We show that the Einstein covariance principle provides an opportunity to generate infinitely many solutions of given covariant equation from a known one. With use of this statement we derive exact expressions for charge and current densities in a medium in an arbitrary external field. We obtain that in a homogeneous nondispersive medium the field of a point particle differs at short-distances from the well known expression. We also demonstrate that in a linear medium second harmonic generation and optical detection become possible in the field of radially polarized radiation.
The equations of electromagnetic fields in a medium is usually written in the rest frame of the medium. We outline a method of generalizing the discussion to arbitrary inertial frames. In the discussion, we also include the possibility that the medium is optically active, a possibility that is often overlooked in discussions of electromagnetic fields in a medium.
While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance -- form invariance under general coordinate transformations, including between accelerating frames -- that led to general relativity. Several lines of inquiry over the past two decades, notably the development of metamaterial-based transformation optics, has spurred a greater interest in the role of geometry and space-time covariance for electrodynamics in ponderable media. I develop a generally covariant, coordinate-free framew…
The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M - these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r,t) and M(r,t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. T…
We provide a simple physical proof of the reciprocity theorem of classical electrodynamics in the general case of material media that contain linearly polarizable as well as linearly magnetizable substances. The excitation source is taken to be a point-dipole, either electric or magnetic, and the monitored field at the observation point can be electric or magnetic, regardless of the nature of the source dipole. The electric and magnetic susceptibility tensors of the material system may vary from point to point in space, but they cannot be functions of time. In the case of spatially non-dispers…
We address two issues in the quantum electrodynamical description of photonic media with some disorder, neglecting material dispersion. When choosing a gauge in which the static potential vanishes, the normal modes of the medium with disorder satisfy another transversality condition than the modes of the ideal medium. Our first result is an integral equation for optical modes such that all perturbation-theory solutions automatically satisfy the desired transversality condition. Secondly, when expanding the vector potential for the medium with disorder in terms of the normal modes of the ideal …
We present a canonical quantization of macroscopic electrodynamics. The results apply to inhomogeneous media with a broad class of linear magneto-electric responses which are consistent with the Kramers-Kronig and Onsager relations. Through its ability to accommodate strong dispersion and loss, our theory provides a rigorous foundation for the study of quantum optical processes in structures incorporating metamaterials, provided these may be modeled as magneto-electric media. Previous canonical treatments of dielectric and magneto-dielectric media have expressed the electromagnetic field opera…
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…
Fluctuational Quantum Electrodynamics of Dispersive Time-Varying Media
Universidad Autónoma de Madrid（马德里自治大学）；Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid（马德里自治大学凝聚态物理中心 (IFIMAC)）；Instituto Nicolás Cabrera (INC), Universidad Autónoma de Madrid（马德里自治大学尼古拉斯·卡布雷拉研究所 (INC)）
A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes - volumes that nevertheless contain a large number of electric and/or magnetic dipoles. Indeed, Maxwell's macroscopic equations are exact and self-consistent mathematical relations between electromagnetic fields and their sources, which consist of free charge, free current, polarization, and magnetization. When necessary, the discrete nature of the constituents of matter and the granularity of material media …
We study light propagation through a slab of cold gas using both the standard electrodynamics of polarizable media, and massive atom-by-atom simulations of the electrodynamics. The main finding is that the predictions from the two methods may differ qualitatively when the density of the atomic sample $ρ$ and the wavenumber of resonant light $k$ satisfy $ρk^{-3}\gtrsim 1$. The reason is that the standard electrodynamics is a mean-field theory, whereas for sufficiently strong light-mediated dipole-dipole interactions the atomic sample becomes correlated. The deviations from mean-field theory app…
The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just as it postulates the existence and properties of electric charges and currents. Maxwell's macroscopic equations are mathematically exact and self-consistent differential equations that relate the electromagnetic (EM) field to its sources, namely, electric charge-density $ρ_{free}$, electric current-density $J_{free}$, polarization P, and magnetization M. At…
We give a detailed account of equilibrium and non-equilibrium fluctuational electrodynamics of hyperbolic metamaterials. We show the unifying aspects of two different approaches; one utilizes the second kind of fluctuation dissipation theorem and the other makes use of the scattering method. We analyze the near-field of hyperbolic media at finite temperatures and show that the lack of spatial coherence can be attributed to the multi-modal nature of super-Planckian thermal emission. We also adopt the analysis to phonon-polaritonic super-lattice metamaterials and describe the regimes suitable fo…
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 cons…
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 …
The relationship between magnetoelectricity and electromagnetism is a subject of a strong interest and numerous discussions in microwave and optical wave physics and material sciences. The definition of the energy and momentum of the electromagnetic (EM) field in a magnetoelectric (ME) medium is not a trivial problem. The question of whether electromagnetism and magnetoelectricity can coexist without an extension of Maxwell theory arises when we study the effects of EM energy propagation and consider group velocity of the waves in a ME medium. The energy balance equation reveals unusual topolo…
We consider a sub-wavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and we show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. …
This paper opens up the field of nonuniform-velocity SpaceTime-Modulated (STM) metamaterials, with the canonical example of an STM metamaterial of constant proper acceleration or, equivalently, hyperbolic acceleration. Combining tools of General Relativity and Classical Electrodynamics, it derives the dispersion relation of this exotic medium and reports its fundamental physics, whose most striking feature is the bending of light in the direction opposite to the direction of the modulation.
Macroscopic Quantum Electrodynamics with Gain: Modified Fluctuations and Their Consequences
RIKEN Centre for Advanced Photonics, RIKEN（RIKEN先进光子学中心）；Instituto Superior Técnico—University of Lisbon and Instituto de Telecomunicações（里斯本高等理工学院与电信研究所）；The Blackett Laboratory, Imperial College London（帝国理工学院布莱克特实验室）
Spin and orbital angular momentum of light plays a central role in quantum nanophotonics as well as topological electrodynamics. Here, we show that the thermal radiation from finite-sized bodies comprising of nonreciprocal magneto-optical materials can exert a spin torque even in global thermal equilibrium. Moving beyond the paradigm of near-field heat transfer, we calculate near-field radiative angular momentum transfer between finite-sized nonreciprocal objects by combining Rytov's fluctuational electrodynamics with the theory of optical angular momentum. We prove that a single magneto-optic…
The duality symmetry between electricity and magnetism hidden in classical Maxwell equations suggests the existence of dual charges, which have usually been interpreted as magnetic charges and have not been observed in experiments. In quantum electrodynamics (QED), both the electric and magnetic fields have been unified into one gauge field, which makes this symmetry inconspicuous. Here, we recheck the duality symmetry of QED by introducing a dual gauge field and a dual symmetric Lagrangian. Within the framework of gauge-field theory, we show that the electric-magnetic duality symmetry cannot …
Masers, the microwave analogue of lasers, promise to deliver ultra-low noise amplification of microwave signals for use in medical MRI imaging and deep-space communication. Research on masers in modern times was rekindled thanks to the discovery of gain media that were operable at room-temperature, eschewing bulky cryogenics that hindered their use. However, besides the two known materials of pentacene doped in para-terphenyl and negatively-charged nitrogen-vacancy defects in diamond, there has been scarce progress in the search for completely new room-temperature gain media. Here we show the …
