Momentum Of Electromagnetic Field Research Articles

Revisiting the Wu–Yang approach to magnetic charge

The Wu–Yang fiber bundle approach to magnetic charge is extended with a disk-like sheet current density and associated magnetic field in the overlap region between the Northern hemisphere and Southern hemisphere, where the different vector potentials connect. This disk magnetic field plays a role similar to the Dirac string in the Dirac approach to magnetic charge — it brings an inward magnetic flux of 4πg which then gives rise to an outward Coulomb magnetic flux of 4πg. As with the Dirac string approach we show that placing an electric charge near this disk magnetic field gives rise to a non-zero electromagnetic field momentum. We discuss some of the possible physical consequences of this electromagnetic field momentum. We conclude by showing that the non-singular, but non-single valued Banderet monopole potential also has a disk-like magnetic flux and non-zero electromagnetic field momentum in the presence of an electric charge.

A spherical version of Feynman’s static field momentum example

The Feynman demonstration that electromagnetic field momentum is real—even for static fields—can be made more pedagogically useful by simplifying its geometry. Instead of Feynman’s disk with charged balls on its surface, this article uses the geometry of a hollow non-conducting sphere with uniform surface charge density. With only methods available in a typical upper-division electrodynamics course, the initial field angular momentum and the final mechanical angular momentum can then be calculated in closed form and shown to be equal.

Tutorial on the conservation of momentum in photonic time-varying media [Invited

Time-varying media break temporal symmetries while preserving spatial symmetries intact. Thus, it represents an excellent conceptual framework to investigate the fundamental implications of Noether’s theorem for the electromagnetic field. At the same time, addressing momentum conservation in time-varying media sheds light on the Abraham-Minkowski debate, where two opposing forms of the electromagnetic field momentum are defended. Here, we present a tutorial review on the conservation of momentum in time-varying media. We demonstrate that the Minkowski momentum is a conserved quantity with three independent approaches of increasing complexity: (i) via the application of the boundary conditions for Maxwell equations at a temporal boundary, (ii) testing for constants of motion and deriving conservation laws, and (iii) applying temporal and spatial translations within the framework of the Lagrangian theory of the electromagnetic field. Each approach provides a different and complementary insight into the problem.

Optical topological lattices of Bloch-type skyrmion and meron topologies

Optical skyrmions, quasiparticles that are characterized by the topologically nontrivial vectorial textures of optical parameters such as the electromagnetic field, Stokes parameters, and spin angular momentum, have aroused great attention recently. New dimensions for optical information processing, transfer, and storage have become possible, and developing multiple schemes for manipulating the topological states of skyrmions, thus, is urgent. Here we propose an approach toward achieving dynamic modulation of skyrmions via changing the field symmetry and adding chirality. We demonstrate that field symmetry governs the skyrmionic transformation between skyrmions and merons, whereas material chirality modulates the twist degree of fields and spins and takes control of the Néel-type–Bloch-type skyrmionic transition. Remarkably, the enantioselective twist of skyrmions and merons results from the longitudinal spin arising from the chirality-induced splitting of the hyperboloid in the momentum space. Our investigation, therefore, acts to enrich the portfolio of optical quasiparticles. The chiral route to topological state transitions will deepen our understanding of light–matter interaction and pave the way for chiral sensing, optical tweezers, and topological phase transitions in quantum matter.

Electromagnetic energy–momentum tensors in general dispersive bianisotropic media

The macroscopic electromagnetic (EM) energy–momentum tensor is one of the most important quantities characterizing the propagation and interaction of light in materials. In recent years, while exotic optical effects in various kinds of bianisotropic materials have been discovered, there still lacks a rigorous analysis of the energy and momentum of EM fields in such general cases. In this paper, using Noether’s theorem and the “Abrahamization” procedure, we obtain generalized Minkowski and Abraham EM energy–momentum tensors, applicable for both arbitrary time-dependent real EM fields and complex-valued analytic signals, in generic lossless bianisotropic media with frequency dispersion. The frequency dispersion of the materials modifies the expressions of EM energy density and Minkowski momentum, making them different from their familiar forms in nondispersive media. Our results reveal that the generalized Minkowski momenta for both real fields and analytic signals are conserved in source-free homogeneous media, while the Abraham momenta, characterizing the centroid motion of light, can change over time, which leads to the counterintuitive phenomenon that wave packets can travel along curved trajectories even in homogeneous bianisotropic media. We also show that the energy–momentum tensor for analytic signals derived from the action principle directly gives the conservation law of time-averaged fields and hence can describe the envelope evolution of waves in quasi-monochromatic approximation.

Is electromagnetic field momentum due to the flow of field energy?

Momentum and energy conservation require electromagnetic field momentum and energy to be treated as physically real, even in static fields. This motivates the conjecture that field momentum might be due to the flow of a relativistic mass density (defined as energy density divided by the square of the speed of light).This article investigates the velocity of such a mass flow and finds a conflict between two different definitions of it, both of which originally seem plausible if the flow is to be taken as real. This investigation is careful to respect the transformation rules of special relativity throughout.The paper demonstrates that the consensus definition of the flow velocity of electromagnetic energy is inconsistent with the transformation rules of special relativity, and hence is incorrect. A replacement flow velocity is derived which is completely consistent with those transformation rules.The conclusion is that these conflicting definitions of flow velocity cannot be resolved in a way that is consistent with special relativity and also allows electromagnetic field momentum density to be the result of relativistic mass flow. Though real, field momentum density cannot be explained as the flow of a relativistic mass density.As a byproduct of the study, it is also shown that there is a comoving system in which the electromagnetic energy-momentum tensor is reduced to a simple diagonal form, with two of its diagonal elements equal to the energy density and the other two diagonal elements equal to plus and minus a single parameter derived from the electromagnetic field values, a result that places constraints on possible fluid models of electromagnetism.

Compact cascaded meta-surface system for controlling the spin and orbital angular momentum of electromagnetic fields simultaneously.

We propose a compact cascaded meta-surface system (CCMS) to produce well converged orbital angular momentum (OAM) vortex waves with tailored spin angular momentum (SAM) by integrating a meta-surface lens (ML) with an assistant meta-mirror (AM). Specifically, the co-linearly polarized (LP) waves from the feed would be reflected by the ML firstly and then twisted into the cross-LP counterparts by the AM to penetrate the ML for the perfect synthesis of the OAM vortex beams while performing the linear-to-circular polarization conversion. Especially, the CCMS can pack the ML and the AM closely together with a quarter of the ML focal length when we apply proper phase distributions on the AM. In addition, the proposed CCMS can readily be extended to the generation of multiple circularly polarized OAM vortex waves with different modes. Our design should thus pave the way for building up more efficient wireless communication systems with expanded channel capacity.

Угловой момент конвективного электромагнитного поля релятивистских заряженных частиц

Угловой момент конвективного электромагнитного поля релятивистских заряженных частиц

Angular momentum properties of hybrid cylindrical vector vortex beams in tightly focused optical systems.

Optical angular momenta (AM) have attracted tremendous research interest in recent years. In this paper we theoretically investigate the electromagnetic field and angular momentum properties of tightly focused arbitrary cylindrical vortex vector (CVV) input beams. An absorptive particle is placed in focused CVV fields to analyze the optical torques. The spin-orbit motions of the particle can be predicted and controlled when the influences of different parameters, such as the topological charge, the polarization and the initial phases, are taken into account. These findings will be helpful in optical beam shaping, optical spin-orbit interaction and practical optical manipulation.

Фундаментальная система уравнений для импульса и энергии электромагнитного поля в неоднородной среде. II. Фундаментальные уравнения в декартовом базисе

Фундаментальная система уравнений для импульса и энергии электромагнитного поля в неоднородной среде. II. Фундаментальные уравнения в декартовом базисе

Фундаментальная система уравнений для импульса и энергии электромагнитного поля в неоднородной среде. I. Фундаментальные уравнения в локальном базисе

Фундаментальная система уравнений для импульса и энергии электромагнитного поля в неоднородной среде. I. Фундаментальные уравнения в локальном базисе

Electromagnetic dynamical characteristics of a surface plasmon-polariton

We consider an electromagnetic field near the interface between two media with arbitrary real frequency-dependent permittivities and permeabilities, under conditions supporting the surface plasmon-polariton (SPP) propagation. The dispersion of the electric and magnetic properties is taken into account based on the recent approach for description of the spin and momentum of electromagnetic field in complex media [Phys. Rev. Lett. 119, 073901 (2017); New J. Phys., 19, 123014 (2017)]. It involves the Minkowski momentum decomposition into spin and orbital parts with the dispersion-modified permittivities and permeabilities. Explicit expressions are derived for spatial densities of the energy, energy flow, spin and orbital momenta and angular momenta of the transverse-magnetic (TM) SPP field. The expressions are free from non-physical singularities; the only singular contribution describes a strictly localized surface part of the spin momentum that can be associated with the magnetization current in the conductive component of the SPP-supporting structure. On this ground, a phenomenological theory of the SPP-induced magnetization (predicted earlier based on the simplified microscopic approach) is outlined. Possible modifications and generalizations, including the transverse-electric (TE) SPP waves, are discussed.

Equations for the Momentum and Energy of an X-ray Wave Field in a Crystal

A new approach for describing the interaction of X rays with a crystalline medium is proposed. General relations for a change in the electromagnetic-field momentum and energy have been derived for a nonmagnetic medium with variable permittivity. A special local coordinate system for an inhomogeneous medium is introduced, in which the Maxwell tension tensor has a canonical form determined by the energy and momentum densities. Main relations for changes in the energy and momentum densities have been obtained in the coordinate system related to the propagation direction of a plane electromagnetic wave pulse in a homogeneous medium.

Role of Radial Charges on the Angular Momentum of Electromagnetic Fields: Spin-3/2 Light.

Electromagnetic fields carry a linear and an angular momentum, the first being responsible for the existence of the radiation pressure and the second for the transfer of torque from electromagnetic radiation to matter. The angular momentum is considered to have two components, one due to the polarization state of the field, usually called spin angular momentum (SAM), and one due to the existence of topological azimuthal charges in the field phase profile, which leads to the orbital angular momentum (OAM). These two contributions to the total angular momentum of an electromagnetic field appear, however, to not be independent of each other, something which is described as spin-orbit coupling. Understanding the physics of this coupling has kept scientists busy for decades. Very recently it has been shown that electromagnetic fields necessarily carry also invariant radial charges that, as discussed in this Letter, play a key role in the angular momentum. Here we show that the total angular momentum consists in fact of three components: one component only dependent on the spin of the field, another dependent on the azimuthal charges carried by the field, and a third component dependent on the spin and the radial charges contained in the field. By properly controlling the number and coupling among these radial charges it is possible to design electromagnetic fields with a desired total angular momentum. Remarkably, we also discover fields with no orbital angular momentum and a spin angular momentum typical of spin-3/2 objects, irrespective of the fact that photons are spin-1 particles.

Electromagnetic power and momentum in N-body Hamiltonian approach to wave-particle dynamics in a periodic structure

To model momentum exchange in nonlinear wave-particle interaction, as in amplification devices like traveling-wave tubes, we use an N-body self-consistent Hamiltonian description based on Kuznetsov's discrete model, and we provide new formulations for the electromagnetic power and field momentum in media. This approach leads to fast and accurate numerical simulations in time domain and in one-dimensional space.

Уравнения для импульса и энергии рентгеновского волнового поля в кристалле

AbstractA new approach for describing the interaction of X rays with a crystalline medium is proposed. General relations for a change in the electromagnetic-field momentum and energy have been derived for a nonmagnetic medium with variable permittivity. A special local coordinate system for an inhomogeneous medium is introduced, in which the Maxwell tension tensor has a canonical form determined by the energy and momentum densities. Main relations for changes in the energy and momentum densities have been obtained in the coordinate system related to the propagation direction of a plane electromagnetic wave pulse in a homogeneous medium.

4.8‐Gbit/s broadband wireless communication link at radio frequency using orbital angular momentum and polarisation multiplexing

Recently, the ability of orbital angular momentum (OAM) of electromagnetic fields at radio frequency to multiplex multiple beams has been investigated. Such OAM multiplexing can be used to increase channel capacity and spectral efficiency. However, the studies of OAM multiplexing are restricted to narrow band. In this Letter, the authors experimentally demonstrate a 4.8-Gbit/s broadband OAM and polarisation multiplexing wireless link in which the operating frequency is from 2.1 to 2.7 GHz, with a relative bandwidth about 25%. The proposed wireless communication link over 2.5 m achieves a spectral efficiency of ∼8 bit/s/Hz by using two independent OAM beams for each of two polarisations. All four independent OAM channels propagate along the same beam axis with crosstalk less than −13.3 dB from 2.1 to 2.7 GHz. All four channel signals are recovered with a bit error rate of 3.5 × 10−3 when the signal-to-noise ratio is 24 dB.

Do the standard expressions for the electromagnetic field momentum need any modifications?

We investigate here the question raised in the literature about the correct expression for the electromagnetic field momentum, especially when static or stationary fields are involved. For this, we examine a couple of simple but intriguing cases. First, we consider a system configuration in which electromagnetic field momentum is present even though the system is stationary. We trace the electromagnetic momentum to be present in the form of a continuous transport of electromagnetic energy from one part of the system to another, without causing any net change in the energy of the system. In a second case, we show that the electromagnetic momentum is zero irrespective of whether the charged system is static or in motion, even though the electromagnetic energy is present throughout. We demonstrate that the conventional formulation of electromagnetic field momentum describes the systems consistently without any real contradictions. Here, we also make exposition of a curiosity where electromagnetic energy decreases when the charged system gains velocity. Then we discuss the more general question that has been raised: Are the conventional formulas for energy-momentum of electromagnetic fields valid for all cases? Specifically, in the case of so-called “bound fields,” do we need to change to some modified definitions? We show that in all cases it is only the conventional formulas that lead to results consistent with the rest of physics, including the special theory of relativity, and that any proposed modifications are thus superfluous.

An alternative resolution to the Mansuripur paradox

In 2013 an article published online by the journal Science declared that the paradox proposed by Masud Mansuripur was resolved. This paradox concerns a point charge-Amperian magnetic dipole system as seen in a frame of reference where they are at rest and one in which they are moving. In the latter frame an electric dipole appears on the magnetic dipole. A torque is then exerted upon the electric dipole by the point charge, a torque that is not observed in the at-rest frame. Mansuripur points out this violates the relativity principle and suggests the Lorentz force responsible for the torque be replaced by the Einstein–Laub force. The resolution of the paradox reported by Science, based on numerous papers in the physics literature, preserves the Lorentz force but depends on the concept of hidden momentum. Here I propose a different resolution based on the overlooked fact that the charge-magnetic dipole system contains linear and angular electromagnetic field momentum. The time rate of change of the field angular–momentum in the frame through which the system is moving cancels that due to the charge-electric dipole interaction. From this point of view hidden momentum is not needed in the resolution of the paradox.

Detection of the Abraham force with a succession of short optical pulses

For over a century, two rival descriptions of electromagnetic field momentum in matter have co-existed, due to Abraham and Minkowski, respectively. We propose a set-up for measuring the difference between Abraham's and Minkowski's predictions in optics. To wit, a set-up is proposed in which the transient "Abraham force", a consequence of the Abraham energy-momentum tensor of 1909 may be measured directly. We show that when a train of short laser pulses is sent through a fiber wound up on a cylindrical drum, the Abraham theory predicts a torque which, by inserting realistic parameters, is found to be detectable. Indeed, the same torque when calculated with the Minkowski tensor takes the opposite sign. Numerical estimates show that with a typical torsion pendulum set-up and standard laser parameters, the angular deflection is in the order of $10^{-3}$ rad, which is easily measurable and even visible to the naked eye. Although its prediction is a century old, the Abraham force has proven experimentally elusive, and to our knowledge no macroscopic experimental demonstration of the difference between the predictions of the two mentioned energy-momentum tensors exists at optical frequencies.