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Magnetically ordering media support spin waves or magnons, which can couple with electromagnetic waves to form magnon polaritons. Based on insulating antiferromagnets, magnon polaritons are situated in the far-infrared or THz frequency range. We investigated Dyakonov surface magnon polaritons (DSMPs) at the antiferromagnetic surface in an external magnetic field, where the external field and antiferromagnetic easy axis lie in the surface plane and are normal to each other. Our numerical results are based on the MnF2 crystal, but the conclusions and qualitative results are also available to other insulating antiferromagnets. We predicted two field-tunable DSMPs and one tunable Dyakonov surface magnon. We discerned the main effects of the external magnetic field on the DSMPs; either DSMPs are sensitively modulated by the external field or there is a cutoff magnetic field. Their individual Poynting vector seriously deviates the propagation direction and is sensitively controlled by the external field. The spin angular momentum contains two components normal to each other, unlike conventional surface magnon polaritons. One of the DSMPs can carry a huge Poynting vector and spin angular momentum in the external magnetic field. These results are interesting for micromechanics and spintronics and relevant technologies in the far-infrared or THz domain. [ABSTRACT FROM AUTHOR]

Terahertz pulses generated by two-color laser plasmas have reported peak field strengths exceeding MV/cm, and when illuminating metal nanotips, the near-field enhancement at the tip apex should result in extremely high bunch charges and electron energies via sub-cycle cold-field emission. Here, electron emission from tungsten nanotips driven by THz pulses generated by a long filament air-plasma is reported. Electron energies up to 1.1 keV and bunch charges up to 2× 10 5 electrons per pulse were detected, well below values expected for peak field calculated via the time-averaged Poynting vector. Investigations revealed a failure in the use of the time-averaged Poynting vector when applied to long filament THz pulses, due to spatiotemporal restructuring of the THz pulse in the focus. Accounting for this restructuring significantly reduces the field strength to approximately 160 kV/cm, consistent with the observed electron bunch charges, peak energies, and their dependence on the tip position in the THz focus. Despite these findings, our results surpass previous THz plasma-driven electron generation by an order of magnitude in both electron energy and bunch charge, and a path to increasing these by an additional order of magnitude by modification of the THz optics is proposed. [ABSTRACT FROM AUTHOR]

The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its derivatives are directly involved. The obtained results, including equations for metric, equations of motion, and equations for fields, are applied to purely vector fields. As a consequence, formulas are determined for calculating the basic quantities necessary to describe physical systems. In this case, not only the pressure field and acceleration field are taken into account, but also the electromagnetic and gravitational fields outside the matter, which contribute to the four-momentum and to the four-dimensional angular momentum pseudotensor of each system. Each of the presented fields, including the gravitational field, has its own four-potential and its own tensor, which allows all calculations to be performed in a covariant way. In particular, when applying the principle of least action, the optimal approach is one in which the four-currents, field four-potentials and metric tensor depend on the observation point and vary independently from each other. In addition to the Euler–Lagrange equation, another equation of motion is derived containing the density of generalized four-force and the time derivative of the volume density of the generalized four-momentum. In order to uniquely calibrate the energy, which is a scalar quantity, the cosmological constant included in the Lagrangian is used. This leads to the fact that both the scalar curvature and the cosmological constant disappear in expression for the four-momentum of the system. In addition, the equation for the metric is simplified. The peculiarity of the equation for the metric is that the total stress-energy tensor of the physical system, presented in the right part of the equation for the metric, is associated only with field tensors and does not depend on particle four-velocities. Moreover, the trace of stress-energy tensor is zero. To calculate the stress-energy tensor, the functional derivative of Lagrangian density with respect to the metric tensor is used. The covariant derivative of stress-energy tensor leads to the equation of particle motion under the action of fields, and to the generalized Poynting theorem. The contractions of the field tensors with the Ricci tensor are equal to zero, so that each field makes its own contribution to the curvature of spacetime in the system. The inertial mass of a system is defined as the value connecting the four-momentum and four-velocity of the center of momentum of the system, and can be calculated using the square of the four-momentum. It is shown that the canonical representation of the angular momentum pseudotensor is its representation with covariant indices. The radius-vector of the center of momentum of a physical system is determined in covariant form. [ABSTRACT FROM AUTHOR]

It is known that the energies associated with reactive power periodically exchange between power supply and energy storage component(s) of capacitor and/or inductor. However, reactive power may be altered by power electronic devices without capacitors or/and inductors, which cannot be reasonably explained following electrical power theory. In this work, the transmission, dissipation, and storage of electromagnetic energy of either a sinusoidal alternating current or an electromagnetic wave traveling in a transmission line are addressed; a positive definite expression of time-averaged stored energy density instead of the usual non-positive definite one is proposed. It is demonstrated that, under certain conditions, the product of voltage and current intensity may be applied to represent instantaneous power, and active power is consistent with dissipated energy. However, reactive power is related to part of stored energy, which indicates that reactive power relates to part of the energy exchange between the power supply and the considered circuit. Furthermore, it is shown that influences of thyristors on stored energy may be attributed to the change of (fundamental frequency) current intensity induced by the thyristor and the contribution of the resistor to stored energy, which may also alter the value of reactive power. This work may be helpful to establish a bridge between electrical power theory and Poynting's theorem, deepen the understanding of reactive power, and improve electrical power theory. [ABSTRACT FROM AUTHOR]

This work discusses the behavior of transverse energy fluxes of the fundamental core mode of a holey fibers and a photonic band gap fibers when the polarization state of this mode changes. The behavior of the transverse component of the Poynting vector of the fundamental core mode is considered for both linear and elliptical polarization. It is demonstrated that despite the difference in the distribution of the Poynting vector stream lines in the cross section of the fibers for the two polarizations, the leakage loss level is maintained constant due to the forward and reverse energy flows in the radial direction. Differences in the level of leakage losses in different micro structured fibers arise from the vortex structure of the Poynting vector of the fundamental core mode. [ABSTRACT FROM AUTHOR]

Source time‐reversal imaging based on wave equation theory can achieve high‐precision source location in complex geological models. For the time‐reversal imaging method, the imaging condition is critical to the location accuracy and imaging resolution. The most commonly used imaging condition in time‐reversal imaging is the scalar cross correlation imaging condition. However, scalar cross‐correlation imaging condition removes the directional information of the wavefield through modulus operations to avoid the direct dot product of mutually orthogonal P‐ and S‐waves, preventing the imaging condition from leveraging the wavefield propagation direction to suppress imaging artefacts. We previously tackled this issue by substituting the imaging wavefield with the energy current density vectors of the decoupled wavefield, albeit at the cost of increased computational and storage demands. To balance artifact suppression with reduced computational and memory overhead, this work introduces the Poynting and polarization vectors mixed imaging condition. Poynting and polarization vectors mixed imaging condition utilizes the polarization and propagation direction information of the wavefield by directly dot multiplying the undecoupled velocity polarization vector with the Poynting vector, eliminating the need for P‐ and S‐wave decoupling or additional memory. Compared with scalar cross‐correlation imaging condition, this imaging condition can accurately image data with lower signal‐to‐noise ratios. Its performance is generally consistent with previous work but offers higher computational efficiency and lower memory usage. Synthetic data tests on the half‐space model and the three‐dimensional Marmousi model demonstrate the effectiveness of this method in suppressing imaging artefacts, as well as its efficiency and ease of implementation. [ABSTRACT FROM AUTHOR]

Angle domain common imaging gathers (ADCIGs) serve as not only an ideal approach for tomographic velocity modeling but also as a crucial means of mitigating low-frequency noise. Thus, they play a significant role in seismic data processing. Recently, the Poynting vector method, due to its lower computational requirements and higher resolution, has become a commonly used approach for obtaining ADCIGs. However, due to the viscoelastic properties of underground media, attenuation effects (phase dispersion and amplitude attenuation) have become a factor, which is important in seismic data processing. However, the primary applications of ADCIGs are currently confined to acoustic and elastic media. To assess the influence of attenuation and elastic effects on ADCIGs, we introduce an extraction method for ADCIGs based on fractional viscoelastic equations. This method enhances ADCIGs accuracy by simultaneously considering both the attenuation and elastic properties of underground media. Meanwhile, the S-wave quasi tensor is used to reduce the impact of P-wave energy on S-wave stress, thus further increasing the accuracy of PS-ADCIGs. In conclusion, our analysis examines the impact of the quality factor Q on ADCIGs and offers theoretical guidance for parameter inversion. [ABSTRACT FROM AUTHOR]

Backflow, or retropropagation, is a counterintuitive phenomenon whereby for a forward-propagating wave the energy locally propagates backward. In the context of backflow, physically most interesting are the so-called unidirectional waves, which contain only forward-propagating plane wave constituents. Yet, very few such waves possessing closed-form analytic expressions for evaluation of the Poynting vector are known. In this study, we examine energy backflow in a novel (2+time)-dimensional unidirectional monochromatic wave and in a (2+1)D spatiotemporal wavepacket, analytic expressions which we succeeded to find. We also present a detailed study of the backflow in the "needle" pulse. This is an interesting model object because well-known superluminal non-diffracting space–time wave packets can be derived from its simple factored wave function. Finally, we study the backflow in an unidirectional version of the so-called focus wave mode—a pulse propagating luminally and without spread, which is the first and most studied representative of the (3+1)D non-diffracting space–time wave packets (also referred to as spatiotemporally localized waves). [ABSTRACT FROM AUTHOR]

Metamaterial absorbers show great potential in many scientific and technological applications by virtue of their sub-wavelength and easy-to-adjust structure, with bandwidth as an important standard to measure the performance of the absorbers. In this study, our team designed a new broadband absorber, which consists of an indium arsenide (InAs) disk at the top, a zinc selenide (ZnSe)-chromium (Cr) stacked disk in the middle and a metal film at the bottom. Simulation results show that the absorber has remarkable absorptivity properties in the mid-long infrared band. In a wavelength range of 5.71–16.01 μm, the average absorptivity is higher than 90%. In the band of 5.86–15.49 μm, the absorptivity is higher than 95%. By simulating the electromagnetic field diagram at each resonant frequency, the reason for high broadband absorptivity is obtained. We also constructed Poynting vector diagrams to further elucidate this phenomenon. Next, we analyzed the influence of different materials and structural parameters on absorptivity properties and tested spectral response at different polarization angles and oblique incidence of the light source in the TM and TE modes. When the source is normally incident, the absorber shows polarization insensitivity. When the angle is 40°, absorptivity is still high, indicating that the absorber also possesses angle insensitivity. The broadband absorber proposed by us has good prospects in infrared detection and thermal radiators. [ABSTRACT FROM AUTHOR]

The article discusses the collection of physics teaching apparatus housed in the museum wing of the Greenslade house in Ohio, dating from 1850 to 1950. Various apparatus named after academic ancestors such as Barker, Boys, Thacher, Sommerfeld, Edison, Braun, Ritchie, Sturgeon, and Poynting are highlighted, each with unique historical significance and contributions to the field of physics. The article provides detailed descriptions and historical context for each apparatus, shedding light on the evolution of physics education and experimentation over time. [Extracted from the article]

To achieve high-precision calculation of the electromagnetic field of layered media and to ensure that the apparent resistivity calculation and sensitivity are not affected by numerical errors, this paper implements high-precision calculation of the layered electromagnetic field based on the weighted average (WA) extrapolation method. Firstly, the 1D electromagnetic field expression of an arbitrary attitude field source is obtained by using the magnetic vector potential; then, the WA extrapolation technique is introduced to achieve the high-precision and fast solution of the Hankel transform, and the effects of the number of Gaussian points and the number of integration intervals on the accuracy are investigated. The theoretical model test shows that, compared with the open-source Dipole1D, the algorithm proposed in this paper has wider adaptability, and can achieve high-precision calculation of electric and magnetic dipole sources with higher efficiency. Compared with the epsilon algorithm studied by previous researchers, the WA extrapolation method proposed in this article can improve the convergence rate by approximately 20% under the same conditions. It can obtain high-precision numerical solutions with less integration time. The relative accuracy can reach the order 10 − 10 , and its computational efficiency is significantly better than the existing epsilon algorithm. Finally, we used two cases of marine controlled source electromagnetic method to show the application. The sensitivity and Poynting vectors are calculated, which provides a technical tool for a deep understanding of physical mechanisms in layered media. [ABSTRACT FROM AUTHOR]

Reverse-time migration (RTM) is widely regarded as one of the most accurate migration methods available today. A crucial step in RTM involves extending seismic wavefields forward and backward. Compared to the conventional central finite-difference (CFD) scheme, the combined compact difference (CCD) scheme offers several advantages, including a shorter difference operator and the suppression of numerical dispersion under coarse grids. These attributes conserve memory and enhance effectiveness while maintaining the same level of differential precision. In this article, we begin with the five-point eighth-order CCD scheme and utilize the least squares method and Lagrange multiplier method to optimize the difference coefficients. This optimization is guided by the concept of dispersion-relation-preserving (DRP). The result is the acquisition of an optimized combined compact difference (OCCD) scheme, further enhancing the ability to suppress numerical dispersion. We thoroughly compare and analyze dispersion relationships and stability conditions. In addition, we examine several crucial steps in the RTM of the second-order acoustic wave equation. These steps include absorption boundary conditions, boundary storage strategy, and Poynting vector imaging conditions. Finally, we apply both the CCD and OCCD schemes in the RTM of the layered model, graben model, and SEG/EAGE salt model. We compare these results with those obtained from CFD's RTM. Numerical findings demonstrate that, in contrast to the CFD scheme, the CCD scheme effectively suppresses numerical dispersion and enhances imaging accuracy. Moreover, the optimized OCCD scheme further improves the ability to suppress numerical dispersion and can obtain better imaging results, which is an effective RTM method suitable for coarse grid conditions. [ABSTRACT FROM AUTHOR]

Radiation energy scattered by a small particle can be expected to travel from the particle to a detector in the far field along the field lines of the Poynting vector. We consider the scattering off a small conducting sphere, for which only the induced electric and magnetic dipole moments contribute to the emitted radiation. Field lines of the energy flow due to interference between fields radiated by the electric and magnetic dipoles appear to form closed loops in the vicinity of the particle. Energy flows out of the particle at one side and then returns to the particle at the other side, and as such, this energy flow does not contribute to the radiated power. At larger distances, energy flows away from the particle at one side of the particle, but on the other side, radiation flows from infinity toward the particle. The energy for the scattered radiation is provided by the incident field. The energy flow is due to interference between the incident field and the scattered radiation, known as extinction. The flow pattern of this energy exhibits numerous singularities and vortices, and closed-loop flows near the particle. In the far field, energy flows along counter-oriented field line bundles, with only the net power flowing inward. [ABSTRACT FROM AUTHOR]

This study investigates the phenomenon of light funneling through a subwavelength plasmonic slit, examining the corner effect resulting from the interaction between the incident wave and the round-trip wave within the slit. Our findings reveal an inconsistent relationship between transmittance and the size of the funneling area. Notably, constructive interference of the waves significantly enhances transmittance, leading to the unexpected emergence of a ring-like Poynting vector contour at the entrance corner of the slit. In cases where transmittance remains moderate and constructive interference continues to dominate, the light funneling area expands due to the presence of the ring. Furthermore, the extent of the ring expansion correlates with the enlargement of the funneling area, and the underlying mechanism can be elucidated through an examination of the dynamics of light fields and Poynting vectors. [ABSTRACT FROM AUTHOR]

It is shown in this work that, with strong focusing of a beam with optical vortex and circular polarization, three energy flows take place in the focal plane: direct longitudinal, reverse longitudinal and azimuthal transverse flows. Calculations are made analytically using the Richards–Wolf formalism and by numerical simulation. Moreover, the energy rotation at different lengths from the optical axis occurs in different directions. Therefore, the focal plane intersects along the optical axis only part of the initial beam energy per unit time. The same energy part (other things being equal) intersects the focal plane along the positive direction of the optical axis when an optical vortex with cylindrical polarization is focused. The difference is that, if an optical vortex is present, then the transverse energy flux at the focus rotates around the optical axis. If an optical vortex is not present (a beam with only cylindrical polarization), then the average transverse flow in the focal plane is zero, though, in some regions in the focal plane, the flow is directed towards the optical axis and, in other regions, away from it. This behavior of the transverse energy flow at the focus (flow direction towards the optical axis and away from the optical axis) of a cylindrical vector beam can be deemed another kind of Hall effect. [ABSTRACT FROM AUTHOR]

The review describes the principles and examples of practical realization of diagnostic approaches based on the coherence theory, optical singularities and interference techniques. The presentation is based on the unified correlation-optics and coherence-theory concepts. The applications of general principles are demonstrated by several examples including the study of inhomogeneities and fluctuations in water solutions and methods for sensitive diagnostics of random phase objects (e.g., rough surfaces). The specific manifestations of the correlation-optics paradigms are illustrated in applications to non-monochromatic fields structured both in space and time. For such fields, the transient patterns of the internal energy flows (Poynting vector distribution) and transient states of polarization are described. The single-shot spectral interference is analyzed as a version of the correlation-optics approach adapted to ultra-short light pulses. As a characteristic example of such pulses, uniting the spatio-temporal and singular properties, the spatio-temporal optical vortices are considered in detail; their properties, methods of generation, diagnostics, and possible applications are exposed and characterized. Prospects of further research and applications are discussed. [ABSTRACT FROM AUTHOR]

We report observations of co-existing rising and falling tone emissions of electromagnetic ion cyclotron (EMIC) waves by THEMIS E spacecraft. The investigation of these fine structures of the EMIC waves is essential from the point of view of understanding the connection between the proton holes and the proton hills in velocity phase-space. The wave packets of rising and falling tones are tracked by Poynting vector analysis, where we observe that the rising tones are propagating northward and the falling tones are propagating southward. The nonlinear wave growth theory supports our observations. We propose a model where the proton velocity distribution function evolves through the formation of proton holes on the negative side of the distribution function and mirrored resonant protons forming proton hills on the positive side of the distribution function, allowing us to observe the co-existing rising and falling tone EMIC waves. [ABSTRACT FROM AUTHOR]

This paper proposes a method for calculating the received power by modeling the environment in which a target and guided weapon encounter each other and analyzing the RCS and gains in the near field. The target encounter environment was modeled by fixing the position of the simple missile shape target and moving the horn antenna. The near-field RCS was analyzed based on the magnitude of the Poynting vector obtained using the HFSS SBR+ simulation. The received power was calculated by substituting the antenna gain, which varies based on the distance from the target, and the previously analyzed near-field RCS into the radar equation. The received power calculated using the proposed method is compared and verified with the received power obtained using the far-field RCS, gain, and the received power obtained through simulation. [ABSTRACT FROM AUTHOR]

In a recent study, we proposed an axion-electrodynamics model that consistently incorporates a lepton Dirac field into the gauge-invariant Lagrangian of a closed physical system. Our investigation delved toward potential applications of the model, with a focus on its implications in the realm of Dark Matter axions interacting with leptons in a nonlinear electrodynamics background. In the present work, we introduce an extended axion-electrodynamics model wherein the Bianchi identities are modified by the axion field. This leads to a modification of the energy conservation law for the fields: the Poynting theorem in a source-free region, in which the axion field is involved. By implementing a quantization scheme, our model can offer a novel approach for addressing the problem of axion production/conversion in the presence of electromagnetic and Dirac fields. [ABSTRACT FROM AUTHOR]

Thin-film optical diodes are important elements for miniaturizing photonic systems. However, the design of optical diodes relies on empirical and heuristic approaches. This poses a significant challenge for identifying optimal structural models of optical diodes at given wavelengths. Here, we leverage a quantum annealing-enhanced active learning scheme to automatically identify optimal designs of 130 nm-thick optical diodes. An optical diode is a stratified volume diffractive film discretized into rectangular pixels, where each pixel is assigned to either a metal or dielectric. The proposed scheme identifies the optimal material states of each pixel, maximizing the quality of optical isolation at given wavelengths. Consequently, we successfully identify optimal structures at three specific wavelengths (600, 800, and 1000 nm). In the best-case scenario, when the forward transmissivity is 85%, the backward transmissivity is 0.1%. Electromagnetic field profiles reveal that the designed diode strongly supports surface plasmons coupled across counterintuitive metal–dielectric pixel arrays. Thereby, it yields the transmission of first-order diffracted light with a high amplitude. In contrast, backward transmission has decoupled surface plasmons that redirect Poynting vectors back to the incident medium, resulting in near attenuation of its transmission. In addition, we experimentally verify the optical isolation function of the optical diode. [ABSTRACT FROM AUTHOR]

This study evaluates the performance of a twisted pair transmission line coil as a transceive element for 7 T MRI in terms of physical flexibility, robustness to shape deformations, and interelement decoupling. Each coil element was created by shaping a twisted pair of wires into a circle. One wire was interrupted at the top, while the other was interrupted at the bottom, and connected to the matching circuit. Electromagnetic simulations were conducted to determine the optimal number of twists per length (in terms of B₁+ field efficiency, SAR efficiency, sensitivity to elongation, and interelement decoupling properties) and for investigating the fundamental operational principle of the coil through fields streamline visualisation. A comparison between the twisted pair coil and a conventional loop coil in terms of B₁+ fields, maxSAR₁₀ g , and stability of S₁₁ when the coil was deformed was performed. Experimentally measured interelement coupling between individual elements of multichannel arrays was also investigated. Increasing the number of twists per length resulted in a more physically robust coil. Poynting vector streamline visualisation showed that the twisted pair coil concentrated most of the energy in the near field. The twisted pair coil exhibited comparable B₁+ fields and improved maxSAR₁₀ g to the conventional coil but demonstrated exceptional stability with respect to coil deformation and a strong self-decoupling nature when placed in an array configuration. The findings highlight the robustness of the twisted pair coil, showcasing its stability under shape variations. This coil holds great potential as a flexible RF coil for various imaging applications using multiple-element arrays, benefiting from its inherent decoupling. [ABSTRACT FROM AUTHOR]

The Poynting vector (Poynting flux) from Earth's magnetosphere downward toward its ionosphere carries the energy that powers the Joule heating in the ionosphere and thermosphere. The Joule heating controls fundamental ionospheric properties affecting the entire magnetosphere‐ionosphere‐thermosphere system, so it is necessary to understand when and where the Poynting flux is significant. Taking advantage of new data sets generated from DMSP (Defense Meteorological Satellite Program) observations, we investigate the Poynting flux distribution within and around the auroral zone, where most magnetosphere‐ionosphere (M‐I) dynamics and thus Joule heating occurs. We find that the Poynting flux, which is generally larger under more active conditions, is concentrated in the sunlit cusp and near the interface between Region 1 and 2 currents. The former concentration suggests voltage generators drive the cusp dynamics. The latter concentration shows asymmetries with respect to the interface between the Region 1 and 2 currents. We show that these reflect the controlling impact of subauroral polarization streams and dawnside auroral polarization streams on the Poynting flux. Plain Language Summary: Earth's upper atmosphere and ionosphere receive energy from space in many ways, and one of them is through an incoming flux of electromagnetic energy. This is expressed as a "Poynting flux," and we investigate how it is distributed in and around the ionosphere's auroral zone, where most activities occur. Our results show that large Poynting fluxes are distributed at locations where dramatic plasma flows appear, indicating a significant role of these flows in the energy circulation of the geospace. Key Points: We examine the distribution of Poynting flux into the ionosphere related to Joule heating using DMSP data with a novel gridding schemeThe highest Poynting flux is near the Region 1 and 2 currents' interface; the sunlit cusp also contains high Poynting fluxThe Poynting flux is asymmetric about the R1/R2 interface, exhibiting distinct peaks in regions associated with SAPS and DAPS [ABSTRACT FROM AUTHOR]

This paper investigates discrete symmetries for dyon and the invariance of Maxwell's field equations in the macroscopic media (material medium). Using advanced mathematical approaches, the paper derived electromagnetic duality and a unique form of Poynting theorem for dyon in macroscopic media. Here, we demonstrate that the combination of parity (P) , charge conjugation (C) , and time reversal (T) symmetry: CPT , is an exact symmetry for dyon in macroscopic media. Furthermore, a comprehensive analysis of the electromagnetic wave equation for dyons in conducting media is also derived. These findings contribute significantly to the understanding of dyon behavior in electromagnetic fields. [ABSTRACT FROM AUTHOR]

The article considers the mechanisms of the formation of transverse energy flows in polychromatic fields with different structures. It is shown that the magnitude of the Poynting vector transverse component and the angular momentum for symmetric polychromatic beams are the same as in coherent monochromatic fields. Changes in the characteristics of energy flows due to the transformation and destruction of beam symmetry are demonstrated. The data of computer ulation are presented. [ABSTRACT FROM AUTHOR]

The phenomenological theory revealing the generic effects of the problem symmetry, its violation, and energy conservation law on the singularities of the Poynting vector field is presented. The bifurcation scenario of formation (annihilation) of the singularities under variations of the problem parameters is elucidated. The results describe the singularities in scattering a linearly polarized plane electromagnetic wave. However, they are valid for any configuration of the incident beam at its scattering by a subwavelength particle. The author shows that topological changes in the pattern of the Poynting vector field occur through a finite number of pitchfork bifurcations. It means that the patterns are topologically stable under variations of the problem parameter(s) that lie between the bifurcation values. The latter ensures that the discussed topological properties of the problem are robust to weak symmetry violation, which is inevitable in any actual experiment. The general consideration is illustrated by a detailed study of singularities in scattering by an infinite right circular germanium cylinder. The results open the possibility of fitting and controlling radiation patterns on subwavelength scales important for various nanotechnologies. [ABSTRACT FROM AUTHOR]

Purpose: This paper presents a novel computational approach to optimize gradient array performance for a given pulse sequence. Specifically, we propose an electromagnetic (EM) approach that minimizes eddy losses within the cryostat while maintaining key performance parameters such as field linearity, gradient strength, and imaging region's dimension and position. Methods: High‐resolution EM simulations on the cryostat's surface are deployed to compute the net EM fields generated by each element of a gradient array coil at different frequencies. The computed fields are stored and combined for each frequency to form a quadratic vector–matrix–vector computation. The overall time‐average eddy power loss within the cryostat assembly for arbitrary pulse sequences is computed using frequency domain superposition. Results: The proposed approach estimates and regulates eddy power losses within the cryostat assembly. When compared to the stray field minimization approach, it can achieve over twice the reduction in eddy power loss. The proposed approach eliminates the need to sample the stray fields on the cryostat surface, which the number and position of the samples would be challenging when designing tunable array coils with capabilities that disrupt field symmetries. Additionally, the loss calculation considers the entire cryostat assembly rather than just the inner cylindrical surface of the warm shield. Conclusion: Our findings highlight the efficacy of an on‐the‐fly tuning method for the development of high‐performance whole‐body gradient array coils, effectively mitigating eddy losses within the cryostat and minimizing stray fields outside the coil assembly. This approach proves particularly advantageous for array coils with variable feeding currents. [ABSTRACT FROM AUTHOR]

This paper proposes a fundamentally new approach to the study of stationary states in atoms, which is based on the analysis of the energy of electric and magnetic fields. The circulation of the electromagnetic field in the stationary states of the atom was discovered and the mechanism of optical transitions due to the continuous change of the circulating energy was clarified. The difference between circulating energy flows in the initial and final states is emitted (or absorbed) in the form of a quantum of light. A universal relation for determining the lifetime of excited states is proposed. [ABSTRACT FROM AUTHOR]

This paper proposes a new, fast, and efficient method for determining the electromagnetic field distribution in two-port E-plane dielectric-loaded uniform rectangular waveguides. The analysis region is divided into individual blocks in the absence and presence of dielectric obstacles. The non-zero electric and magnetic field components are constructed throughout the system via the proposed method by utilizing the generalized scattering matrix method between blocks for unimodal or multimodal excitation. The resulting field distributions are compared to those obtained from commercial software, with very close agreement achieved, but with a significantly reduced computational time for the proposed method. The method is applicable in a straightforward manner and has been tested on both a filter device with relatively complex geometry and a disjoint system with a modal coupling challenge between its elements. The field components' accuracy is also tested by calculating the Poynting vector along the system. Additionally, this approach provides the global scattering parameters at the physical ports as a co-product. The proposed method has the potential to be applied to various two-port networks by using the proposed method according to the considered problem. [ABSTRACT FROM AUTHOR]

This paper presents the calculation of the electrical power transported by the electromagnetic fields of two parallel wires carrying opposite DC currents. The Poynting vector is developed in bipolar coordinates and symbolically integrated over different surfaces. For perfectly conducting wires, the purely longitudinal power in the space surrounding the wires is shown to be equal to that which is produced by the battery (and consumed by the load resistor). For resistive wires, the longitudinal power transported by the fields is shown to diminish according to the distance traveled, and the loss is proved to be equal to the power entering the wires via the fields at their surfaces. [ABSTRACT FROM AUTHOR]

The streamlines of the energy flux (Poynting vectors) and chirality flux as well as the intensity of the electric field around various plasmonic nanostructures (nanocube, nanocuboid, nanotriangle, hexagonal nanoplate and bowtie nanoantenna) induced by a circularly polarized (CP) or linearly polarized (LP) light were studied theoretically. The boundary element method combined with the method of moment was used to solve a set of surface integral equations, based on the Stratton–Chu formulation, for analyzing the highly distorted electromagnetic (EM) field in the proximity of these nanostructures. We discovered that the winding behavior of these streamlines exhibits versatility for various modes of the surface plasmon resonance of different nanostructures. Recently, using plasmonic nanostructures to facilitate a photochemical reaction has gained significant attention, where the hot carriers (electrons) play important roles. Our findings reveal a connection between the flow pattern of energy flux and the morphology of the photochemical deposition around various plasmonic nanostructures irradiated by a CP light. For example, numerical results exhibit vertically helical streamlines of the Poynting vector around an Au nanocube and transversely twisted-roll streamlines around a nanocuboid. Additionally, the behaviors of the winding energy and chirality fluxes at the gap and corners of a plasmonic bowtie nanoantenna, implying a highly twisted EM field, depend on the polarization of the incident LP light. Our analysis of the streamlines of the Poynting vector and chirality flux offers an insight into the formation of plasmon-enhanced photocatalysis. [ABSTRACT FROM AUTHOR]

Recently, interactions between putative axions and magnetic monopoles have been revisited by two of the authors.[1] It is shown that significant modifications to conventional axion electrodynamics arise due to these interactions, so that the axion–photon coupling parameter space is expanded from one parameter gaγγ$g_{a\gamma \gamma }$ to three (gaγγ,gaAB,gaBB)$(g_{a\gamma \gamma },g_{aAB},g_{aBB})$. Poynting theorem is implemented to determine how to exhibit sensitivity to gaAB$g_{aAB}$ and gaBB$g_{aBB}$ using resonant haloscopes, allowing new techniques to search for axions and a possible indirect way to determine if magnetically charged matter exists. [ABSTRACT FROM AUTHOR]

Heaviside reformulated the Maxwell equations because he considered that electromagnetic fields and waves have duality. As a result of the reformulation, the Poynting vector was obtained. When the variations of an electromagnetic field propagate in space as waves, this wave is referred to as an electromagnetic wave. The Poynting vector represents the traveling direction of the electromagnetic wave. In this Session, we reexamine electromagnetic fields and waves by focusing on the relationship between the Poynting vector and the duality. According to Wikipedia, no current flows in a vacuum because there are no electrons or electric charges. However, this seems to be incorrect, and the current I(x) given by rotH = I(x) flows in a vacuum. Moreover, a voltage V(x) given by rotE = -V(x) is generated because the magnetic field is the dual of the electric field and the current is the dual of the voltage. As a result, the presence of a coil in a vacuum is expressed by rotE = -V (x) = -∂B I ∂t = - pLI (x). Namely, the Maxwell equations indicate that "self-induction can occur everywhere in the atmosphere", as described by Heaviside in the book written by Nahin. Moreover, a capacitor in the atmosphere, including a vacuum, is also given by an equation because it is the dual of the coil. Thus, electromagnetic waves have physical properties of circuit elements including coils and capacitors, which are different from those of lines of forces, such as lines of electric and magnetic forces. The physics of electromagnetic waves is included in classical physics but is different from Newtonian mechanics and uses complex numbers. [ABSTRACT FROM AUTHOR]

Thought experiments are effective tools of theoretical physics, and historically they have led to the discovery of many useful ideas and relations. Yet they also give rise to paradoxes that persist for long periods of time despite enormous efforts to resolve them. A problem par excellence, one that falls within the realm of classical electrodynamics and has been investigated exclusively by means of thought experiments, is the famous problem of hidden momentum. It concerns the conversion of the electromagnetic momentum generated by static electromagnetic fields into momentum of a non-electromagnetic nature and the resulting momentum balance. As a rule, this effect, which takes place in ponderable systems, is very subtle, of the order of ∼ 1/c2; thus, until now it has only been studied theoretically and has never been demonstrated experimentally. The main subject of this paper is the analysis of a robust and experimentally well-established phenomenon operating in static electromagnetic fields—the ordinary Hall effect—which has been interpreted anew in terms of the Poynting vector and proven to be sufficiently sensitive for direct comparison with typical quantitative estimates encountered in the hidden momentum problem. Confrontation of hypothetical models with a real experiment enables us to formulate the general conditions and rules that should be observed when designing thought experiments in classical electrodynamics. [ABSTRACT FROM AUTHOR]

By developing the previously proposed method of combining continuum mechanics with Einstein's field equations, it has been shown that the classic relativistic description, curvilinear description, and quantum description of the physical system may be reconciled using the proposed Alena Tensor. For a system with an electromagnetic field, the Lagrangian density equal to the invariant of the electromagnetic field was obtained, the vanishing four-divergence of canonical four-momentum appears to be the consequence of the Poynting theorem, and the explicit form of one of the electromagnetic four-potential gauges was introduced. The proposed method allows for further development with additional fields. [ABSTRACT FROM AUTHOR]

The polarization of light is a valuable information channel that has been studied extensively in optical devices. There has been limited progress in developing low‐refractive index contrast and large‐scale chiral meta‐devices that are easy to integrate and mass‐produce. In this image, a chiral imaging meta‐device with a large area and broadband chirality control is experimentally demonstrated. The centimeter‐scale Moiré meta‐device is achieved using nanoimprint technology. The Poynting vector and singularity features in the near field and chiral optical response in the far field are discussed. The proposed Moiré meta‐devices can achieve circular dichroism (CD) of more than 10%. Further chiral imaging harnessing CD mechanisms are demonstrated, which may lead to significant potential in various fields, including encryption and security, materials science, biochemistry, and medicine. [ABSTRACT FROM AUTHOR]

Maxwell's verbal statement of Coulomb's experimental verification of his hypothesis, concerning force between two electrified bodies, is suggestive of a modification of the respective computable expression on logical grounds. This modification is in tandem with the completeness condition for a physical theory, that was stated by Einstein, Podolsky and Rosen in their seminal work. Working with such a modification, I show that the first Maxwell's equation, symbolically identifiable as ∇ · E = ρ / ϵ 0 from the standard literature, is unprovable. This renders Poynting's theorem to be unprovable as well. Therefore, the explanation of 'light' as 'propagation of electromagnetic energy' comes into question on theoretical grounds. [ABSTRACT FROM AUTHOR]

The multicore fibre (MCF) is an effective and auspicious technology to overawe the limitation of the single-mode fibre. One of the important applications of MCF is power over fibre. In this paper, we have been designed eight different hexagonal structures by using 6, 7, 8, 9, 10, 11, 12 and 13 cores MCF. Those designs are categorized as even core multicore fibre (ECMCF) for 6, 8, 10 and 12 cores and odd core multicore fibre (OCMCF) for 7, 9, 11 and 13 number of cores. We also studied the impact analysis of odd or even number of the cores. The proposed designs having 140 µm diameter, large effective area of 1256 µ2m and two pitches d1=20 µm and d2=10 µm. The comparative analysis has been done by core multiplicity factor, electric field, coupled power, cross overpower parameter calculated for 10,000 samples. The hexagonal core shape MCF shows better performance if the number of the core in even number. [ABSTRACT FROM AUTHOR]

It is still difficult to accurately evaluate the reactive electromagnetic energy and the radiative electromagnetic energy of a radiator, because there are no explicit expressions for them. This paper proposes to borrow the energy concept in the charged particle theory and separate the total electromagnetic energy of a radiator into three parts: a Coulomb–velocity energy, a radiative energy and a macroscopic Schott energy. Consequently, the Poynting vector is considered to include a real radiative power flow by the radiative energy and a pseudo power flow caused by the fluctuation of the reactive energy. The energies involved in the electromagnetic mutual coupling are separated in a similar way. All energies are defined with explicit expressions in which the vector potential plays an important role. The time domain formulation and the frequency domain formulation of the theory are consistent with each other. The theory is verified with the Hertzian dipole. Numerical examples demonstrate that this theory may provide proper interpretations for electromagnetic radiation and mutual coupling problems. [ABSTRACT FROM AUTHOR]

We study the sharp focusing of the input structured light field that has a non-uniform elliptical polarization: the parameters of the ellipse depend on the position in the input plane (we limited ourselves to the dependence only on the angular variable). Two types of non-uniformity were considered. The first type corresponds to the situation when the semi-axes of the polarization ellipse are fixed while the slope of the major semi-axis changes. The second type is determined by the situation when the slope of the major semi-axis of the polarization ellipse is constant, and the ratio between the semi-axis changes (we limited ourselves to the trigonometric dependence of this ratio on the polar angle). Theoretical and numerical calculations show that in the case of the first type of non-uniformity, if the tilt angle is a multiple of the polar angle with an integer coefficient, then the intensity distribution has rotational symmetry, and the energy flow is radially symmetric and has the negative direction near the optical axis. In this second case, the intensity symmetry is not very pronounced, but with an odd dependence of the ratio of the semi-axes of the polarization ellipse, the focused field at each point has a local linear polarization, despite the rather complex form of the input field. In addition, we investigate the distribution of the longitudinal component of the Poynting vector. The obtained results may be used for the formation of focused light fields with the desired distributions of polarization, Poynting vector density, or spin angular momentum density in the field of laser manipulation and laser matter interaction. [ABSTRACT FROM AUTHOR]

Volumetric scattering prevents imaging modalities in biomedical optics from imaging deep inside tissue. The optimization of the incident wavefront has the potential to improve these imaging modalities. To investigate the optimization and light propagation of such beams inside scattering media rigorously, full-vectorial simulations based on solutions of Maxwell's equations are necessary. In this publication, we present a versatile two-step beam synthesis method to efficiently simulate the scanning and phase optimization of a focused beam inside a static scattering medium. We present four different approaches to the phase optimization of the energy density and the absolute value of the Poynting vector. We find that these quantities have two regions with different, almost exponential decays over depth for a non-optimized beam. Optimization by conjugating the phase of the projected electric field in various directions at the focus shows an improvement below a certain penetration depth. Seeking global solutions to the optimization problems reveals an even better enhancement in the energy density and the absolute value of the Poynting vector in the focus. For Poynting vector optimization, the differences between the presented optimization approaches are more significant than for the energy density. With the presented method, it is possible to efficiently simulate different imaging methods improved by wavefront shaping to investigate their possible penetration depths. [ABSTRACT FROM AUTHOR]

In this paper, the effect of the Poynting vector force field on periodically forced neutrally buoyant spherical particles at low Reynolds numbers is studied numerically. The mathematical formulation of six nonlinear coupled integro–differential equations was obtained by modifying the Lovalenti and Brady formalism for the hydrodynamic force acting on a spherical particle. The governing equations were solved using an adaptive step size Runge–Kutta method by integrating the integral using the trapezoidal rule. The forces acting on the particle-provided phase space trajectories are similar to Jeffery's orbits. The paper also discusses the possible outcomes of the rheology due to the Poynting vector on the periodically forced neutrally buoyant sparsely spaced non-interacting spherical particles in a fluid at low Reynolds numbers. The computed rheological parameters in this study are first normal stress difference, second normal stress difference, intrinsic pressure and relative viscosity. The study shows that the first normal stress difference is nearly zero and the second normal stress difference is nonzero indicating the dominance of the Poynting vector field over the magnetic field on the bulk stress of the fluid. The intrinsic pressure and the relative viscosity changed due to the stress caused by the electromagnetic force and periodic force on the spherical particles. [ABSTRACT FROM AUTHOR]

Energy transfer accompanying with current is usually described by using Poynting's vector. Here, combining Kirchhoff's law, Joule's law and Slepian's postulation, we demonstrate that, for the case of a current travels along a wire, component of total energy flow flux parallel to the wire (CTEFFPW) may be equivalently described by using product of current intensity and electric potential (voltage), furthermore, the law of conversion and conservation of energy accompanying with current, which is equivalent to Poynting's theorem, may be obtained based on circuit method. Noting that product of current intensity and voltage relates to CTEFFPW instead of the electric power, physical meaning of usual definitions of powers adopted in electric power theory are readdressed. Our work may provide possibility to achieve the long-time expectation that power properties of power systems are described on the basis of Poynting's theorem and Poynting's vector, and to address the unsolved problems arised in the electric power theory. [ABSTRACT FROM AUTHOR]

A brief review is given of the author's recent achievements in classifying singular points of the Poynting vector patterns in electromagnetic fields of complex configuration. The deep connection between the topological structure of the force lines pattern and the law of energy conservation, the symmetry of the problem, and the dimension of the space has been unveiled. [ABSTRACT FROM AUTHOR]

A simple and coherent approach to fluid mechanics is presented using a proper formalism of geometric algebra. The analogy between the equations of electromagnetism and fluid mechanics provides reinterpretation of the equations for two constituent (vorticity and the Lamb vector) fields. Identifying certain quantities as the source fields, the guiding Navier–Stokes (NS) equations of fluid mechanics can be formulated as a set of four geometrically distinct field equations, resembling exactly the Maxwell equations for the constituent magnetic and electric fields. The same set of equations works for all the cases of compressible, incompressible, viscous and the inviscid fluid motions with appropriately modified source terms. The analogy is completed by defining the combined ‘fluidomechanic’ bivector field in space–time algebra and further extended to the fluidic analogue of the Poynting theorem, Poynting vector and Lorentz force. [ABSTRACT FROM AUTHOR]

When applying what is called Kelvin's principle to the elementary currents of two permanent magnets that attract each other, an apparent energy paradox appears. For Kelvin's principle says that when constant electric currents are displaced with respect to one another, the mechanical work yielded as a result of the action of magnetic forces is equal in amount to the increase (not decrease) in the energy of the total magnetic field. The energy provided by the power supply in order to keep the currents constant is thus twice as large as the mechanical work yielded during the displacement of the current-carrying wires. But when dealing with permanent magnets and their polarization currents, there is still the yield of mechanical work and also the increase in energy of the total magnetic field, but no such thing as a visible power supply. In this article, things are analyzed by using the Poynting vector as an instrument. As a result, the topological assumption of a hidden reservoir of energy sitting in the direction of a fourth spatial dimension turns out to be indispensable in order to save the principle of local conservation of energy and of action by contact. A recognition of this kind was foreshadowed by Mie 100 years ago, who postulated that, in certain, but nevertheless common situations, energy flowed into ambient space out of the particles themselves both in the gravitational and the electromagnetic case. [ABSTRACT FROM AUTHOR]

Since its launch in 2000, the Cluster fleet visited a vast domain of the circum‐terrestrial environment, from the upstream solar wind and the distant tail, down to the plasmasphere, scanning in detail all magnetospheric regions during over two solar cycles. This led to an unprecedentedly rich data collection of multi‐point measurements which will be used for years to come to decipher the mechanisms of Solar‐Terrestrial interactions. The large volume of data gathered by Cluster requires special strategies to make efficient use of it. To address this issue we constructed a browsable database containing parameters of the detected Ultra low frequency waves and of the spacecraft formation geometry. The primary data used to derive the parameters are the magnetic field, the electric field and the electron density. The data is resampled to a cadence of 1 s and processed using a sliding analysis window of 2,048 s with a step of 256 s over 24 hr intervals. This results in time‐frequency arrays for each parameter covering the 0.5 mHz to 0.5 Hz frequency range. The database is accessible at http://plasma.spacescience.ro/cluster.html. In total there are 47 wave parameters in the database, among them being the ellipticity, the degree of polarization, the (unsigned) wave vector direction, and the Poynting vector. Plots for the planarity, elongation, and degeneration of the Cluster tetrahedron are also available. At the moment, the database covers measurements made between 01 January 2001 and 31 December 2020 with more data being added in time. Here we present this database, discuss the methods used to derive the parameters and give practical examples. Plain Language Summary: This work describe an on‐line database containing data and plots of physical quantities characterizing low frequency waves detected by the Cluster spacecraft fleet in the space plasma around the Earth. These quantities are derived using measurements of the magnetic field, electric field, and particles taken by the four spacecraft over 20 years. The plots can be used to quickly assess the plasma waves activity over a certain time interval, while the data can be used for further analysis. Key Points: The Cluster Virtual Observatory (CVO) is an on‐line archive of low frequency wave parameters based on Cluster measurementsThe CVO also provides the tetrahedron geometrical configuration parametersThe waves and configuration parameters are available as quick‐plots as well as binary Hierarchical Data Format data [ABSTRACT FROM AUTHOR]

In a heat-assisted magnetic recording, the thermal effect of the head/disk interface has an important influence on the stability of the recording data. In this paper, we will discuss the thermal radiation from the disk, more specifically, the magnetic recording layer, which is at high temperature after laser heating, to the magnetic head, which is at room temperature. The radiative heat flux can be represented by the Poynting vector. In the near-field band, an effective way to obtain the electromagnetic fields is to solve the Maxwell's equations combined with fluctuational electrodynamics. The near-field back radiation between specific head and disk material is calculated by the fluctuation-volume-current method. The radiative heat energy will induce the thermal deformation of the magnetic head, which will be discussed by the simulation, laying the foundation for adjusting and controlling the flying status. [ABSTRACT FROM AUTHOR]

In this paper, we consider the behavior of the local energy flow velocity of the fundamental air-core mode at the core-cladding boundary in two types of hollow-core fibers: hollow-core fibers with a negative curvature of the core boundary and single-capillary fibers with similar geometrical parameters. It is demonstrated that the behavior of both axial and radial components of the local energy velocity of the fundamental air-core mode is completely different for these two types of hollow-core fibers. The negative curvature of the core boundary leads to an alternating behavior of the radial projection of the local energy velocity and a decrease of two orders of magnitude compared to the values of this projection for a single capillary. In our opinion, this behavior of the local energy velocity of the fundamental air-core mode is caused by a periodic set of Poynting vector vortices that appear in the cladding capillary walls. [ABSTRACT FROM AUTHOR]

In this paper, there are researched resonance effects occurring when an electromagnetic wave falls on a cylinder. The nature of the effects depends on the ratio between the diameter of the cylinder and the wavelength of the radiation and on the cylinder material. In thick cylinders (D ≫ λ) without absorption, surface wave resonances occur in the form of peaks regularly following each other on the curve of dependence of scattering on the diameter. The follow-up period is determined by the refractive index. In very thin metal wires (D ≪ λ) the effect of abnormally strong absorption of electromagnetic radiation is observed. The absorption efficiency factor of a metal wire with a diameter of several micrometers in the centimeter range of wavelengths reaches several hundred. Calculations of the distribution of the electromagnetic field inside and outside the wire showed a significant increase in the intensity of the electromagnetic field inside the cylinder at certain ratios between the diameter of the wire and the wavelength of radiation. The trajectories of the Poynting vector flow are distorted, and energy enters the wire from all sides. This effect is non-resonant. Fano resonances occur in thin cylindrical wires with a high refractive index and low absorption. At the same time, for some diameters, the scattering increases, and a very narrow resonant peak appears, while for others, the scattering is very small. The wire becomes invisible at a certain wavelength. [ABSTRACT FROM AUTHOR]