvement in measurement sensitivity of 40 times over conventional Raman measurements in cuvettes by loading polymer nanoparticles into the hollow core of a microstructured optical fiber. We apply this “fiber-enhanced” system to measure the concentration of two separate samples of polystyrene particles (diameters of 60 nm and 120 nm respectively) with concentrations in the range from 0.07 to 0.5 mg/mL. The nanoliter volume formed by the fiber presents unique experimental conditions where nanoparticles are confined within the fiber core and prevented from diffusing outside the incident electromagnetic field, thereby enhancing their interaction. Our results suggest an upper limit on the size of particle that can be measured using the hollow-core photonic crystal fiber, as the increasing angular distribution of scattered light with particle size exceeds the acceptance angle of the liquid-filled fiber. We investigate parameters such as the fiber filling rate and optical properties of the filled fiber, with the aim to deliver repeatable and quantifiable measurements. This study thereby aids the on-going process to create compact systems that can be integrated into nanoparticle production settings for in-line measurements.

Tailoring light-matter interaction in WS2 –gold nanoparticles hybrid systems

Recently, considerable attention has been paid to tune the emission using hybrid systems composed of layered transition-metal dichalcogenides and metal nanoparticles (NPs) since metal NPs have the ability to enhance and localize the incident electromagnetic field. Furthermore, these hybrid systems show great interest from the standpoint of fundamental science as it constitutes an atomic scale prototype of charge-transfer complexes. Here, we realized ${\mathrm{WS}}_{2}$--gold (Au) NPs hybrids by chemically growing Au NPs at the edges of the mechanically exfoliated bilayer ${\mathrm{WS}}_{2}$. The Au NPs significantly increase the light-matter interaction which has been studied through Raman and photoluminescence (PL) spectroscopy. A substantial enhancement of the PL intensity in the ${\mathrm{WS}}_{2}$--Au composite concerning the pristine ${\mathrm{WS}}_{2}$ has been observed, and it increases as the number and size of the Au NPs on ${\mathrm{WS}}_{2}$ is increased. Geometry-dependent modification of plasmon resonance energy of Au NP alters the coupling strength between the emission pathways of ${\mathrm{WS}}_{2}$ and the plasmon which is manifested by a change in relative intensity between trion $({X}^{\ensuremath{-}})$ and exciton $(X)$ emissions. We probe the mechanism of the PL intensity modulation through polarization-dependent measurements and simulation. We have demonstrated that, in ${\mathrm{WS}}_{2}$, the internal quantum efficiency increases and activation energy decreases due to coupling with Au NPs. Compared to pristine ${\mathrm{WS}}_{2}$, a faster change in optical band gap with temperature in ${\mathrm{WS}}_{2}$--Au may be due to enhancing electron-phonon interaction and lattice expansion in the latter. Our paper indicates the possibility to develop high performance transition-metal dichalcogenide-based photonic devices.

Modeling radiofrequency responses of realistic multi-electrode leads containing helical and straight wires

PurposeTo present a modeling workflow for the evaluation of a lead electromagnetic model (LEM) consisting of a transfer function (TF) and a calibration factor. The LEM represents an analytical relationship between the RF response of a lead and the incident electromagnetic field. The study also highlights the importance of including key geometric details of the lead and the electrode when modeling multi-electrode leads.MethodsThe electrical and thermal responses of multi-electrode leads with helical and straight wires were investigated using 3D electromagnetic (EM) and thermal co-simulations. The net dissipated power (P) around each lead electrode and the net temperature increase at the electrodes (ΔT) were obtained for a set of incident EM fields with different spatial distributions. A reciprocity approach was used to determine a TF for each electrode based on the results of the computational model. The evaluation of the calibration factors and the TF validation were performed using the linear regression of P versus the LEM predictions.ResultsP and ΔT were investigated for four multi-electrode leads and four single-electrode leads containing either helical or straight wires. All electrodes of the multi-electrode lead were found to be points of high power deposition and temperature rise. The LEMs for the individual electrodes varied substantially. A significant dependence of the calibration factors on the surrounding tissue medium was also found. Finally, the model showed that the TF, the calibration factor, P and ΔT for multi-electrode leads differ significantly from those for single-electrode leads.ConclusionThese results highlight the need to evaluate a LEM for each electrode of a multi-electrode lead as well as for each possible surrounding medium. It is also shown that the results derived from simulations based on simplified single-electrode leads can significantly mislead multi-electrode lead analyses.

Contribution to the Theory of Planar Wire Loop Antennas Used for Reception

Using “electromagnetic field” to designate an electric field and a magnetic field which satisfy Maxwell's equations, we define a decomposition of an arbitrary incident time-harmonic electromagnetic field into four elementary time-harmonic electromagnetic fields F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> , F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> , F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> , and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> . A formula, which gives the response of an arbitrary planar wire loop antenna used for reception, is based on this decomposition. This formula is applicable to any incident field configuration, and valid at any frequency at which the thin wire approximation applies. It separates the response of the antenna into three parts, one of which may be viewed as the intended response of the antenna. Our analysis teaches that F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> have no effect on the antenna and how F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> excite the antenna. Thus, it allows us to better understand the characteristics and limitations of a planar wire loop antenna used as a measuring antenna or as a direction finder.