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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., (© 2023 International Society for Magnetic Resonance in Medicine.)

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]

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 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]

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]

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]

This work applies the contact formalism of classical mechanics and classical field theory, introduced by Herglotz and later developed in the context of contact geometry, to describe electromagnetic systems with dissipation. In particular, we study an electron in a non-perfect conductor and a variation of the cyclotron radiation. In order to apply the contact formalism to a system governed by the Lorentz force, it is necessary to generalize the classical electromagnetic gauge and add a new term in the Lagrangian. We also apply the k-contact theory for classical fields to model the behavior of electromagnetic fields themselves under external damping. In particular, we show how the theory describes the evolution of electromagnetic fields in media under some circumstances. The corresponding Poynting theorem is derived. We discuss its applicability to the Lorentz dipole model and to a highly resistive dielectric. [ABSTRACT FROM AUTHOR]

Developing simulation models for electromagnetic field problems often deals with approximations of the full set of Maxwell’s equations, to obtain performant methods. This is also the case for the so-called Darwin model, which has the capability of including resistive, inductive, and capacitive effects without the need of solving full-wave Maxwell’s equations. However, an issue is the difficulty of prescribing realistic excitations of the model, e.g., via a terminal voltage. In this article, the straightforward prescription of the scalar potential on electric ports is investigated via Poynting’s theorem, with the outcome that it can be considered as physical voltage excitation up to frequencies, where the validity of the Darwin model itself is lost. [ABSTRACT FROM AUTHOR]

The phenomena of light absorption, fluorescence and laser emission are accounted for within a unique picture. The atomic dipole is dealt with in a quantum framework, whereas the electromagnetic field is assumed to be a classical sine-wave. The on and off resonance cases are investigated. This is achieved owing to a novel application of Poynting's theorem. Observable predictions are made, regarding absorption of the electromagnetic energy and the frequency bandwidth of light emitted either by fluorescence or laser effect. [ABSTRACT FROM AUTHOR]

This study analyzes the instantaneous spatial energy density and Poynting vector in the WPT system and presents time-varying distributions and animations of this energy density and Poynting vector. First, the energy density is decoupled by two self-energy densities of each coil and the mutual energy density of the two coils. Result reveals how the energy is stored in the WPT system. Second, the Poynting vector is analyzed, and it is found that the power is transferred only in the last half period of the Poynting vector, not at every moment of the whole period. This instantaneous Poynting vector also possesses a characteristic that shows no power flow on the condition that the current phase difference equals zero. This finding is different from the energy density and indicates that the instantaneous Poynting vector can perfectly interpret how power is transferred in the WPT system. Finally, a simulation and an experiment were conducted to verify the correctness of the analysis. This study contributes to a deeper and better understanding of the intrinsic characteristics of energy storage and power flow in the WPT system, and can be referred to for WPT system design and optimization when one considers the EMC or human electromagnetic field exposure problem. [ABSTRACT FROM AUTHOR]

The existing methods for calculating the energy of stationary states relate it to the energy of the electron, considering it negative in the atom. Formally, choosing a point that corresponds to zero potential energy you can assign a negative value to the electron energy. However, this approach does not answer many other questions, for example, the actual value of the energy of stationary states is unknown, but only the difference in energies between stationary states is known; the concept of "minimum energy of the system" loses its meaning (choosing the origin of the energy reference, we replace the minimum with the maximum, or vice versa); the physical reason for the stability of stationary states is not clear; it is impossible to reveal the physical reason for the introduction of selection rules, since the Heisenberg uncertainty relations exclude the analysis of the transition mechanism, replacing it with the concept of a "quantum leap". Let us show that the energy of stationary states is the energy of a spherical capacitor, the covers of which are spheres whose radii are equal to the radius of the nuclear and corresponding stationary state. The energy of the ground state in the hydrogen atom is 0.8563997 MeV. The presence of charges and a magnetic field presupposes the circulation of energy in the volume of the atom (the Poynting vector is not zero). Revealed quantization of the angular momentum of the electromagnetic field in stationary states is L n = n ℏ. The change in the angular momentum of the electromagnetic field during transitions between stationary states in atoms removes the physical grounds for introducing selection rules. The analysis shows that the Heisenberg uncertainty relations are not universal, and their application in each specific case must be justified. [ABSTRACT FROM AUTHOR]

Topological complex transient electromagnetic fields give access to nontrivial light-matter interactions and provide additional degrees of freedom for information transfer. An important example of such electromagnetic excitations are space-time non-separable single-cycle pulses of toroidal topology, the exact solutions of Maxwell's equations described by Hellwarth and Nouchi in 1996 and recently observed experimentally. Here we introduce an extended family of electromagnetic excitation, the supertoroidal electromagnetic pulses, in which the Hellwarth-Nouchi pulse is just the simplest member. The supertoroidal pulses exhibit skyrmionic structure of the electromagnetic fields, multiple singularities in the Poynting vector maps and fractal-like distributions of energy backflow. They are of interest for transient light-matter interactions, ultrafast optics, spectroscopy, and toroidal electrodynamics. Topology in electromagnetic fields can lead to a range of intriguing and unexpected phenomena. Here the authors describe a family of supertoroidal light pulses that exhibit skyrmionic topological structure flying in free space. [ABSTRACT FROM AUTHOR]

Electromagnetic energy backflow is a phenomenon that occurs in regions where the direction of the Poynting vector is opposite to that of the propagation of the wave field. It is particularly remarkable in the nonparaxial regime and has been exhibited in the focal region of sharply-focused beams, for vector Bessel beams, and vector-valued spatiotemporally localized waves. A detailed study is undertaken of this phenomenon and the conditions for its appearance are examined in detail in the case of a superposition of four plane waves in free space, the simplest electromagnetic arrangement for the observation of negative energy flow, as well as its comprehensive and transparent physical interpretation. It is shown that the state of polarization of the constituent components of the electromagnetic plane wave quartet determines whether or not energy backflow takes place and what values the energy flow velocity assumes. Depending on the polarization angles, the latter can assume any value from c (the speed of light in vacuum) to −c in certain spatiotemporal regions of the field. [ABSTRACT FROM AUTHOR]

In electromagnetism, the concept of Poynting vector as measured by an observer is well known. A mathematical analogue in general relativity is the super-Poynting vector of the Weyl tensor. Observers for which the (super-)Poynting vector vanishes are called principal. When, at a given point, the electromagnetic field is non-null, or the gravitational field is of Weyl–Petrov type I or D, principal observers instantaneously passing through that point always exist. We survey characterizations of such observers and study their relation to arbitrary observers. In the non-null electromagnetic case it is known that, given any observer, there is a principal observer which moves relative to the first in the direction of his Poynting vector. Replacing Poynting by super-Poynting yields a possible gravitational analogue; we show that this analogy indeed holds for any observer when the Petrov type is D, but only for a one-dimensional variety of observers when the Petrov type is I. We provide algorithms to obtain the principal observers directly from the electric and magnetic fields (in the electromagnetic case) or electric and magnetic parts of the Weyl tensor (in the gravitational case) relative to an arbitrary observer. It is found that in Petrov type D doubly aligned non-null Einstein–Maxwell fields (which include all classical charged black hole solutions) the Poynting and super-Poynting vectors are aligned, at each point and for each observer, and the principal observers coincide. Our results are illustrated in simple examples. [ABSTRACT FROM AUTHOR]

In this work, we consider axially symmetric stationary electromagnetic fields in the framework of special relativity. These fields have an angular momentum density in the reference frame at rest with respect to the axis of symmetry; their Poynting vector form closed integral lines around the symmetry axis. In order to describe the state of motion of the electromagnetic field, two sets of observers are introduced: the inertial set, whose members are at rest with the symmetry axis; and the noninertial set, whose members are rotating around the symmetry axis. The rotating observers measure no Poynting vector, and they are considered as comoving with the electromagnetic field. Using explicit calculations in the covariant 3 + 1 splitting formalism, the velocity field of the rotating observers is determined and interpreted as that of the electromagnetic field. The considerations of the rotating observers split in two cases, for pure fields and impure fields, respectively. Moreover, in each case, each family of rotating observers splits in two subcases, due to regions where the electromagnetic field rotates with the speed of light. These regions are generalizations of the light cylinders found around magnetized neutron stars. In both cases, we give the explicit expressions for the corresponding velocity fields. Several examples of relevance in astrophysics and cosmology are presented, such as the rotating point magnetic dipoles and a superposition of a Coulomb electric field with the field of a point magnetic dipole. [ABSTRACT FROM AUTHOR]

In this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation is developed and implemented in software, which allows us to demonstrate the general properties of electromagnetic field in the media described by FO models (FOMs). The differences in interpretation of the fundamental theorems of electromagnetics (i.e. Poynting's theorem, the uniqueness theorem and the Lorentz reciprocity theorem) in comparison to integer-order electromagnetics are analysed. It is demonstrated that all the properties of electromagnetic field, related to these fundamental theorems are preserved when time derivatives are generalized towards FO in Maxwell's equations. [ABSTRACT FROM AUTHOR]

The article describes a numerical approach for Massive MIMO channel modeling that accounts for the effects of electromagnetic coupling between a user and the receiving device. The modeling is performed by a combination of the Finite-Difference Time-Domain and the Ray-Tracing methods, supplemented with a stochastic geometry model of the propagation environment. The influence of user-coupling on the channel properties was studied statistically using the singular value spread and matrix power ratio metrics of the channel correlation matrix. The time-averaged Poynting vector distribution in the near-field of the receiver was evaluated using a realistic human phantom model and the Maximum Ratio Transmission precoding scheme in the downlink. The average enhancement of the time-average Poynting vector magnitude at the receiver location, compared to the surrounding area, was found to be around 10 dB when using 36 antenna elements at the base station. The electromagnetic field exposure of the phantom was assessed in terms of the 10g-average peak-spatial Specific Absorption Rate and compared with the existing public guidelines. Comparison of the EMF and exposure results provides a new perspective on the future regulatory procedures. [ABSTRACT FROM AUTHOR]

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In this study, the electromagnetic fields are developed in the presence of both the electric and magnetic induction fields by quaternion algebra. In this sense, the polarization and magnetization effects, which are valid in the material media, gain much importance. Quaternions are one of the most convenient tools for representing electromagnetism with regard to having non-commutative but associative algebraic division ring. By defining the quaternion induction field, the quaternion source term has been obtained in basic and elegant notation for the first time. In addition, one type of Poynting theorem, named as the Minkowski form, has been presented including the permittivity and permeability constants by quaternions. [ABSTRACT FROM AUTHOR]

This paper reviews recent progress in the measurement and modelling of stochastic electromagnetic fields, focusing on propagation approaches based on Wigner functions and the method of moments technique. The respective propagation methods are exemplified by application to measurements of electromagnetic emissions from a stirred, cavity-backed aperture. We discuss early elements of statistical electromagnetics in Heaviside's papers, driven mainly by an analogy of electromagnetic wave propagation with heat transfer. These ideas include concepts of momentum and directionality in the realm of propagation through confined media with irregular boundaries. We then review and extend concepts using Wigner functions to propagate the statistical properties of electromagnetic fields. We discuss in particular how to include polarization in this formalism leading to a Wigner tensor formulation and a relation to an averaged Poynting vector. [ABSTRACT FROM AUTHOR]

In the present study, the Poynting vector of an ELF electromagnetic wave in the presence of a three-layered ocean floor is treated both analytically and numerically. It is verified that the derived locus of the Poynting vector in a three-layered region reduces to exactly the same form for a two-layered region once the thickness of the intermediate layer decreases to zero. When studying the magnitude of the Poynting vector, it is found that the locations of the turning points accurately match the coordinates of maximum penetration. Moreover, despite that the lateral wave can reach a larger depth of penetration as the propagation distance increases, the electromagnetic field at the receiving point will also bear greater attenuation. Figuring out the required penetration depth before determining the location of the receiver is a possible way to ease this issue. [ABSTRACT FROM AUTHOR]

The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic (EM) field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and by the Lorentz force law. Whereas Maxwell's equations relate the fields to their material sources, Poynting's theorem governs the flow of EM energy and its exchange between fields and material media, while the Lorentz law regulates the back-and-forth transfer of momentum between the media and the fields. An alternative force law, first proposed by Einstein and Laub, exists that is consistent with Maxwell's equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetized medium, the Einstein-Laub (E-L) formulation of EM force and torque does not invoke hidden entities under such circumstances. Moreover, total force/torque exerted by EM fields on any given object turns out to be independent of whether the density of force/torque is evaluated using the law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions inside matter. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality. [ABSTRACT FROM AUTHOR]

It is difficult for an instructor to just make up valid numbers for Bx, By, Bz, Ex, Ey, and Ez in the creation of homework problems and test questions calculating the Poynting vector. In this paper, 25 examples are given of the electric and magnetic fields of electromagnetic waves, obeying the condition that the electric field is perpendicular to the magnetic field, and the condition that the magnitude of the electric field is equal to the magnitude of the magnetic field times the speed of light. These easy-to-use numbers lend themselves to the calculation of the Poynting vector, which leads to the calculation of energy density and other macroscopic quantities. A separate list is presented for the Gaussian CGS system of units. [ABSTRACT FROM AUTHOR]

The ultra-short optical pulses can be used for the confinement of neutral particles by an additional optical longitudinal force, connected with the Poynting vector and the influence of the magnetic field on their polarizability. The Poynting vector is connected also to the intensity of the electromagnetic field. On other hand, the intensity of a laser pulse can be manipulated by an optical lens, and thus, indirectly, the optical force can be increased or decreased or its direction to be changed. This in turn enables a unique possibility for the compression of neutral atoms, molecules, and particles into the focus of the lens. Here, we reported on an experimental study of neutral particle confinement in the focus of femtosecond laser pulses and further confirmed by a theoretical investigation. The findings demonstrate an innovative approach to the compression and confinement of neutral particles within the focal plane of a lens and their further manipulation. Feasible applications could be in the field of cold nuclear fusion and cooling of light-neutral atoms and molecules. [ABSTRACT FROM AUTHOR]

Propagation characteristics of electromagnetic field (EMF) is crucial to identify and position the potential defects when using eddy current testing (ECT) method for conductive medium. Therefore, in this work, the EMF propagation characteristics in carbon fiber reinforced polymer (CFRP) composites are thoroughly investigated by using finite element (FE) method. Considering the layered structure, stacking sequence, and interlaminar interface, we utilize a contact impedance interior boundary condition to model CFRP laminates, and then discuss the calculation accuracy and mesh refinement. The numerically solved results are compared to the theoretically calculated ones, and clearly point out the significant discrepancy between the true skin depth and the standard one. The findings reveal that the electrical anisotropy is one of the important factors in affecting the EMF propagation. The strong anisotropy results in more power loss and a frequency-independent decay rate than the ones in the weak and isotropic cases, which is proved by introducing Poynting theorem. Additionally, the other critical factor affecting the EMF attenuation is the lay-up stacking sequence of CFRPs, which is quite different from that of the isotropic mterials. Besides, the driving coil geomerty is another factor in affecting the EMF propagation characteristics from the point of the incident field. [ABSTRACT FROM AUTHOR]

We address to the Poynting theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy-momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product $${\varvec{j}} \cdot {\varvec{E}}$$ (where the current density $${\varvec{j}}$$ and bound electric field $${\varvec{E}}$$ are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, ), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy-momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy-momentum tensor. [ABSTRACT FROM AUTHOR]

We show that the familiar 4/3 problem originates from the incorrect determination of the momentum of the electromagnetic field generated by an isolated charged particle, which results from an incorrect application of the Poynting theorem to the field. To demonstrate this, we consider a macroscopic problem: splitting a charged oil droplet into two identical smaller droplets in the rest frame K of the original droplet, and in another inertial frame moving with respect to K with some constant velocity, and arrive at a physically senseless solution in the framework of the standard approach. To solve this problem in a correct way, we suggest a modified Poynting theorem for an isolated charge and recalculate the momentum of the electromagnetic field of this charge, which yields the usual relativistic relationship between the field energy and momentum. Our approach is not at odds with the idea about 'Poincaré stresses'; however, in contrast to the standard method, it provides a usual relationship between the 'Poincaré stress-energy' and the associated momentum stress component. Finally, the continuity equation in four-dimensional form for the case of isolated moving charge is also proposed, which completely resolves the 4/3 problem. [ABSTRACT FROM AUTHOR]

For a short time, the electron creates a Poynting vector B S b carrying momentum. That electric field crosses the particle path and takes away or adds momentum, resulting in the observed phase difference between both paths. As indicated in the figure above (adapted from the authors'), an electron taking either of the paths around the solenoid has an electric field B E b extending into the solenoid, where there is a nonzero magnetic field B H b . [Extracted from the article]

A method for arbitrarily controlling the phase progression and power flow of electromagnetic fields within a region of space is introduced. Specifically, we describe how a 2D inhomogeneous, anisotropic medium can be designed that supports desired spatial distributions of the wave vector and Poynting vector direction. Plane-wave relations in anisotropic media are used in conjunction with an impedance matching process to find the required material parameters. The developed formulation allows one to independently tailor the phase and amplitude of a field profile. The work will find application in the design of electromagnetic or optical guiding structures and radiating apertures. [ABSTRACT FROM AUTHOR]

Abstract: Power of an electromagnetic field in a plane is derived exactly as a function of the angular spectrum of only electric field components at another plane based on Maxwell equations and Poynting vector. Then, this quantity is acquired as a function of the electric field components. In this calculation, a function appears that is general and does not depend on the electromagnetic field function. [Copyright &y& Elsevier]

A multipolar formulation is adopted to investigate the absorption and scattering processes involved in near-field interactions. This approach allows one to determine the upper bounds for the absorbed and radiated powers that would be achieved by an ideal lossless sensor, which are of particular interest, for example, to wireless power transfer (WPT), wireless sensors and near-field coupled radiators. The multipolar formulation also helps to extricate the fundamental compromises that must be addressed in the design of such systems, as well as to identify strategies that could approach their best possible performances. The general theory is illustrated with an example consisting of a coated sensor illuminated by a Hertzian dipole, which is a representative example of any scattering or radiating system based on small resonators. The example also serves to compare the performance characteristics obtained with different phenomena such as multipolar resonances, phase-induced interference effects and cloaking. [ABSTRACT FROM AUTHOR]

Closed form expressions are derived in time domain to calculate the electric and magnetic energy linked to the electromagnetic field surrounding an electromagnetic device. The expressions are rigorous, general, and explicit in terms of the time dependent currents flowing on the device. They are computationally very efficient since they involve integrals solely over the device generating the field. The expressions can also be applied to and interpreted in frequency domain. This will lead to a new interpretation of stored energy in the frequency domain. [ABSTRACT FROM PUBLISHER]

In his textbook, Gustav Mie states, that the radiation field consists solely of transverse electrical field lines, which are closed. The longitudinal field lines goes without interruption from the positive to the negative charges; they cannot be expelled. This raises the question about the speed of propagation along them. For this, a mathematical description of Mie's field lines is developed (the Helmholtz-transverse and longitudinal components of \vec{E} are non-local auxiliary quantities and thus not suitable for that). On the other hand, Mie also states, that the propagation of electromagnetic fields is governed by Maxwell's equations and Poynting's theorem. Here, however, there is a single wave equation for all vector components of the electrical field. In this contribution, a minimum modification of Maxwell's equations is proposed, which yields both, an instantaneous Coulomb field and longitudinal electrical radiation. [ABSTRACT FROM AUTHOR]

Most problems related to contactless energy transfer are usually dealt within the framework of transformer theory, employing equivalent electric circuits as a tool for their analysis. Here, however, a physics approach based on the Maxwell equations is followed. Electric and magnetic fields are utilized to evaluate the Poynting vector, which defines the direction and power density carried by the electromagnetic field. The concepts of magnetic voltage and magnetic flux are utilized to define the instantaneous power guided within the magnetic transmitter. Contactless energy transfer requires two separate parts, a transmitter and a receiver circuit. In this paper, we pay attention to the electromagnetic field guided and emitted by the transmitter; internal skin effect (eddy currents losses) is accounted for; electromagnetic energy leaving the transmitter is evaluated using short-dipole antenna theory. This paper does not offer a new practical application of contactless energy transfer. Its scope is rather different; its aim is to provide a fresh look on contactless energy transfer in the context of an electromagnetics framework. [ABSTRACT FROM PUBLISHER]

An alternative, field-based formulation of transformation optics is proposed. Field transformations are expressed in the language of boundary conditions for the electromagnetic fields facilitated through the introduction of generalized potential functions. It is shown that the field-based approach is equivalent to the conventional coordinate-transformation approach but is preferable when looking for specific field distribution. A set of example devices such as invisibility cloaks, concentrators, rotators, and transformation optics lenses capable of creating light beams with predetermined field distribution (e.g., Gaussian and sinusoidal) is studied to validate the effectiveness of the field-based formulation. As for the boundary conditions for the cloaked region the absence of the normal component of the Poynting vector is justified. In the frames of the field- based approach the physical reasons behind infinite components (singularities) of the material parameters of transformation optics devices are straightforwardly revealed. [ABSTRACT FROM AUTHOR]

Since its discovery in 1931, the Hopf fibration has played an important role in physics in seemingly unrelated situations ranging from qubits to Taub-NUT spaces in general relativity [1]. Recently the structure of this fibration has been considered in relation to solutions of the source-free Maxwell equations and led to linked and knotted forms of electromagnetic fields [2, 3]. In twistor theory, it was the structure of the Hopf fibration that gave a twistor its name [4]. Here we present a deeper correspondence between a (non-null) twistor and the knotted electromagnetic fields, in which the Poynting vector plays a central role. [ABSTRACT FROM AUTHOR]

The quantization scheme for the electromagnetic field in planar absorbing heterostructures has been developed. The scheme is based on the field expansion over a complete set of orthonormal modes. We used two types of the field modes. The first one is defined as the field created by a plane wave incident at the surface of the structure from the non-absorbing half space. The second type of modes corresponds to the field generated by electric current fluctuations in the absorbing media. To normalize the field modes, the following conditions were used: 1) the time-averaged Poynting vector attributed to the incident wave equals the density of energy flow of elementary quanta of the field energy; 2) for the given frequency and polarization, the total time-averaged Poynting vector equals to zero. The theory is applied to calculate the rate of spontaneous transitions between electron subbands in a quantum well placed near the absorbing layer that can support the surface phonon or plasmon polaritons. [ABSTRACT FROM AUTHOR]

Much of the confusion in the preceding Comment is resolved once the correct origin and definition of the phrase Negative Phase Velocity (NPV) propagation is recognised. Markel's claim that [image omitted] is a predictor for negative refraction is incompatible with taking [image omitted] as the absolute measure of the electromagnetic flux, and gives distinct results to P · Re(k) < 0 for anisotropic media. We argue that [image omitted] is the appropriate electromagnetic flux vector for defining negative refraction since its normal component is conserved across an interface. We also show how an induced magnetisation affects both the work done by the electromagnetic field on bound currents and the resultant electromagnetic flux. [ABSTRACT FROM AUTHOR]