In this manuscript we provide a fully geometric formulation for the induced electromagnetic fields and their corresponding constitutive relations in moving media. To this end, we present the reader with a brief geometric summary to show how vector calculus electromagnetic theory is embedded in the more general language of differential forms. Then, we consider the class of \emph{metric} constitutive relations describing the medium in which electromagnetic fields propagate. We explicitly obtain the components of the induced fields in a moving medium, as seen in the the lab \emph{rest} frame. This allows us to read the expressions for the permitivity, permeability and magnetoelectric matrices for the moving medium which, in turn, can be interpreted as a different physical material from the lab point of view
The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the Lienard-Wiechert potentials. The derivation uses arguments based on Lorentz invariance and a physically transparent expression originally due to J.J.Thomson for the field of a charge that experiences an impulsive acceleration.
Using the Lagrangian formalism, the electromagnetic force on a moving dipole derived by Kholmetskii, Missevitch and Yarman (2011, Eur. J. Phys. 32, 873) is found to be missing some important terms.
In the paper [B.M.Bolotovskii, S.N.Stoliarov, Uspekhi Fizicheskich Nauk, v.162, No 3, p.195, 1992] the energy conservation law was applied to a problem of radiation of a charged particle in an external electromagnetic field. The authors consecutively and mathematically strictly solved the problem but received wrong result. They derived an expression which includes a change of the energies of the electromagnetic fields accompanying the moving particle corresponding to the initial and final velocity of the particle. The energy of the field accompanying the particle is the energy of the particle …
Two previously studied classes of electromagnetic media, labeled as those of Q media and P media, are decomposed according to the natural decomposition introduced by Hehl and Obukhov. Six special cases based on either non-existence or sole existence of the three Hehl-Obukhov components, are defined for both medium classes.
The problem of the electromagnetic energy-momentum tensor is among the oldest and the most controversial in macroscopic electrodynamics. In the center of the issue is a dispute about the Minkowski and the Abraham tensors for moving media. An overview of the current situation is presented. After putting the discussion into a general Lagrange-Noether framework, the Minkowski tensor is recovered as a canonical energy-momentum. It is shown that the balance equations of energy, momentum, and angular momentum are always satisfied for an open electromagnetic system despite the lack of the symmetry of…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the Floquet modes. A complete set of approximate solutions is calculated which are valid when the inhomogeneity is small. This is applied to inhomogeneous wire media. A new feature arises when considering spatially dispersive media, that is the existence of coupled modes.
Recently, Feigel has predicted a new effect in magnetoelectric media. The theoretical evaluation of this effect requires a careful analysis of a dynamics of the moving magnetoelectric medium and, in particular, the derivation of the energy-momentum of the electromagnetic field in such a medium. Then, one can proceed with the study of the wave propagation in this medium and derive the mechanical quantities such as the energy, the momentum, and their fluxes and the corresponding forces. In this paper, we develop a consistent general-relativistic variational approach to the moving dielectric and …
We investigate the electromagnetic field generated by a point charge moving along a helical trajectory inside a circular waveguide with conducting walls filled by homogeneous dielectric. The parts corresponding to the radiation field are separated and the formulae for the radiation intensity are derived for both TE and TM waves. It is shown that the main part of the radiated quanta is emitted in the form of the TE waves. Various limiting cases are considered. The results of the numerical calculations show that the insertion of the waveguide provides an additional mechanism for tuning the chara…
In the recent work~\cite{Wang:2021p2}, the author proposed the expanded Maxwell's equations for moving charged media system, which seems subtle. Considering a very short time, we can approximately define the inertial frame of reference. If we assume all the physical quantities are defined in the same reference frame by default, Maxwell's equations for the static media system and moving media system are definitely the traditional Maxwell's equations, which are covariant and consistent with the two fundamental postulates of special relativity. We even prove the covariance of Maxwell's equations …
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly used Maxwell's equations is the issue of polar versus axial vectors; the electromagnetic field E is a polar vector, whereas the magnetic field B is an axial vector, where the direction of rotation remains the same even after the axial vector is inverted. This effort first derived the rotation matrix for quaternion geometry. This rotation matrix was then appl…
Within the framework of unified approach we study the Casimir-Lifshitz interaction, the van der Waals friction force and the radiative heat transfer at nonequilibrium conditions, when the interacting bodies are at different temperatures, and they move relative to each other with the arbitrary velocity $V$. The analysis is focused on the surface-surface and surface-particle configuration. Our approach is based on the exact solution of electromagnetic problem about the determination of the fluctuating electromagnetic field in the vacuum gap between two flat parallel surfaces moving relative to e…
Several results concerning active media or metamaterials are proved and discussed. In particular, we consider the permittivity, permeability, wave vector, and refractive index, and discuss stability, refraction, gain, and fundamental limitations resulting from causality.
It is proposed a natural and consistent division of the momentum of electromagnetic waves in linear, non-dispersive and non-absorptive dielectric and magnetic media into material and electromagnetic parts. The material part is calculated using directly the Lorentz force law and the electromagnetic momentum density has the same form than in vacuum, without an explicit dependence on the properties of the media. The consistency of the treatment is verified through the obtention of a correct momentum balance equation in many examples and showing the compatibility of the division with the Einstein'…
Telegraph equation describing the compression of electromagnetic waves in a waveguide (resonator) with moving boundary are derived. It is shown that the character of oscillations of the compressed electromagnetic field depends on the parameters of the resonator, and under certain conditions, the oscillations of voltage (current) yield the exponential growth, leading to a noticeable change in the radiation losses.
Two basic classes of electromagnetic media, recently defined and labeled as those of P media and Q media, are generalized to define the class of PQ media. Plane wave propagation in the general PQ medium is studied and the quartic dispersion equation is derived in analytic form applying four-dimensional dyadic formalism. The result is verified by considering various special cases of PQ media for which the dispersion equation is known to decompose to two quadratic equations or be identically satisfied (media with no dispersion equation). As a numerical example, the dispersion surface of a PQ med…
In this paper, we show how the electromagnetic phenomena in moving magnetodielectric media can be emulated using artificial composite structures at rest. In particular, we introduce nonreciprocal periodically loaded transmission lines which support waves obeying the same rules as plane electromagnetic waves in moving media. Because the actual physical structure is at rest, in these transmission lines there are no fundamental limitations on the velocity values, which may take values larger than the speed of light or even complex values (considering complex amplitudes in the time-harmonic regime…
The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which the medium has a time-dependent volume, shape and boundary and may move at an arbitrary velocity field v(r,t) and along a general trajectory, we derived the Maxwell's equations for a mechano-driven slow-moving media system directly starting from the integral forms of four physics laws, which should be accurate enough for describing the coupling among mechano…
In this paper an analytical approach for calculating scattering matrix elements for the case of normal incidence of the plane electromagnetic waves on the square patch-type Frequency Selective Surface (FSS), which is placed at the interface between two dielectric media is proposed. Analytical expressions for the reflection and transmission coefficients are shown to be accurate enough for practical purposes.
Two key types of inhomogeneous spatially dispersive media are described, both based on a spatially dispersive generalisation of the single resonance model of permittivity. The boundary conditions for two such media with different properties are investigated using Lagrangian and distributional methods. Wave packet solutions to Maxwell's equations, where the permittivity varies and is periodic in the medium, are then found.
We extend the usual derivation of the wave equation from Maxwell's equations in vacuum to the case of electromagnetic fields in dispersive homogeneous isotropic linear media. Usually, dispersive properties of materials are studied in Fourier space. However, it can be rewarding to consider these properties as causal functions of time. Due to temporal non locality, this procedure gives rise to an integrodifferential equation for the electromagnetic fields, which we also call a wave equation. We have not found this equation in the literature and we show in this paper why it can be useful.
We derive an expression for the Maxwell stress tensor in a magnetic dielectric medium specified by its permittivity "epsilon" and permeability "mu." The derivation proceeds from the generalized form of the Lorentz law, which specifies the force exerted by the electromagnetic E and H fields on the polarization P and magnetization M of ponderable media. Our stress tensor differs from the well-known tensors of Abraham and Minkowski, which have been at the center of a century-old controversy surrounding the momentum of the electromagnetic field in transparent materials.
A low loss propagating electromagnetic wave is shown to exist at a gradual interface between two lossy conductive media. The electromagnetic frequency range of this phenomenon may span from UV optics to RF range. In particular, it is demonstrated that such a surface wave may be guided by a seafloor-seawater interface and it may be used in radio communication and imaging underwater. Similar surface waves may also be guided by various tissue boundaries inside a human body. For example, such surface wave solutions may exist at planar interfaces between skull bones and grey matter inside a human h…
We analyse the propagation of electromagnetic waves in magnetoelectric media. Recently, Feigel has predicted that such a medium may ``extract momentum from vacuum" in the sense that the total momentum of the virtual waves (vacuum fluctuations of the electromagnetic field) is nontrivial. Our aim is to check the feasibility of this effect. The crucial point in our study is an assumption of the finite size of the magnetoelectric sample, which allows us to reduce the calculation of the momenta and forces of the electromagnetic waves acting on the sample to the vacuum region outside of the medium. …
Following the arguments presented by Mansuripur [Opt. Express 16, 14821-14835 (2008)], we suggest a form for the macroscopic electromagnetic stress tensor appropriate for ionized media. The generalized Lorentz force includes the effects of polarization forces as well as those on the free charge and current densities. The resulting tensor is written in terms of the fields D, B, E, and H. Its expression for a fully ionized medium subject to an external electromagnetic field is discussed, as are the plasma conservation equations. An apparatus is suggested for its experimental discrimination.
The refraction of a light ray by a homogeneous, isotropic and non-dispersive transparent material half-space in uniform rectilinear motion is investigated theoretically. The approach is an amalgamation of the original Fermat's principle and the fact that an isotropic optical medium at rest becomes optically anisotropic in a frame where the medium is moving at a constant velocity. Two cases of motion are considered: a) the material half-space is moving parallel to the interface; b) the material half-space is moving perpendicular to the interface. In each case, a detailed analysis of the obtaine…
Vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The rapid development in quantum optics calls for electromagnetic solutions that straddle quantum physics as well as classical physics. The vector potential formulation is a good candidate to bridge these two regimes. Hence, there is a need to generalize this formulation to inhomogeneous media. A generalized gauge is suggested for solving electromagnetic problems in inhomogenous media which can be extended to the anistropic case. The advantages of the resulting equations are their absence of low…
We study the direct and inverse scattering problems when the incident electromagnetic field is a time harmonic point- generated wave in a chiral medium and the scatterer is a perfectly conducting sphere. The exact Green s function and the electric far-field patterns of the scattering problem are constructed. For a small sphere, a closed-form approximation of the scattered wave field at the source of the incident spherical wave is obtained. These near-field results lead to the solution of an inverse problem. We also treat the same inverse problem using far-field results via the leading order te…
We examine the force of the electromagnetic radiation on linear, isotropic, homogeneous media specified in terms of their permittivity epsilon and permeability mu. A formula is proposed for the electromagnetic Lorentz force on the magnetization M, which is treated here as an Amperian current loop. Using the proposed formula, we demonstrate conservation of momentum in several cases that are amenable to rigorous analysis based on the classical Maxwell equations, the Lorentz law of force, and the constitutive relations. Our analysis yields precise expressions for the density of the electromagneti…
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic 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 …
A simulation of electric current pulses formed by a packet of gamma-quanta moving through an absorptive medium is presented. The electromagnetic fields of the current pulse moving along the straight line with super light velocity are obtained
We investigate the reflection properties of electromagnetic/optical waves in isotropic chiral media. When the chiral parameter is strong enough, we show that an unusual \emph{negative reflection} occurs at the interface of the chiral medium and a perfectly conducting plane, where the incident wave and one of reflected eigenwaves lie in the same side of the boundary normal. Using such a property, we further demonstrate that such a conducting plane can be used for focusing in the strong chiral medium. The related equations under paraxial optics approximation are deduced. In a special case of chi…
In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive equations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive…
