Electrodynamics Of Continuous Media Research Articles

To the numerical simulation of the correlation picture in Dicke superradiance

The paper discusses some approaches to elucidating the picture of electromagnetic field correlations emerging and developing in the Dicke system of two-level atoms interacting via field. Based on the reduced description method, a set of differential equations for the reduced description parameters including field correlation functions is constructed using different quantum evolution pictures and regarding field-matter interaction as a small parameter. Calculations are based on the electrodynamics of continuous media. Meaningful results are obtained in the second-order in interaction. The material equations are found in the class of generalized functions and the material coefficients are estimated in the dependence of coordinates for applying to the spatial description of correlations. Initial and border conditions are discussed. A simplified form of the set of equations is proposed for the initial stage of the process with the supposition about the fixed orientation of emitters acceptable for a one-dimensional system.

Nature of Photoelectric Effect in a Ge-on-Si SPAD at Ultralow Energy in Incident Pulsed Laser Radiation

The photoelectric effect in a Ge-on-Si single-photon avalanche detector (SPAD) at an ultralow energy in incident pulsed laser radiation is considered in the frame of the classical theory of the electrodynamics of continuous media. It is shown that the energy of incident laser radiation which is shared among a huge number of electrons in a Ge matrix can concentrate on only one of these through the effect of the constructive interference of the fields re-emitted by surrounding electrons. Conservation of energy in this case is upheld because of a substantial narrowing of the effective bandgap in heavily doped p-Ge, which is used in the design of the SPAD considered.

РОЗРАХУНКОВІ МЕТОДИ ПРОЕКТУВАННЯ ЕЛЕКТРОМАГНІТНИХ ЕКРАНІВ ІЗ ЗАДАНИМИ ЗАХИСНИМИ ВЛАСТИВОСТЯМИ

На сьогоднішній день основна частина досліджень та прикладних розробок щодо розроблення матеріалів для екранування електромагнітних полів різних частотних діапазонів є експериментальними, особливо це стосується сучасних композиційних матеріалів. Встановлено, що актуальною є задача вироблення раціональної методології розрахункового прогнозування ефективності матеріалів для екранування електромагнітних полів. Мета роботи − надання зручного у використанні розрахункового апарату для прогнозування захисних властивостей матеріалів для екранування електромагнітних полів, що дозволить мінімізувати обсяги експериментальних робіт під час проектування захисних конструкцій. Наведено, виходячи з фундаментальних співвідношень електродинаміки суцільних середовищ, зручні у використанні залежності коефіцієнтів екранування металевих та композиційних матеріалів від їх геометричних, магнітних та електрофізичних властивостей. Обґрунтовано співвідношення щодо визначення внеску відбиття електромагнітних хвиль у загальний коефіцієнт екранування. Це дозволяє розрахувати товщину електромагнітного екрана на принципах розумної достатності. Показано, що для ефективного використання розрахункових методів оцінювання захисних властивостей композиційних матеріалів для екранування магнітних та електромагнітних полів потрібна наявність надійних експериментальних даних щодо магнітних та електрофізичних властивостей найбільш поширених за складом композиційних матеріалів

On laws of conservation in the electrodynamics of continuous media (on the occasion of the 100th anniversary of the S I Vavilov State Optical Institute)

This article discusses conservation laws in the electrodynamics of dissipative continuous media, with particular emphasis on the electric area conservation rule for electromagnetic pulses and its application to short pulse propagation problems in resonant media.

External versus induced and free versus bound electric currents and related fundamental questions of the classical electrodynamics of continuous media: discussion

Standard textbooks on classical electrodynamics frequently operate with the notions of free and bound currents (charges). Alternative terminology of external and induced currents also exists. However, a clear physical definition of these physical objects is rarely given. The term "free current" can refer in some cases to the conductivity current, which is subject to constitutive relations in a material sample. In other cases, free current refers to the current that is completely extrinsic to a given material sample and is assumed to be known a priori or manipulated by the experimentalist at will. Although one can argue that all currents flowing in material media are subject to some constitutive relations, there is a clear distinction in the construction of the classical electrodynamics between the external and induced currents. The aim of this paper is to clarify this distinction while pointing out that the traditional distinction between free and bound currents is arbitrary and can be abandoned. In addition, the paper considers some relevant fundamental questions of classical electrodynamics, including the derivation of macroscopic Maxwell's equations, the properties of the external currents, and the physical interpretation of some auxiliary fields such as the field of polarization P.

О законах сохранения в электродинамике сплошных сред (к 100-летию Государственного оптического института им. С.И. Вавилова)

О законах сохранения в электродинамике сплошных сред (к 100-летию Государственного оптического института им. С.И. Вавилова)

On spacetime structure and electrodynamics

Electrodynamics is the most tested fundamental physical theory. Relativity arose from the completion of Maxwell–Lorentz electrodynamics. Introducing the metric [Formula: see text] as gravitational potential in 1913, versed in general (coordinate-)covariant formalism in 1914 and shortly after the completion of general relativity, Einstein put the Maxwell equations in general covariant form with only the constitutive relation between the excitation and the field dependent on and connected by the metric in 1916. Further clarification and developments by Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923 together with the corresponding developments in electrodynamics of continuous media by Bateman in 1910, Tamm in 1924, Laue in 1952 and Post in 1962 established the premetric formalism of electrodynamics. Since almost all phenomena electrodynamics deal with have energy scales much lower than the Higgs mass energy and intermediate boson energy, electrodynamics of continuous media should be applicable and the constitutive relation of spacetime/vacuum should be local and linear. What is the key characteristic of the spacetime/vacuum? It is the Weak Equivalence Principle I (WEP I) for photons/wave packets of light which states that the spacetime trajectory of light in a gravitational field depends only on its initial position and direction of propagation, and does not depend on its frequency (energy) and polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum. With this principle it is proved by the author in 1981 in the weak field limit, and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011 without assuming the weak-field condition that the constitutive tensor must be of the core metric form with only two additional degrees of freedom — the pseudoscalar (Abelian axion or EM axion) degree of freedom and the scalar (dilaton) degree of freedom (i.e. metric with axion and dilaton). In this paper, we review this connection and the ultrahigh precision empirical tests of nonbirefringence together with present status of tests of cosmic Abelian axion and dilaton. If the stronger version of WEP is assumed, i.e. WEP II for photons (wave packets of light) which states in addition to WEP I also that the polarization state of the light would not change (e.g. no polarization rotation for linear polarized light) and no amplification/attenuation of light, then no Abelian (EM) axion and no dilaton, and we have a pure metric theory.

Foreword

In the last two decades we have seen important mutual stimulations between the community working on electrodynamics of continuous media and the community working on spacetime structure. This is highlighted by the publication of two important monographs from two communities: Foundations of Classical Electrodynamics by F. W. Hehl and Yu. N. Obukhov (Birkh\"auser, Boston 2003) and Differential Forms in Electromagnetics by I. V. Lindell (IEEE Press-Wiley, Piscataway, NJ 2004; see also a new book "Multiforms, Dyadics, and Electromagnetic Media" by the same author in 2015). Starting around 1960, magnetoelectric effects and magnetoelectric media have been a focus of study. Somewhat later, the constitutive tensor density framework was used to construct spacetime structure theoretically and empirically. Earlier, in putting Maxwell equations into a form compatible with general relativity, Einstein noticed that the Maxwell equations can be formulated in a form independent of the metric gravitational potential in 1916; only the constitutive tensor density depends on the metric. This was followed by further stimulating and clarifying works of Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923. Year 2016 is the centennial of the start of this historical development. International Journal of Modern Physics D of World Scientific is celebrating the occasion by publishing this special issue on Spacetime Structure and Electrodynamics. We have invited researchers to submit original research articles that would contribute to a better understanding of the phenomena inherent to spacetime structure and electrodynamic media.

On the electrodynamics of continuous media

Radiation of fast charged particles in the presence of the interface between hollow space and “left-handed” ferrodielectric is considered. The quantitative identity of various phenomena in the case of “different-right-handed” media is revealed. It is shown that transition radiation at the interface with a “left-handed” medium is quantitatively identical to the case of annihilation radiation at the interface with a “right-handed” medium with participation of various charged particles. Transition radiation of the charged particle at the interface with a uniaxial crystal is generalized to radiation with participation of particles with various charges and velocities.

On the “area” of an electromagnetic field

A general formulation of retained integral characteristics (“areas” of an electromagnetic field) has been obtained from the Maxwell equations for electrodynamics of continuous media. The relations found can be used to monitor the accuracy of computer simulation of the field dynamics.

Simulation of a spectral inhomogeneous broadening

The standard approach that is used to simulate effects of inhomogeneous spectral broadening in a medium consisting of two- or multilevel systems is to calculate the microscopic polarization (the dipole moment of an individual system) as a function of the frequency detuning and further to average this quantity over detunings with corresponding weights. This just leads to the macroscopic polarization that appears in Maxwell’s equations of electrodynamics of continuous media. Here, we study and develop an alternative method that has been recently proposed by N.V. Vysotina, N.N. Rozanov, and V.E. Semenov (Opt. Spectrosc. 106 (5), 713 (2009)) for calculation of the macroscopic polarization and that has been aimed at solving problems of computational quantum optics. In this approach, the frequency detuning is considered as a stochastic function of coordinates; in one-dimensional problems, of longitudinal coordinate z. At each step of evolution, the microscopic polarization is calculated for a randomly chosen fixed value of the detuning. Therefore, calculating the macroscopic polarization does not need an additional averaging over detunings; it is replaced by averaging over spatial coordinates, which is naturally performed when describing the radiation propagation through an ensemble of quantum systems. This radically reduces the amount of computations, especially in the context of the finite-difference time domain (FDTD) method.

Electro-Rheological Model of HP-Indigo ElectroInk

ElectroInk is a dispersion of micron and submicron size polymer particles containing nanometer size colorant pigments in non-polar fluid. ElectroInk is in the core technology of digital printing press machines developed and manufactured by HP Indigo Division the world leader in the field of digital press machines. ElectroInk is a complex fluid exhibiting non-linear rheological properties. During the print process electrical field is applied to the ink that causes the ink particles to move in the field. Also, as the ink propagates from the container to the final substrate (paper) to be printed on, the concentration continuously increases; the ink is subjected to changes in temperature, pressure, shear, and electrical field; all transforming the rheological properties. As the concentration increases the ink ceases behaving as simple dispersion of non-interacting particles. Instead, the ink is better described as an interwoven structure of two continuous phases one being an elasto-viscous solid like substance made of from strongly interacting particles and dissolved liquid the other being the pure solvent.This model reminding a wet sponge is called the two-continuous phases model of ElectroInk. The movement of individual particles is replaced by the deformation of the solid like part described by the tools of mechanics and electrodynamics of continuous media. This model adequately describes the transfer process of the ink from roller to roller in the press under electrical field and predicts the relevant parameters leading to 100% transfer which is necessary to meet the principal requirement to digital printing vis. that each printed page can be different.In this presentation a short introduction to Indigo's special technology will be given followed by some general findings on the unique rheological and electrical properties of ElectroInk, and the two-continuous phases model will be introduced and applied to electrically assisted ink transfer process.Experimental data showing good agreement with the model will also be presented.

Electrodynamics of metamaterials and the Landau–Lifshitz approach to the magnetic permeability

We discuss a relationship between the traditional framework of the frequency-dependent dielectric permittivity ɛ ( ω ) and magnetic permeability μ ( ω ) in the electrodynamics of continuous media and the spatial dispersion framework utilizing the dielectric tensor ɛ i j ( ω , k ) depending both on the frequency ω and wavevector k . For electromagnetic waves, the latter approach includes the former as a specific limiting case for small k within the k 2 accuracy. While the dispersion of the transverse electromagnetic waves in this approximation is captured by the ɛ ( ω ) – μ ( ω ) phenomenology, the dispersion of the longitudinal electric waves would be missed. The general ɛ i j ( ω , k ) framework also accommodates more complex situations such as excitonic resonances and additional electromagnetic waves. We also review the well-known Landau–Lifshitz arguments on the physical meaning of μ ( ω ) at sufficiently high frequencies. In that context, the need is discussed for the effective medium response to include contributions from the spatial dispersion of the electric-dipole polarization and from the electric-quadrupole polarization on an equal footing with contributions from the magnetic-dipole resonances.

Metamaterials and the Landau–Lifshitz permeability argument: Large permittivity begets high-frequency magnetism

Homogeneous composites, or metamaterials, made of dielectric or metallic particles are known to show magnetic properties that contradict arguments by Landau and Lifshitz [Landau LD, Lifshitz EM (1960) Electrodynamics of Continuous Media (Pergamon, Oxford, UK), p 251], indicating that the magnetization and, thus, the permeability, loses its meaning at relatively low frequencies. Here, we show that these arguments do not apply to composites made of substances with Im square root(epsilon(S)) >> lambda/l or Re square root(epsilon(S)) approximately lambda/l (epsilon(S) and l are the complex permittivity and the characteristic length of the particles, and lambda >> l is the vacuum wavelength). Our general analysis is supported by studies of split rings, one of the most common constituents of electromagnetic metamaterials, and spherical inclusions. An analytical solution is given to the problem of scattering by a small and thin split ring of arbitrary permittivity. Results reveal a close relationship between epsilon(S) and the dynamic magnetic properties of metamaterials. For |square root(epsilon(S))| << lambda/a (a is the ring cross-sectional radius), the composites exhibit very weak magnetic activity, consistent with the Landau-Lifshitz argument and similar to that of molecular crystals. In contrast, large values of the permittivity lead to strong diamagnetic or paramagnetic behavior characterized by susceptibilities whose magnitude is significantly larger than that of natural substances. We compiled from the literature a list of materials that show high permittivity at wavelengths in the range 0.3-3000 microm. Calculations for a system of spherical inclusions made of these materials, using the magnetic counterpart to Lorentz-Lorenz formula, uncover large magnetic effects the strength of which diminishes with decreasing wavelength.

On some applications of Galilean electrodynamics of moving bodies

We discuss the seminal article by Le Bellac and Lévy-Leblond in which they identified two Galilean limits (called “electric” and “magnetic” limits) of electromagnetism and their implications. Recent work has shed new light on the choice of gauge conditions in classical electromagnetism. We show that the recourse to potentials is compelling in order to demonstrate the existence of both (electric and magnetic) limits. We revisit some nonrelativistic systems and related experiments, in the light of these limits, in quantum mechanics, superconductivity, and the electrodynamics of continuous media. Much of the current technology where waves are not taken into account can be described in a coherent fashion by the two limits of Galilean electromagnetism instead of an inconsistent mixture of these limits.

Theory of giant magneto-impedance effect in amorphous wires with different types of magnetic anisotropy

The effect of various types of magnetic anisotropy on the giant magneto-impedance spectra of amorphous wires with low magnetostriction is studied theoretically. For the first of the model considered the easy anisotropy axis is supposed to be parallel to the wire axis, whereas for the second model it has circumferential direction. In case of a wire with axial type of magnetic anisotropy the transverse magnetic permeability is obtained as a function of external magnetic field amplitude H 0 and other magnetic parameters of the wire. A strong dependence of this quantity on H 0 is shown to explain the giant magneto-impedance (GMI) effect in this type of amorphous wire. Besides, the amplitude of the GMI effect depends substantially on the value of a phenomenological damping parameter. In case of a wire with circumferential anisotropy the classical expression [Landau and Lifshitz, Electrodynamics of Continuous Media, 2nd ed, Pergamon, New York, 1984] for the wire impedance is not valid in the range of external magnetic field 0⩽ H 0⩽ H a, where H a is the anisotropy field. In this range of external magnetic field the wire impedance becomes a tensor. It has both longitudinal and transverse components that can be measured experimentally [Antonov et al., IEEE Trans. Magn. 33 (1997) 3367]. In case of a wire with circumferential anisotropy the peak of the longitudinal component of wire impedance as the function of H 0 corresponds to the anisotropy field, whereas in case of axial anisotropy it is found at zero magnetic field. The results obtained show that the good magnetic softness of amorphous wire is one of the most important conditions to observe the GMI effect; neither any domain structure nor circumferential anisotropy are strictly necessary.

On the existence of exact conditions in the theory of electrical double layers

It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of Continuous Media (Pergamon, Oxford, 1960)] and by a more recent statistical mechanical method of Blum et al. [J. Chem. Phys. 72, 1902 (1981)]. Here we describe statistical mechanical analyses for both constant and fluctuating charge models. It is shown that the derivation of Blum et al. is in error and that correct statistical mechanical treatments do not determine the sign of ∂V/∂σ. However, some rigorous bounds for related quantities are found. We also point out a mathematical problem in the method of Landau and Lifshitz which appears to invalidate their argument. We conclude that at present there is no rigorous proof that ∂V/∂σ must be positive and that the existence of negative values cannot be ruled out.

Wave beam shaping on diffraction of a whispering gallery wave at a convex cylindrical surface

LITERATURE CITED i. M.L. Ter-Mikaelyan, Izv. Akad. Nauk ArmSSR, Erevan (1969). 2. V.L. Gunzburg and V. N. Tsytovich, Transition Radiation and Transition Scattering [in Russian, Nauka, Moscow (1984). 3. V.G. Baryshevskii and I. D. Feranchuk, Zh. ~ksp. Teor. Fiz., 61, No. 3(9), 949 (1971). 4. V.G. Baryshevskii, Materials from the 2nd Symposium on Transition Radiation of High- Energy Particles [in Russian], Erevan (1983), p. 184. 5. L.D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media [in Russian], Nauka, Moscow (1982). WAVE BEAM SHAPING ON DIFFRACTION OF A WHISPERING GALLERY WAVE AT A CONVEX CYLINDRICAL SURFACE S. N. Vlasov, M. A. Shapiro, and E. V. Sheinina UDC 517.934+621.371 The problem of transforming a whispering gallery wave into a wave beam is re- solved numerically for the case of diffraction at a convex cylindrical surface. Conditions have been determined under which the conversion factor is close to unity. i. When the waves of a whispering gallery are propagated near a surface with a variable curvature the field separates from the surface in the vicinity of the point of flexure. In the case of linearly changing curvature [i], on radiation of the whispering gallery mode exhibiting only a single field variation along the transverse coordinate, a single-lobed radiation pattern is formed (a bell-shaped field structure), while on radiation of higher types of modes with two and more variations, the radiation pattern is multilobed [2]. On the other hand, as follows from the ray representation of the whispering gallery mode [3], the radiation pattern of the wave from the edge of a cylindrical concave surface is represented by the congruence of rays tangent on the segment of a simple caustic (Fig. i). Within the scope of such a representation, valid for higher types of modes, radiation from an edge exhibits a quasiuniform transverse structure in the far zone. However, the radiation pattern corresponds only to the main lobe of the radiation pattern; diffraction at the edge leads to the formation of side lobes~ From the standpoint of forming a bell-shaped field structure, there is interest in ana- lyzing the diffraction of whispering gallery waves from convex surfaces that do not disrupt the radiation pattern from an edge, but which block the formation of side lobes. Such a formulation of the problem, unlike [i] in which the coordinate system is connected to a dis- torted surface, corresponds to a greater degree to a system of radial coordinates [4]. It is difficult to analyze the lateral structure of the radiation in radial coordinates. A simplifying circumstance is the case in which the radiation is formed by a congruence of paraxial rays (Fig. i), and for the solution of the problem we can make use of Cartesian coordinates connected to a reference beam. 2. Our determination of the lateral structure of the radiation is based on the para- bolic equation method. Let the z coordinate be calculated in the direction of the reference beam and let the shape of the surface be described by the function x = x(z); the Cartesian coordinates (x, z) have been normalized to the radius of surface curvature a for z < 0 (Fig~ Institute of Applied Physics, Academy of Sciences of the USSR. Translated from Izvest- iya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 12, pp. 1482-1487, December, 1988. Original article submitted January 27, 1987. 1070 0033-8443/88/3112-1070512.50 9 1989 Plenum Publishing Corporation

Perturbation theory in the electrodynamics of continuous media

In this article the authors formulate a perturbation theory in canonical variables, general in the sense that any experimentally observable quantity is calculated in a unique manner. The evolution of an arbitrary dynamic quantity due to the interaction of a field and particles is represented as a series, each term of which corresponds to a specific radiation effect, with the spontaneous and induced processes being explicitly distinguished.

A description of the gravitational red shift borrowed from the electrodynamics of continuous media

The description of the effects of a gravitational field on the classical electromagnetic field equations in terms of generalized electric and magnetic permittivities is shown to define an “equivalent” medium with special properties. In particular it is remarked that such a medium can be chosen so as to include the behavior, in the presence of gravity, of the bodies that are used to produce and to detect the electromagnetic field. This is illustrated by the example of the gravitational red shift. The introduction of the proper time of the emitting and of the absorbing atoms, at rest in the gravitational field, is shown to define a medium interacting with the electromagnetic field through a drag velocity which increases linearly with time. For the sake of simplicity this example is described in the weak-field approximation.