Equivalent Dipole Research Articles

Chirality sorting with 3D-arbitrarily-oriented circularly polarized ultra-long optical needle field

We propose an all-optical sorting method for chiral nanoparticles by use of a 3D-arbitrarily-oriented circularly polarized ultra-long optical needle field, which is constructed through reversing the radiation patterns from an array of spin dipole located in the focal volume of a 4Pi microscopy. It is demonstrated that particles with different chirality can be trapped at different positions along the optical needle by the chiral gradient force, and the direction and distance of sorting are determined by the orientation and length of the circularly polarized optical needle respectively, which can be easily controlled by modifying the quantity and orientation of the equivalent spin dipoles. This scheme combines the advantages of controllable sorting direction and long sorting distance, providing a feasible route toward all-optical enantiopure chemical syntheses and enantiomer separations in pharmaceuticals.

Closed-form expressions for magnetic polarizabilities of circular apertures excited by nonuniform magnetic fields

Abstract The problem of electromagnetic penetration through an aperture in a perfectly electrically conducting plane is a classical problem in electromagnetic theory and applications. This work aims to investigate the behavior of an electrically small aperture when excited by nonuniform magnetic fields. Based on the Taylor expansion of the exact solution in integral form of the corresponding mixed boundary problem, we derive the equivalent magnetic dipole moment of a circular aperture. Closed-form expressions of dipole moments are derived. Also, for the special case of axisymmetric excitation where the dipole moment vanishes, we develop a quadrupole model to describe the aperture behavior. The effectiveness of the obtained expressions is verified by comparisons with accurate analytical solutions in special cases and the exact solutions in integral form.

Spontaneous Orientation Polarization of Anisotropic Equivalent Dipoles Harnessed by Entropy Engineering for Ultra-Thin Electromagnetic Wave Absorber

HighlightsThe strengthening mechanism of spontaneous orientation polarization of anisotropic equivalent dipoles within high-entropy alloys (HEAs) is proposed for enhancing dielectric attenuation of HEAs.The source of carbon supporter is expanded to the biomass category, which can construct the shell-core heterointerfaces with HEAs by means of a reformative carbothermal shock method.The sample carbonized cellulose paper/HEAs-Mn2.15 achieves efficient electromagnetic wave absorption of -51.35 dB at an ultra-thin thickness of 1.03 mm.This work combines theoretical calculations and electromagnetic simulations to propose feasible strategies for the design and application of electromagnetic functional devices such as ultra-wideband bandpass filter.

Reconfigurable terahertz stretchable spoof surface plasmon polariton waveguide for filter applications

In this paper, a reconfigurable terahertz spoof surface plasmon polariton (SPP) waveguide is proposed on a stretchable polydimethylsiloxane (PDMS) substrate. The SPP unit incorporates a folded stub and a conventional V-shaped SPP groove, enhancing the equivalent capacitance and consequently reducing the cutoff frequency. The cutoff frequency of the proposed SPP unit can be tuned from 285 to 390 GHz with stretchable factors of 1 ∼ 1.2, thereby achieving a reconfigurable operating frequency. The horizontal dimension of the proposed SPP waveguide can be tuned from 6.36 mm to 7.12 mm. Moreover, the SPP waveguide can generate transmission continuous phase shifts of −30°, −60°, −90°, and −120° with stretchable factors of 1.05, 1.1, 1.15, and 1.2, respectively, in the 150–190 GHz band. Applying the characteristic mode theory, a split ring resonator (SRR) functions as the equivalent magnetic dipole, which remains unaffected by stretchable deformation. When loaded with four SRR cells, the proposed SPP waveguide generates a tunable passband with a fixed notched frequency at 193 GHz. Another stretchable SPP resonator serves as the equivalent electric dipole, operating from 284 GHz to 256 GHz in 1∼1.2 stretchable states. By loading three SPP resonators, the SPP waveguide can achieve a passband for the initial state, and a tunable stopband is introduced under 1.1 and 1.2 stretchable states. The proposed stretchable method provides a promising solution for planar terahertz components and systems with reconfigurable functions.

Band-Stop Frequency-Selective Surface (FSS) with Elliptic Response Designed by the Extracted Pole Technique.

This paper describes and validates an advanced synthesis design process of Frequency-Selective Surfaces (FSSs) with elliptic band-stop responses. A systematic procedure based on the Generalized Chebyshev Function and the extracted pole technique enables control of the position of the transmission zeros and the attenuation level to obtain an equiripple rejection response. A systematic process is followed to obtain the lumped LC values of the resonator circuits extracted as poles and the impedance inverters. Then, equivalent dipoles and transmission lines are obtained to carry out the electromagnetic design at normal incidence for a linearly polarized field. The impact of the higher-order modes of the periodic structure on the electrical response of the FSS, which can be relevant due to the stringent selected specifications, has been also analyzed. A fourth-order band-stop filter with a 3 GHz bandwidth centered at 30 GHz and its attenuation at 50 dB has been designed considering three different implementations: two filters using a vacuum as a transmission line with different connection lengths and a third one using a dielectric substrate to enable its manufacturing. In order to verify the design procedure using experimental results, the third filter with printed dipoles in the dielectric substrate has been manufactured and measured, thus validating the developed process.

Modeling and Evaluation of a Multi-Stable Hybrid Energy Harvester

This article develops a multi-stable hybrid energy harvester (MSHEH) which consists of a piezoelectric energy harvester (PEH) and an electromagnetic energy harvester (EMEH). By tuning two parameters, the MSHEH can achieve a mono-stable, bi-stable, and tri-stable state, respectively. A numerical procedure is developed to compute the EMEH’s transduction factor. The obtained result is validated experimentally. Using the equivalent magnetic 2-point dipole theory, the restoring force model of the magnetic spring is established. The obtained model is verified experimentally. The energy harvesting performances of the MSHEH under the four different configurations (linear, mono-stable, bi-stable and tri-stable) subjected to frequency sweep excitations are evaluated by simulation and validated by experiment. The comparative analysis focuses on power output, accumulated harvested energy, and effective energy-harvesting bandwidth. The optimum load resistances are investigated by Pareto front optimizations. The following key findings are obtained. When subjected to high-level frequency sweep excitation, the tri-stable configuration exhibits the widest frequency bandwidth and the highest total accumulated harvested energy. When subjected to low-level frequency sweep excitation, the bi-stable configuration is more efficient in energy harvesting. The best performance trade-off between the PEH and EMEH can be achieved by selecting the optimum load resistances properly.

An Equivalent Modeling Method for Wideband Magnetic Radiation Interference of Power-Electronic Equipment

As more and more new power electronics with high switching frequencies are used in power-electronic equipment on ships and other platforms, the wideband radiation that power-electronic equipment gives off could affect sensitive equipment on the platform. Therefore, it is crucial to accurately model and characterize its wideband radiation properties to predict the wideband field distribution near such equipment. The traditional equivalent dipole method is commonly used to model power-electronic equipment at a single frequency. It is difficult to apply this method to wideband applications, and the precision of equivalent dipole array modeling at each frequency is insufficient. Additionally, acquiring the near-field phase data necessary for comparable modeling through practical measurement is frequently difficult. To solve the above problems, this paper proposes an equivalent dipole hybrid modeling method for power-electronic equipment’s broadband radiation characteristics. Starting with the near-field data at finite frequency points in a wideband, the method employs a global optimization algorithm to find the best equivalent dipole array, which characterizes the power-electronic equipment’s radiation characteristics. Furthermore, the interpolation technique is used to predict the wideband radiation properties of power-electronic equipment. Finally, test and numerical examples demonstrate the method’s accuracy and effectiveness.

The cerebellum monitors errors and entrains executive networks

Frontal midline θ (Fmθ) activity occurs in medial prefrontal cortices (mPFC), when expected and actual outcomes conflict. Cerebellar forward models could inform the mPFC about this mismatch.To verify this hypothesis we correlated the mPFC activation during a visuomotor tracking task (VM) with performance accuracy, in control and cerebellum-lesioned participants. Additionally, purely visual (V), motor (M) and a motor plus visual tasks (V + M) were performed.An Independent Component, with a mid-frontal topography scalp map and equivalent dipole location in the dorsal anterior cingulate cortex accounted for Fmθ.In control participants Fmθ power increased during VM, when the error level crossed a threshold, but not during V + M, M and V. This increase scaled with tracking error.Fmθ power failed to increase during VM in cerebellar participants, even at highest tracking errors.Thus, in control participants, activation of mPFC is induced when a continuous monitoring effort for online error detection is required. The presence of a threshold error for enhancing Fmθ, suggests the switch from an automatic to an executive tracking control, which recruits the mPFC.Given that the cerebellum stores forward models, the absence of Fmθ increases during tracking errors in cerebellar participants indicates that cerebellum is necessary for supplying the mPFC with prediction error-related information. This occurs when automatic control falters, and a deliberate correction mechanism needs to be triggered.Further studies are needed to verify if this alerting function also occurs in the context of the other cognitive and non-cognitive functions in which the cerebellum is involved.

Basis and applicability of noninvasive inverse electrocardiography: a comparison between cardiac source models.

The body surface electrocardiogram (ECG) is a direct result of electrical activity generated by the myocardium. Using the body surface ECGs to reconstruct cardiac electrical activity is called the inverse problem of electrocardiography. The method to solve the inverse problem depends on the chosen cardiac source model to describe cardiac electrical activity. In this paper, we describe the theoretical basis of two inverse methods based on the most commonly used cardiac source models: the epicardial potential model and the equivalent dipole layer model. We discuss similarities and differences in applicability, strengths and weaknesses and sketch a road towards improved inverse solutions by targeted use, sequential application or a combination of the two methods.

Modeling ventricular repolarization gradients in normal cases using the equivalent dipole layer

Background Electrical activity underlying the T-wave is less well understood than the QRS-complex. This study investigated the relationship between normal T-wave morphology and the underlying ventricular repolarization gradients using the equivalent dipole layer (EDL).Methods Body-surface-potential-maps (BSPM, 67‑leads) were obtained in nine normal cases. Subject specific MRI-based anatomical heart/torso-models with electrode positions were created. The boundary element method was used to account for the volume conductor effects. To simulate the measured T-waves, the EDL was used to apply different ventricular repolarization gradients: a) transmural, b) interventricular c) apico-basal and d) all three gradients (a-c) combined. The combined gradient (d) was optimized using an inverse procedure (Levenberg-Marquardt). Correspondence between simulated and measured T-waves was assessed using correlation coefficient (CC) and relative difference (RD).Results Realistic T-waves were simulated if repolarization times of: (a) the epicardium were smaller than the endocardium; (b) the left ventricle were smaller than the right ventricle and (c) the apex increased towards the base. The apico-basal gradient resulted in the highest correspondence between measured and simulated T-waves (CC = 0.84(0.81–0.91);RD = 0.68(0.60–0.71)) compared to a transmural gradient (CC = 0.77(0.71–0.80);RD = 1.46(0.82–1.75)) and an interventricular gradient (CC = 0.71(0.67–0.80);RD = 0.85(0.75–0.87)). All three gradients combined further improved the correspondence between measured and simulated T-waves (CC = 0.83(0.82–0.89);RD = 0.60(0.51–0.63)), especially after optimization (CC = 0.96(0.94–0.98);RD = 0.27(0.22–0.34)).Conclusion The application of all repolarization gradients combined resulted in the largest agreement between simulated and measured T-waves, followed by the apico-basal repolarization gradient. With these findings, we will optimize our EDL-based inverse procedure to assess repolarization abnormalities.

Unifying the stationary and convective Ffowcs Williams and Hawkings solutions for aeroacoustic predictions via a Lorentz transformation

The convective Ffowcs Williams and Hawkings (FW-H) equation and its integral solutions are often used for noise predictions of aeroacoustic phenomena in moving mediums. In this study, a set of unified integral solutions for stationary and convective FW-H equations are proposed by making use of the extended Lorentz transformation for arbitrary mean flow orientations. The new solutions in Euclidean coordinates have compact forms that resemble the well-known F1 and F1A solutions of Farassat, with the main differences from existing ones in the definitions of the equivalent monopole and dipole sources, and also their associated equivalent thickness noise and loading noise. Validations have been performed for two benchmark problems in moving mediums, one is a stationery monopole source and the other is a rotating dipole source. Apart from the well-recognized distorted acoustic fields due to the convective amplification, the results also show that the convective effects induce dipole-like acoustic components for a pure monopole source and monopole-like acoustic components for a pure dipole source. These are explained well by the newly-derived unified integral solutions and provide more insights on the noise source mechanisms.

Reduction to the pole near the equator with a Fourier-domain equivalent dipole layer

Reduction to the pole (RTP) transforms the phase of the observed total-field anomaly, making magnetic interpretation easier. However, RTP operations are notoriously unstable at low latitudes and produce singularities at the equator. The equivalent-source approach is an appropriate method to address the well-known difficulties of RTP at low latitudes. Although we routinely use equivalent-source RTP algorithms in the spatial domain, they consume massive computational resources. In contrast, the equivalent-source method in the Fourier domain is more efficient and also invalid for RTP because of the inevitable use of the RTP operator in the inversion. To overcome this problem, we introduce a simple approximation of the RTP operator instead and then develop a novel algorithm to calculate the magnetic moments of the equivalent dipole layer from the total-field anomaly near the equator. Because the calculations are mainly performed in the Fourier domain, this algorithm is more efficient than the conventional spatial-domain method. We also impose a nonnegative constraint on the dipole layer to improve the results and significantly reduce the undesired striation associated with the low-latitude RTP. We evaluate the effectiveness of our approach with synthetic data near the equator, and the results indicate that the algorithm can produce an RTP field that is an accurate representation of the real field at the pole, even when accounting for the existence of noise. The new approach is applied to field data collected near the geomagnetic equator in the South China Sea. In the central part of the anomaly, we obtain a robust spindle shape of the RTP field, which is identical to the shape of a basalt formation in that location. Recent 1:1,000,000 scale marine geologic mapping has confirmed this presence, proving that our solution is an applicable approach to the problem.

Progressive Expansion Sampling of Quasi-Static Magnetic Fields in Unconfined Regions

We present a fast and accurate measurement technique for quasi-static magnetic fields by employing a progressive sampling method in an unconfined input space. The proposed machine learning algorithm is tested against uniform sampling on printed circuit board test structures and a buck converter. We prove allocation of multiple, separated regions with predefined lateral field limits at MHz frequencies. The feasibility of equivalent magnetic dipole source modeling based on a small number of samples is demonstrated. Compared to uniform testing, progressive expansion sampling identifies contours of given field limits in less than 3% of the reference measurement time.

Transfers of the OAM and SAM densities of Bessel beam into the orbital and spin torques upon gold nanorod

The optomechanical interplay of a Bessel beam (an optical vortex) with a gold nanorod (GNR) in water is theoretically studied. The optical force and torque exerted on the GNR are analyzed using Maxwell's stress tensor to investigate the transfer rates of the orbital angular momentum (OAM) and the spin angular momentum (SAM) densities of Bessel beam into the orbital and spin torques upon GNR, respectively. From the numerical analysis, we find that the ratio of the orbital torque to the spin torque on the GNR matches the ratio of OAM to SAM of Bessel beam, corresponding to the order (topological charge) of the Bessel beam. This is to say that the transfer rate of the OAM density of Bessel beam into the orbital torque exerted on GNR nearly equals that of the SAM density into the spin torque. It implies that the spin-orbit interaction (SOI) of the optical vortex beam via a GNR is very weak. In addition, the spin torque is nearly equal to the corresponding zilch torque, the surface integral of Lipkin's zilch stress tensor. This could be because a GNR can be regarded as a perfect electric dipole particularly when the wavelength of the incident light is close to and little longer than the longitudinal surface plasmon resonance of GNR; the dipole's orientation is along the long axis of GNR. In contrast, the SOI via a spherical gold nanoparticle (GNP) is strong due to no preferred orientation for the equivalent dipole; a part of SAM of the optical vortex is transferred to the orbital torque upon GNP. Our results demonstrate that GNR, functioning as an ideal electric dipole, is a highly effective probe for detecting the OAM and SAM densities of an optical vortex individually through its distinct orbital and spin motions, without any crosstalk.

A highly accurate and robust source reconstruction method of printed circuit boards based on complex‐valued neural network

SummaryPrinted circuit boards play an increasingly important role in modern electronic systems. Equivalent dipole moments are widely used to reconstruct the radiated fields of printed circuit boards in view of the extremely high complexity. In this paper, an improved source reconstruction method based on complex‐valued neural network is proposed to investigate the radiation properties of printed circuit boards working in microwave frequency band. Firstly, the magnetic field data obtained from the near‐field scanning are utilized to construct a matrix equation based on the source reconstruction theory. Secondly, the kernel of the complex‐valued neural network is constructed through the algorithm of complex numbers, which eventually end up with the novel neural network with the help of the principle of regression optimization. Thirdly, the data obtained from the near‐field scanning are fed into the neural network for effective training to get the equivalent dipole model. Finally, several numerical examples and available measurement results are given to validate the method. Compared with the commonly used Tikhonov regularization method, the proposed method possesses higher accuracy and better robustness in noise suppression.

Electrostatic levitations of anisotropic dielectric oblate and prolate spheroids

AbstractThe paper presents analytical approach to electrostatic field for dielectric spheroids problem. For both oblate and prolate spheroids fields distributions are derived. The variable separation method is applied. Electrostatic force is evaluated with the help of the Maxwell stress tensor generalized method, material force density, coenergy and equivalent dipole. Levitation forces for both oblate and prolate dielectric spheroids versus axis permittivities and spheroids height are presented.

Localization and Identification of EMI Sources in Shielding Enclosures Based on a Two-Step Source Reconstruction Method

Localization and identification of unknown electromagnetic interference (EMI) sources in shielding enclosures is a great challenge due to the complex electromagnetic environment. In this work, a two-step source reconstruction method is proposed to address this issue. The actual EMI sources are initially modeled by equally distributed equivalent electric dipoles in the shielding enclosure. Effects of surrounding environments are rigorously incorporated using the numerical Green's function which bridges between the equivalent dipoles and planar scanned tangential magnetic near-field. Next, the initial equivalent sources are downsized via evaluating the contribution of each equivalent dipole. The parameters of remaining equivalent dipoles are updated by another source reconstruction process, in which additional equivalent magnetic dipoles are added to improve precision of the equivalent model. The locations and geometries of EMI sources in the shielding enclosure can be identified clearly in terms of the updated equivalent dipoles. Furthermore, the radiated emissions from individual EMI sources can be estimated accurately. The effectiveness of this approach is validated by representative numerical examples.

On the Calculation of the Magnitude of Induced Charges and the Electrostatic Dipole of an Oblate Spheroid with an Axis of Symmetry Collinear to an External Homogeneous Electrostatic Field

The values of the surface induced charges, the positions of their centers and the value of the equivalent dipole of an oblate conducting spheroid are determined by transition from spheroidal coordinates to a spherical system of coordinates in the analytical asymptotic calculations of the first order of smallness with respect to the squared eccentricity. The characteristics of the equivalent dipole are obtained depending on the value of the electrostatic field strength, squared eccentricity, and the radius of an equal sphere.

Dipole-Moment-Based Reciprocity for Practical Desensitization Identification and Mitigation

Radio frequency interference can degrade the receiving sensitivity of antennas. The interference is usually caused by certain coupling structures, such as layouts without adequate grounding for the radio frequency signal return path. Those structures can be modeled as a set of equivalent dipole moments when they are electrically small. Herein, the dipole moment model-based coupling framework is applied to a practical cellphone design case to devise an engineering solution. The coupling framework incorporates dipole moments as radiation sources and a coupling model based on the reciprocity theorem. Unfortunately, near-field scan probes often lack access to all locations, owing to the complex phone platform structure. A combined measurement-simulation method is used to obtain the field quantities lacking direct access to measurements. The dipole-moment-based coupling framework helps estimate the couplings from different noise sources individually. Thus, the priority of solving for better layout designs can be determined according to the coupling estimations. Furthermore, the physics associated with the reconstructed dipole moment can provide insights and suggest possible mitigation methods. Several practical mitigation methods are discussed, including the suppression of the dominant noise source (reducing/cancelling the radiation or suppressing the specific noise spectrum) and the coupling path to the victim antenna.

Effects of magnetic field direction on [formula omitted] vertical transport in the Martian ionosphere

The directions of Martian magnetic field, which depends on the interaction between the crustal magnetic field and the time-various interplanetary magnetic field (IMF), is in a state of disorder and plays a significant role in ions vertical transport, such as ions upwelling and precipitation. In general, vertical diffusion transport of ionospheric plasma tends to be promoted around vertical magnetic field regions but be suppressed around horizontal magnetic field area. However, the mechanism behind this phenomenon is not clear to date. Based on three-dimensional multi-fluid Hall magneto-hydrodynamic (MHD) equations in conjunction with an equivalent source dipole (ESD) model, we investigated mechanism behind the control of vertical transport by different magnetic field directions in the Martian ionosphere. Numerical results showed that the same direction of interplanetary magnetic field with ESD results in the formation of mini-magnetosphere to protect the ionosphere, which reflected in higher density distributions comparing to the no-ESD case due to joint effects of thermal pressure increasing and plasma vertical transport. At low altitude of ionosphere, O+ ion inward transport (precipitation) tends to be inhibited particularly around horizontal magnetic field, with high contribution from the motional electric force. In addition, at high altitude, O+ outward transport (upwelling) is likely to be facilitated over vertical-field areas in significant part controlled by the ambipolar electric force, whereas it is likely to be inhibited in horizontal-field region, contributed mainly from the Hall electric force. These results will enrich our understanding of mechanisms behind the control of ions vertical transport by magnetic field directions.