Abraham-Minkowski Dilemma Research Articles

Investigation of the Abraham–Minkowski dilemma in Smith–Purcell radiation from photonic crystals

The debate over whether light’s momentum within a medium is accurately described by Abraham or Minkowski formulation has persisted for over a century. To our knowledge, this dilemma has not been explored within the context of Smith–Purcell radiation. This is because, in conventional Smith–Purcell radiation scenarios, the refractive index is equal to one, leading both the Abraham and Minkowski formulations to yield identical results. Here, we investigate the Abraham–Minkowski dilemma within the realm of Smith–Purcell radiation from photonic crystals, where the refractive index deviates from one. In particular, we find that 3 MeV free electrons impinge a photonic crystal with a grating length of 2.1 μm, resulting in the emission of red light when analyzed based on Abraham’s momentum and blue light when analyzed based on Minkowski’s momentum. In addition, our findings reveal that the disparity in wavelength as predicted by Abraham’s momentum and Minkowski’s momentum depends on the grating length and the refractive index. Our findings offer a method to address the Abraham–Minkowski dilemma within the context of Smith–Purcell radiation, thereby enhancing our understanding of both the Abraham–Minkowski dilemma and Smith–Purcell radiation.

ANALOGUE OF THE ABRAHAM–MINKOWSKI CONTROVERSY IN ELECTRONIC OPTICS

In the problem of electron diffraction by a standing light wave (the Kapitza–Dirac effect), an electronic refractive index can be defined as the ratio of electron momenta in the wave field and outside it. Moreover, both kinetic and canonical electron momenta can be used for this purpose, which corresponds to the Abraham–Minkowski controversy in photonic optics. It is shown that in both cases the same expression for the electronic refractive index is obtained. This is consistent with Barnett's resolution of the Abraham–Minkowski dilemma.

Example of a simple thought experiment that goes in favor of the Minkowski form of the photon momentum in medium

A novel approach to the Abraham-Minkowski dilemma based on a simple thought experiment is presented. The mathematical analysis of the simple thought experiment, which is based on a plane, monochromatic, uniform electromagnetic wave that propagates through the infinite, homogeneous, linear and isotropic dielectric medium without losses and impinges the surface of a perfect mirror, shows that the presented thought experiment goes in favor of the Minkowski form of the photon momentum in medium.

Balazs thought experiment and its implications for the electromagnetic force density in continuous media. Relativistic analysis

We analyze the Balazs thought experiment under minimal assumptions and show that the two expressions for the force density that have been recently discussed in the literature (the conventional Lorentz force density and the generalized or Einstein–Laub force density) are fully consistent with conservation of energy, conservation of momentum and the center-of-energy theorem. This conclusion contradicts some of the previously published claims that the conventional Lorentz force density is inconsistent with the center-of-energy theorem. We identify the sources of errors in these claims. We conclude that the conventional Lorentz force density captures all experimentally-observable effects of interaction of electromagnetic fields with matter and no other law or postulate (such as a resolution of the so-called Abraham–Minkowski dilemma) is necessary.

Electromagnetic momenta for wave-particle systems in vacuum waveguides

Whenever light is slowed down, for any cause, two different formulas give its momentum. The coexistence of those momenta was the heart of the century-old Abraham-Minkowski dilemma, recently resolved for dielectrics. We demonstrate that this framework extends to momentum exchange in wave-particle interaction; in particular to vacuum waveguides of electron tubes (dispersive metallic slow-wave structures). In waveguides, the dilemma can be easily investigated since energy and force are well established through the use of Maxwell equations in vacuum, and since waveguides can have a strong refractive index. Our theory is assessed with simulations validated against measurements from a traveling-wave tube. In addition, we show that the dilemma resolution is not limited to discriminating between kinematic and canonical momenta but also involves a non-negligible flowing momentum from Maxwell’s electromagnetic stress. The existence of two momenta for diverse systems like materials, plasmas and waveguides, for which light velocity modification has entirely different origin, points to the universality of the Abraham-Minkowski dilemma.

Mass-polariton theory of light in dispersive media

We have recently shown that the electromagnetic pulse in a medium is made of mass-polariton (MP) quasiparticles, which are quantized coupled states of the field and an atomic mass density wave (MDW) [M. Partanen et al., Phys. Rev. A 95, 063850 (2017)]. In this work, we generalize the MP theory of light for dispersive media assuming that absorption and scattering losses are very small. Following our previous work, we present two different approaches to the coupled state of light: (1) the MP quasiparticle theory, which is derived by only using the fundamental conservation laws and the Lorentz transformation; (2) the classical optoelastic continuum dynamics (OCD), which is a generalization of the electrodynamics of continuous media to include the dynamics of the medium under the influence of optical forces. We show that the total momentum and the transferred mass of the light pulse can be determined in a straightforward way if we know the field energy of the pulse and the dispersion relation of the medium. In analogy to the nondispersive case, we also find unambiguous correspondence between the MP and OCD theories. For the coupled MP state of a single photon and the medium, we obtain the total MP momentum ${p}_{\mathrm{MP}}={n}_{\mathrm{p}}\ensuremath{\hbar}\ensuremath{\omega}/c$, where ${n}_{\mathrm{p}}$ is the phase refractive index. The field's share of the MP momentum is equal to ${p}_{\mathrm{field}}=\ensuremath{\hbar}\ensuremath{\omega}/({n}_{\mathrm{g}}c)$, where ${n}_{\mathrm{g}}$ is the group refractive index and the share of the MDW is equal to ${p}_{\mathrm{MDW}}={p}_{\mathrm{MP}}\ensuremath{-}{p}_{\mathrm{field}}$. Thus, as in a nondispersive medium, the total momentum of the MP is equal to the Minkowski momentum and the field's share of the momentum is equal to the Abraham momentum. We also show that the correspondence between the MP and OCD models and the conservation of momentum at interfaces gives an unambiguous formula for the optical force. The dynamics of the light pulse and the related MDW lead to nonequilibrium of the medium and to relaxation of the atomic density by sound waves in the same way as for nondispersive media. We also carry out simulations for optimal measurements of atomic displacements related to the MDW in silicon. In the simulations, we consider different waveguide cross sections and optical pulse widths and account for the breakdown threshold irradiance of materials. We also compare the MP theory to previous theories of the momentum of light in a dispersive medium. We show that our generalized MP theory resolves all the problems related to the Abraham-Minkowski dilemma in a dispersive medium.

Relativistic kinetic equation for spin-1/2 particles in the long-scale-length approximation.

In this paper, we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long-scale-length limit, where the fields vary on a scale much longer than the localization of the particles; we work to first order in ℏ. Our starting point is a Foldy-Wouthuysen (FW) transformation, applicable to this regime, of the Dirac Hamiltonian. We derive the corresponding evolution equation for the Wigner quasidistribution in an external electromagnetic field. Using a Lagrangian method we find expressions for the charge and current densities, expressed as free and bound parts. It is furthermore found that the velocity is nontrivially related to the momentum variable, with the difference depending on the spin and the external electromagnetic fields. This fact that has previously been discussed as "hidden momentum" and is due to that the FW transformation maps pointlike particles to particle clouds for which the prescription of minimal coupling is incorrect, as they have multipole moments. We express energy and momentum conservation for the system of particles and the electromagnetic field, and discuss our results in the context of the Abraham-Minkowski dilemma.

Optical Momentum, Spin, and Angular Momentum in Dispersive Media.

We examine the momentum, spin, and orbital angular momentum of structured monochromatic optical fields in dispersive inhomogeneous isotropic media. There are two bifurcations in this general problem: the Abraham-Minkowski dilemma and the kinetic (Poynting-like) versus canonical (spin-orbital) pictures. We show that the kinetic Abraham momentum describes the energy flux and group velocity of the wave in the medium. At the same time, we introduce novel canonical Minkowski-type momentum, spin, and orbital angular momentum densities of the field. These quantities exhibit fairly natural forms, analogous to the Brillouin energy density, as well as multiple advantages as compared with previously considered formalisms. As an example, we apply this general theory to inhomogeneous surface plasmon-polariton (SPP) waves at a metal-vacuum interface and show that SPPs carry a "supermomentum," proportional to the wave vector k_{p}>ω/c, and a transverse spin, which can change its sign depending on the frequency ω.

Abraham-Minkowski dilemma in the light of the first principle

A novel approach to the Abraham-Minkowski dilemma based on the first principle is presented. Typically the Abraham form of the photon momentum has been considered to be inherent to the particle nature of photon. However, it was shown that by taking into consideration only the photon characteristics as a particle and implementing energy conservation law in the presented simple thought experiment the Minkowski form of the photon momentum also appears.

Propagation of a light pulse inside matter in a context of the Abraham–Minkowski dilemma

It is shown that a light pulse propagating in an optical medium exerts the optical pressure on the medium in the regions where leading and trailing edges are propagating. This effect is derived from analysis of unambiguous thought experiments which results contradict one other. It is shown that a magnitude of the pressure is equal to (n−1/n)W0, where n and W0 is the refractive index of the medium and the momentum flux density of the same pulse in free space, respectively. The Abraham form of the momentum of light is redundant if the optical pressure is taken into account. In this case the dilemma disappears because one of the rival alternatives disappears.

Enhanced optical angular momentum in cylinder waveguides with negative-index metamaterials

The optical angular momentum (AM) of helical electromagnetic (EM) modes in cylinder waveguides with negative-index metamaterials (NIM) is investigated. The AM density in NIM is shown to be negative valued with respect to the azimuthal mode index, in sharp contrast to that in regular dielectrics and vacuum. Furthermore, the AM flux per single-photon flux is found to be greatly enhanced in the NIM waveguides; its value depends on the form of EM momentum used in the AM. This interesting phenomenon is shown to be associated with the unique trapped EM modes in the NIM waveguides. Our investigation results could contribute to many potential applications, especially in realizing high density optical memory and buffers, and in solving the Abraham–Minkowski dilemma.

Equivalence of the Abraham momentum and the Minkowski momentum of photons in media

The century-long debate on the momentum of light in a medium involves two rival forms of momentum, namely those of Abraham and Minkowksi. In this Letter, we analyze this dilemma from the view of the quantum theory of light, the result of which can be easily extended to the classical level. It is found that the Abraham momentum of one polariton mode in linear and dispersive dielectrics differs from its Minkowski momentum, by a considerable factor. However, after taking all branches into consideration, we find the two lead to the same end, which unifies the two rival forms of momentum. The sum rule is traditional, but our conclusion provides a new perspective on the Abraham–Minkowski dilemma, and is consistent with existing experiments including a recent measurement of recoil momentum of atoms using an atom interferometer with Bose–Einstein Condensates [G. K. Campbell et al. Phys. Rev. Lett. 94, 170403 (2005).] , the Cerenkov effect, the Doppler effect and the phase matching conditions in nonlinear optical processes.

Crucial experiment to resolve Abraham–Minkowski controversy

Abraham–Minkowski dilemma concerning the momentum of light within media has persisted over 100 years [1,2] and conflicting experiments were reported until recently [3,4]. We perform a reversed Fizeau experiment to test the composition law of light speeds in media and the result accords with the extended Lorentz transformation where the light speed c is changed to c/n There is a crucial evidence that Minkowski's formulation p = n( E/ c) is correct although the momentum is not measured directly.

On diffraction within a dielectric medium as an example of the Minkowski formulation of optical momentum

The Abraham-Minkowski dilemma relates to the disputed value of the optical momentum within a dielectric medium and whether the free-space value should be divided (Abraham) or multiplied (Minkowski) by the refractive index. Although undoubtedly simplistic, these two approaches provide intuitive insight to many subtle problems in optical physics. This paper reviews a modified version of the Einstein box argument that supports an Abraham formulation, then considers diffraction within a dielectric medium and shows it supports a simple Minkowski formulation, i.e. that the optical momentum should be multiplied by the refractive index.

Interaction of Photons with Electrons in Dielectric Media

AbstractThe question of the field energy‐momentum tensor in a medium is not new and many workers, in the past, attempted to find the answer to it. Nevertheless, there was no general agreement about the form of such a tensor, thus resulting in a confusion involving the very fundaments of physics. Although the present work uses well established theories, the underlying philosophy is completely novel. Investigations are mainly centered around the collisionless plasma as, in that state, development of the argument is most transparent.On the basis of a simple theoretical reasoning, it is, first of all, postulated that the momentum of the photon in a plasma is given by the Minkowski expression. This hypothesis becomes more viable as it directly leads to the accepted form for the field energy density. Furthermore, utilizing the concepts of stimulated and spontaneous emission and absorption, it is confirmed that, in the equilibrium (between radiation and plasma), the transferred momentum has the value given by the Minkowski theory. However, as will be seen, this result is valid only in the region of high frequencies. Put otherwise, when conditions are such that the laws of geometrical optics apply, the momentum of the photon is, to a good approximation, given by the Minkowski theory.In order to arrive at a more general result, valid in the domain of wave optics, a similarity between the dispersion relation (describing the wave propagation through a medium) and the relativistic energy‐momentum of a particle moving through vacuum, is explored. Accepting the equivalence of these two relations implies that some of the properties of radiation in a medium, can also be described by a massive particle travelling through empty space. In other words, the task of analysing the behaviour of electromagnetic waves in a medium, can be replaced by the analysis of the free neutral vector meson field. Adoption of this equivalence results in the field energy‐momentum tensor being symmetrical.A thorough study of the field theory then provides the basis for interpreting the Abraham tensor as the sum of the “orbital” and “spin” tensors. The former is directly connected with the energy transport, whereas the latter one is not. Realising that the magnitude of the spin term increases towards the lower end of the frequency spectrum provides the resolution of the Abraham‐Minkowski dilemma: the energy‐momentum tensor, corresponding to the electromagnetic wave in a medium, is that given by Abraham, while the one of Minkowski is only an approximation valid at high frequencies.Although this conclusion stems from studies involving collisionless isotropic plasma, it is in excellent agreement with the experimental data.