Flux Density of the Umov Electromagnetic Energy during Uniform Motion of an Extended Electron

Bulletin of the Lebedev Physics Institute - Abstract—The flux density vector of the electromagnetic energy in the Poynting form and the problem of the electron electromagnetic momentum,...     

Exact equations for radiative transfer of energy and momentum in free electromagnetic fields

In a recent paper a new theory of radiative energy transfer in free electromagnetic fields was formulated. The basic quantities in this theory are the so-called angular components of the average electromagnetic energy density and of the average Poynting vector. In the present paper it is shown that these angular components obey differential equations that may be considered to be rigorous equations for the radiative transfer of energy and of momentum in free electromagnetic fields.     

Bandlimiting in conflict with spatial bounding of radiative sources

The curl of the Poynting vector for the bandlimited electromagnetic field of a timeharmonic point-source dipole is expanded asymptotically for large axial and off-axial distances of a halfspace. Truncating the plane-wave spectrum of the dipole field at any finite value of spatial frequency produces whirls in the time-averaged energy flux which are at variance with the expansion theorem for the field of a bounded source; due to bandlimiting, the angular and radial coordinates of the Poynting vector are not for all directions separable and the curl of the Poynting vector has the wrong orderr ^−5/2, at least for some directions, when the radial distancer approaches infinity.     

非傍轴衍射光束横截面上的光强及其能量传输

运用角谱表示的矢量衍射理论,以平面波微小圆孔的非傍轴衍射为例,给出了垂直于光束传输方向的横截面上不同定义的三种光强（传统光强I、功率密度Jz、时间平均能流密度矢量的z分量〈Sz〉）的计算公式,并进行了详细的数值计算和比较研究.指出对微小孔衍射的能量传输,必须考虑光场的矢量特性.应用能流密度矢量S和功率流密度矢量J,分别计算了微小孔非傍轴衍射的透射系数,得到了一些新的结论.     

Scattering forces and electromagnetic momentum density in crossed circularly polarized standing waves

We analyze the forces on a small dipolar particle and the electromagnetic momentum density in a configuration consisting in two perpendicular circularly polarized stationary waves. The field distribution shows regions in which the electric and magnetic fields are parallel corresponding to a null Poynting vector. Although the average value of the momentum density, proportional to the Poynting vector, is zero in these regions, there are scattering forces acting on small particles due to light's spin force. The total scattering force suggests a new definition of the average value of the momentum density for free propagating electromagnetic fields.     

The electromagnetic optical theorem revisited

We revisit the optical theorem relevant to the far-field electromagnetic scattering by an arbitrary particle. We compute both the Poynting vector and the energy density of the total field and demonstrate once again that, despite a recent claim to the contrary, the extinction is caused by the interference of the incident and the forward-scattered field. However, caution must be exercised when one describes electromagnetic scattering using a formalism based on the coherency dyad since this approach may lead to unphysical artifacts.     

Scattering forces and electromagnetic momentum density in crossed circularly polarized standing waves

We analyze the forces on a small dipolar particle and the electromagnetic momentum density in a configuration consisting in two perpendicular circularly polarized stationary waves. The field distribution shows regions in which the electric and magnetic fields are parallel corresponding to a null Poynting vector. Although the average value of the momentum density, proportional to the Poynting vector, is zero in these regions, there are scattering forces acting on small particles due to light's spin force. The total scattering force suggests a new definition of the average value of the momentum density for free propagating electromagnetic fields.     

Double pulse quasi-collinear high harmonic generation scheme as a tool for X-ray laser plasma gain probing

We calculate the field distribution based on the vector diffraction theory for a superposition of spirally phase shifted radially polarized beams. Twisted longitudinally polarized field is found in the focal region. The total intensity as well as the polarization components rotates around the beam axis near the focus. Calculation of the Poynting vector at the focal plane shows that the electromagnetic energy is redistributed between different polarization components. Nonzero value of transverse components of the Poynting vector implies the transverse flow of the energy in the focal region.     

The Equivalence Principle and an Electric Charge in a Gravitational Field II. A Uniformly Accelerated Charge Does Not Radiate

The electromagnetic field of a charge supported in a uniform gravitational field is examined from the viewpoint of an observer falling freely in the gravitational field. It is argued that such a charge, which from the principle of equivalence is moving with a uniform acceleration with respect to the (inertial) observer, could not be undergoing radiation losses at a rate implied by Larmor's formula. It is explicitly shown that the total energy in electromagnetic fields, including both velocity and acceleration fields, of a uniformly accelerated charge, at any given instant of the inertial observer's time, is just equal to the self-energy of a non-accelerated charge moving with a velocity equal to the instantaneous present velocity of the accelerated charge. At any given instant of time, and as seen with respect to the present position of the uniformly accelerated charge, although during the acceleration phase there is a radially outward component of the Poynting vector, there is throughout a radially inward Poynting flux component during the deceleration phase, and a null Poynting vector at the instant of the turn around. From Poynting's theorem, defined for any region of space strictly in terms of fixed instants of time, it is shown that a uniformly accelerated charge does not emit electromagnetic radiation, in contrast to what is generally believed. Contrary to some earlier suggestions in the literature, there is no continuous passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer.     

Zur Reflexion und Transmission elektromagnetischer Wellen bei senkrechtem Einfall auf ebene Grenzflächen zwischen unterschiedlich absorbierenden Medien

On Reflection and Transmission of Electromagnetic Waves Propagating Perpendicular to Plane Surfaces between Different Absorbing Media Born and Ladenburg already in 1911 pointed out that to describe reflection and transmission of electromagnetic waves through a plane surface between two different absorbing media in addition to the usual Poynting vectors of the running waves the so called “mixed” Poynting vector is necessary to maintain the balance of energy on the boundary plane. The flow of energy connected with this vector always points toward the region of maximal wastage of this energy and is closely related to the spatial modulation of the energy consumption within the partially standing interference pattern between the incoming and the reflected wave. In almost all substances the energy absorption is caused by the electric field whereas practically a direct contribution from the magnetic field can be neglected. But taking account of these magnetic effects we may get a better understanding of the mixed Poynting vector. To that end we add to the second of the Maxwell equations a quantity analogous to the electric current term in the first Maxwell equation. The amplitude of the “mixed” Poynting vector then turns out to depend essentially on the ratio of the energy absorption by the electric and the magnetic field. To confirm this fact we consider a medium, which shows in addition to the usual electric losses also magnetic ones of comparable magnitudes. In such materials the resultant energy consumption is distributed more similar to the spatial distribution of the fieldenergy. As a result the amplitude of the mixed Poynting vector disappears if the percentage of energy absorption by the electric and the magnetic field and their energy densities themselves are made equal to each other.     

Nonexponentially Decaying Electromagnetic Waves Localized at the Boundary of Anisotropic Metal–Dielectric Structures

The possibility of the existence of a special class of surface electromagnetic waves with amplitude decreasing nonexponentially as they pass into an anisotropic metal–dielectric structure that borders the isotropic dielectric has been shown. The dispersion equation describing the propagation of such special surface waves has been obtained, and their attenuation coefficients and formula for electric and magnetic fields in contacting media have also been found. The expressions for the longitudinal and transverse components of the Poynting vector and volume density of electric and magnetic energy of special surface waves have been obtained. Numerical calculations for the layered metal–dielectric nanostructure that is described by a uniaxial tensor of effective dielectric permeability have been carried out Decaying.     

Energy Characteristics of Wave Fields Radiated from Elementary Oscillators in a Nondispersive Medium Moving with Subluminal Velocity

We study the energy characteristics of fields radiated from electric, magnetic, and toroidal dipoles in a nondispersive medium moving with velocity lower than the speed of light in this medium. The angular dependences of Abraham's energy-flux density of electromagnetic field are analyzed. In particular, it is shown that if the medium velocity is high enough, then the radial component of the vector of energy-flux density is negative in a certain angular range. Expressions for the electromagnetic energy flux through a sphere of large radius are obtained. It is shown that if the velocity of a moving medium is high enough, then the energy flux is negative and its absolute value can exceed the energy losses of sources.     

On “Gauge Renormalization” in Classical Electrodynamics

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined.     

Micromorphic Electromagnetic Theory and Waves

This paper introduces a continuum microelectromagnetic theory (also called micromorphic electromagnetic theory), to discuss electromagnetic phenomena in bodies with microstructures. Balance laws of microelectromagnetic media of the first-grade are given. Constitutive equations are developed. The field equations are obtained . It has been shown that, this theory gives rise to several new vector and tensor waves. A theorem of conservation of energy (Poynting type) is proved. Dispersion relations are obtained for both vector and tensor waves. Relations of tensor waves to microscopic phenomena (such as spin waves) are discussed.     

Confinement of infrared radiation to nanometer scales through metallic slit arrays

One-dimensional metallic slit array has been intensively studied in the spectral range from ultraviolet to near-infrared due to its enhanced transmission for transverse magnetic waves. However, the transmission enhancement is sensitive to the wavelength of incident radiation because of resonance characteristics. In this paper, we theoretically demonstrate that confining mid-infrared radiation to nanometer scales with a large transmission enhancement can be achieved from an aluminum slit array in a wavelength-insensitive manner, for potential applications in localized heating and nanothermal patterning. The Poynting vector and energy density calculated from the rigorous coupled-wave analysis (RCWA) are used to explain the strong localization of electromagnetic energy in the near-field regime. Furthermore, the localization of energy is also studied when a dielectric substrate is used to support the slit array in practical applications.     

双曲余弦高斯涡旋光束的远场特性研究

运用电磁光束的角谱法和稳相法, 推导出双曲余弦高斯(ChG) 涡旋光束的TE波和TM波在自由空间远场传输和能流密度的解析表达式, 用以研究了ChG涡旋光束在远场中的位相奇点和能流密度分布特性. 结果表明, 改变ChG 涡旋光束中的离心参数或束腰宽度, 位相奇点的密度、位置会发生变化. 涡旋离轴量的变化会导致能流密度分布的不对称性. 当离心参数增大时, 原点周围黑核会向原点中心移动. 关键词： 双曲余弦高斯涡旋光束 位相奇点 能流密度     

介质损耗与电磁能量

根据能流密度公式,推出时谐场中存在线性有损介质情形的坡印亭定理.与能量守恒定律结合,得到极化损耗、磁化损耗和焦耳损耗功率密度公式,以及有损介质中的电磁场能量密度公式.最后,推出上述各量的平均值公式.     

各向异性的非相干矢量光束的传播特性

利用坡印亭矢量,研究了相干性为各向异性的非相干矢量光束在自由空间的传输特性,得到了光束横截面上能量分布及演化,导出了角偏振光束中心出现能量峰值的条件,详细分析了相干性对偶极子光束能量旁瓣的影响,并发现各向异性的偶极子光束具有三种不同的演化形式,得到了具体判据.     

Poynting vector in transfer-matrix formalism for the calculation of light absorption profile in stratified isotropic optical media

In spite of the fact that solutions to Maxwell's equations in stratified isotropic optical media are well known, it appears that an explicit expression of the Poynting vector flux spatial evolution inside such a medium has not been derived so far. Based on exact electromagnetic field solutions in the transfer-matrix formalism, I derive such an expression and show that, due to the presence of counterpropagating waves in the medium, an additional contribution to the flux appears that exists only in optically absorbing layers and arises from the interference between these waves. Based on this theory, the concept of incremental absorption is introduced for the calculation of the light absorption profile along the stratification direction. As an illustration of this concept, absorption profiles in a Si-based thin-film tandem solar cell are predicted at typical wavelengths.     

Characteristics of surface waves in anisotropic left-handed materials

We report the coexistence of TE and TM surface modes in certain same frequency domain at the interface between one isotropic regular medium and another biaxially anistotropic left-handed medium. The conditions for the existence of TE and TM polarized surface waves in biaxially anisotropic left-handed materials are identified, respectively. The Poynting vector and the energy density associated with surface modes are calculated. Depending on the system parameters, either TE or TM surface modes can have the time averaged Poynting vector directed to or opposite to the mode phase velocity. It is seen that the characteristics of surface waves in biaxially anisotropic left-handed media are significantly different from that in isotropic left-handed media.