Abraham Force Research Articles

Local model for the optical energy and momentum transfer in dielectric media and the microscopic origin of Abraham's force density

Local model for the optical energy and momentum transfer in dielectric media and the microscopic origin of Abraham's force density

QED corrections to the Abraham and Aharonov-Casher forces on Rydberg atoms

We calculate the Abraham force and the Aharonov-Casher force exerted by the electromagnetic quantum vacuum on alkaline atoms in highly excited, long-living Rydberg states. Because of their high polarizability and long-life time such atoms are good candidates to observe these forces.

Proposal to repeat the Abraham force experiment using giant permittivity materials

In the more than 100 years-old Abraham–Minkowski problem in macroscopic electrodynamics, the issue of how to observe the so-called Abraham term [Formula: see text] has been a main point. Such a measurement is rather delicate. Recent years have seen a number of beautiful experiments in radiation optics, but these experiments usually give no information about the Abraham term as this term simply fluctuates out. So, one is left with somewhat indirect verifications of this force, as in the radiation pressure of Jones et al. in the 1950s, testing the radiation pressure on a mirror immersed in a dielectric liquid. Now, there is a different way to test the existence of [Formula: see text], namely to work with low (quasi-stationary) frequencies enabling one to observe the sinusoidal variation of the force directly. These kind of experiments were actually done by Walker et al. in the 1970s, using BaTiO3 as a high-frequency dielectric (permittivity [Formula: see text]). The outcome of these experiments was convincing. Now, in recent years there have appeared dielectric materials with giant permittivities, of order 105 or even higher. It is therefore natural to consider the idea of Walker et al. anew, in order to test if this demanding experiment can be facilitated and give better accuracy. That is the main topic of this paper. The positive outcome of these kinds of experiments clearly supports the Abraham energy–momentum tensor at low frequencies. The Minkowski tensor is unable to predict a torque at all. The low-frequency and the high-frequency regimes are in this way highly contrasted, as it is obvious that in optical experiments the Minkowski tensor is by far the simplest and most convenient one to use. We end this note by commenting upon the use of the Einstein–Laub tensor (1908) in explaining this experiment, and discuss also the influence from air friction.

Динамика несимметричного проводника с токами Фуко

Цель настоящей работы ‒ измерение силы, действующей на проводник, находящийся в переменном магнитном поле. Поскольку токи Фуко являются индукционными, средняя за период осцилляций переменного магнитного поля сила, действующая на проводник, должна быть равна нулю. На основе этого положения проведены подробные измерения изменения веса проводника при включении магнитного поля. Изучен характер магнитного поля, создаваемого источником, что позволило определить область, где магнитное поле однородно. Показано, что даже при расположении несимметричного проводника в области, где поле однородно, средняя сила, действующая на проводник, не равна нулю. Особое внимание обращено на зависимость изменения веса проводника в форме половины кольца от угла наклона по отношению к горизонтали. Это дало возможность отделить фоновую составляющую от силы Абрагама, представляющей собой силу реакции излучения на проводник. Отмечено, что максимальное значение измеренной силы Абрагама существенно выше известных экспериментальных значений и наблюдается при горизонтальном расположении проводника с цилиндрической поверхностью, расположенной снизу.

Токи смещения Фуко в динамике несимметричной системы

Рассмотрены пондеромоторные силы, действующие на незамкнутые токи проводимости Фуко в симметричном проводнике. Приведен пример симметричного проводника, находящегося в аксиально-симметричном внешнем переменном магнитном поле. Эти токи замыкаются токами смещения, на которые действует магнитное поле токов проводимости в проводнике, создавая силу Абрагама. Показано, что переменное магнитное поле, создаваемое токами смещения, не оказывает действие на токи проводимости в проводнике. Единственной магнитной силой, среднее значение которой за период изменения внешнего магнитного поля не равно нулю, является сила самодействия, с которой проводник действует сам на себя. Сумма сил Абрагама и самодействия равна нулю, что соответствует закону сохранения импульса. Сила тяги, роль которой играет сила самодействия, максимальна при наибольшей неоднородности источника внешнего переменного магнитного поля на его периферии.

MOMENTUM OF AN ELECTROMAGNETIC WAVE IN TIME-VARYING DIELECTRIC MEDIA

In the context of the Abraham–Minkowski controversy, the problem of the propagation of electromagnetic waves in a linear dielectric medium with a time-varying dielectric constant is considered. It is shown that the momentum of an electromagnetic wave in the form of Minkowski is preserved with an instantaneous change in the dielectric permittivity of the medium. At the same time, the Abraham momentum is not conserved, despite the spatial homogeneity of the problem. This circumstance is interpreted as a manifestation of the Abraham force.

Dynamics of a Conductor with Unclosed Alternative Electric Current

The ponderomotive interaction of displacement currents and conduction currents in an open conductor through which an alternating electric current flows is considered. The calculation is performed for a flat conductor of arbitrary shape. It has been shown that the displacement current does not create a nonzero force that would act on an open conductor. The so-called force of self-action, with which the conductor acts on itself, is compensated by the force of Abraham, transmitted to the electromagnetic field. The absolutely exact fulfillment of the law of conservation of momentum, which includes the latent momentum of the field, has been demonstrated. The density of Abraham's force is determined by the vector product of the derivative of the electric field in-duction by the magnetic field induction. As an example, a numerical calculation of the self-force and the Abraham force for a thin ring conductor is carried out. The ratio of Abraham's force to the square of the conduction current depends only on the relative dimensions of the conductor. The maximum Abraham's force is observed for a conductor representing half of a flat ring.

Generalized Abraham forces on molecules: From classical to quantum

Abraham forces are defined as electromagnetic forces on neutral objects caused by the presence of slow, time-dependent, homogeneous electromagnetic fields. Only a few experimental observations have been reported, and different formulations exist in literature. The ``standard" Abraham force is usually associated with the full derivative $\partial_t(\mathbf{E} \times \mathbf{B})$ of homogeneous electric and magnetic fields. We show that this full derivative is wrong in general, since the classical Maxwell theory contains subtle induced-dipole forces that contribute to the Abraham force, which thus breaks the dual symmetry between electric and magnetic components. We investigate other manifestations of Abraham forces and torques and estimate orders of magnitude, e.g related to chiral, moving or rotating matter. Some of them are also severely violating dual symmetry. We provide a quantum description of the Abraham force. Apart from being more elegant and less technical, this quantum treatment paves the way for future studies of Abraham forces on complex molecules involving spin and spin-orbit coupling, and also facilitates the inclusion of the quantum vacuum.

Lagrangian dynamics of the coupled field-medium state of light

In the recently introduced mass-polariton (MP) theory of light (Partanen et al 2017 Phys. Rev. A 95 063850), the optical force of light drives in a medium forward an atomic mass density wave. In this work, we present the Lagrangian formulation of the MP theory starting directly from the principle of least action and the well-known Lagrangian densities of the electromagnetic field and the medium within the special theory of relativity. The Lagrangian densities and the resulting Euler–Lagrange equations lead directly and without any further postulates to the unique expression of the optical Abraham force that dynamically couples the electromagnetic field and the medium in the MP theory of light. The field-medium coupling is symmetric and bi-directional and it fulfills the law of action and counteraction. The coupled dynamical equations also enable the exact description of the very small kinetic energy of the medium as a part of the total energy of the coupled state of light. Thus, the Lagrangian formulation of the present work is a complementary approach to Lorentz covariance properties of the MP theory discussed in our recent work (Partanen and Tulkki 2019 Phys. Rev. A 99 033852). We show how the coupled dynamical equations of the field and the medium can be solved analytically for a Gaussian light pulse. It is astonishing how the simple analytic results for the dynamical equations, the optical force, and the stress-energy-momentum tensor of the MP theory follow ab initio from the Lagrangian densities that have been well known for almost a century.

On choosing the energy–momentum tensor in electrodynamics and on the Abraham force

The highly debated problem of choosing the energy–momentum tensor in electrodynamics is examined. Electromagnetic forces in a continuum medium that follow from the Minkowski and Abraham tensors are considered. It is shown that the conservation equations for both Minkowski’s momentum density and Abraham’s momentum simultaneously follow from the Minkowski tensor and that they are the components of a composite electromagnetic momentum in the medium. It is shown that choosing canonical matter equations reduces the Abraham force to zero. We argue in favor of choosing the Minkowski tensor and show the incompleteness of the Abraham tensor.

Momentum of a wave and additional forces connected with the momentum

The question of the magnitude of the momentum remains open even for a light wave propagating in matter. In accordance with Minkowski, the momentum of light in matter increases by n times as compared with that in vacuum. On the contrary, in accordance with Abraham, the momentum of light in matter decreases by n times, but in the same time an additional force arises. At present there is no generally accepted notion about a magnitude of the momentum of a light wave. Moreover, if Abraham is right, an additional type of force exists in nature. Based on thought experiments where only laws of mechanics are used, we show that the Abraham force exists and shows itself not only at an interaction between light and matter but also at an interaction between matter and any wave propagating in matter. An experimental confirmation of an existence of the Abraham force produced by a sound wave propagating in gases or liquids is presented.

О выборе тензора энергии-импульса в электродинамике и силе Абрагама

О выборе тензора энергии-импульса в электродинамике и силе Абрагама

Optomechanical measurement of the Abraham force in an adiabatic liquid-core optical-fiber waveguide

We report quantitative experimental measurements of the Abraham force associated with a propagating optical wave. We isolate this force using a guided light wave undergoing an adiabatic mode transformation (AMT) along a liquid-filled hollow optical fiber (HOF). Utilizing this light intensity distribution within the liquid, we were able to generate a time-averaged non-vanishing Abraham force density, while simultaneously suppressing the Abraham-Minkowski force density. The incident laser field induced a linear axial displacement of the air-liquid interface inside the HOF, which provided a direct experimental measure of the Abraham force density. We find good agreement between the experimental results and theoretical determinations of the Abraham force density

Ponderomotive forces in electrodynamics of moving media: The Minkowski and Abraham approaches

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 relations 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 forces in the Abraham and Minkowski approaches as the Abraham force not only under consideration of media at rest but also in the case of moving media. The Lorentz force is found which is exerted by external electromagnetic field on the conduction current in a medium, the covariant Ohm law, and the constitutive Minkowski relations being taken into account. The physical argumentation is traced for the definition of the 4-vector of the ponderomotive force as the 4-divergence of the energy-momentum tensor of electromagnetic field in a medium.

Radiation pressure on plane dielectric surfaces

It is shown on the basis of unambiguous thought and real experiments regarding the pressure produced by light on a plane boundary of optical medium that the Abraham force takes part in the production of the pressure. As a result, all hitherto known information obtained by using another approach based on the Lorentz force should be corrected. Radiation pressures produced by a continuous light wave and a light pulse on the simplest plane dielectric surfaces are presented. The pressure produced by a continuous traveling light wave incident from free space on a semi-infinite dielectric is negative and is equal −W0(n−1)/(n+1) where W0 is the energy density of light in free space, n is the refractive index. The pressure produced by the leading edge of a light pulse at the entrance to the dielectric is positive and equal W0(n−1)/(n+1). Pressures produced by a continuous light wave and light pulse on a semi-infinite dielectric with anti-reflection λ/4 coating are equal W0(1−n) and W0(1−1/n), respectively.

Erratum: Detection of the Abraham force with a succession of short optical pulses [Phys. Rev. A86, 025801 (2012)

Erratum: Detection of the Abraham force with a succession of short optical pulses [Phys. Rev. A<b>86</b>, 025801 (2012)

QED corrections to the electromagnetic Abraham force

We develop a QED approach to find the contribution of the quantum vacuum to the electromagnetic Abraham force. Semi-classical theories predict diverging contributions from the quantum vacuum. We show that the divergencies disappear by Kramers-Bethe mass-renormalization. The finite remainder is compared to the relativistic corrections to the Abraham force. This work generalizes an earlier paper [1], dedicated to the harmonic oscillator, to the hydrogen atom and corrects two subtle errors.

Detection of the Abraham force with a succession of short optical pulses

For over a century, two rival descriptions of electromagnetic field momentum in matter have co-existed, due to Abraham and Minkowski, respectively. We propose a set-up for measuring the difference between Abraham's and Minkowski's predictions in optics. To wit, a set-up is proposed in which the transient "Abraham force", a consequence of the Abraham energy-momentum tensor of 1909 may be measured directly. We show that when a train of short laser pulses is sent through a fiber wound up on a cylindrical drum, the Abraham theory predicts a torque which, by inserting realistic parameters, is found to be detectable. Indeed, the same torque when calculated with the Minkowski tensor takes the opposite sign. Numerical estimates show that with a typical torsion pendulum set-up and standard laser parameters, the angular deflection is in the order of $10^{-3}$ rad, which is easily measurable and even visible to the naked eye. Although its prediction is a century old, the Abraham force has proven experimentally elusive, and to our knowledge no macroscopic experimental demonstration of the difference between the predictions of the two mentioned energy-momentum tensors exists at optical frequencies.

Observation of the Intrinsic Abraham Force in Time-Varying Magnetic and Electric Fields

The Abraham force exerted by a time-dependent electromagnetic field on neutral, polarizable matter has two contributions. The one induced by a time-varying magnetic field and a static electric field is reported here for the first time. We discuss our results in the context of the radiative momentum in matter. Our observations are consistent with Abraham's and Nelson's versions for radiative momentum.

Total longitudinal momentum in a dispersive optical waveguide

Using the Lorentz force law, we derived simpler expressions for the total longitudinal (conserved) momentum and the mechanical momentums associated with an optical pulse propagating along a dispersive optical waveguide. These expressions can be applied to an arbitrary non-absorptive optical waveguide having continuous translational symmetry. Our simulation using finite difference time domain (FDTD) method verified that the total momentum formula is valid in a two-dimensional infinite waveguide. We studied the conservation of the total momentum and the transfer of the momentum to the waveguide for the case when an optical pulse travels from a finite waveguide to vacuum. We found that neither the Abraham nor the Minkowski momentum expression for an electromagnetic wave in a waveguide represents the complete total (conserved) momentum. Only the total momentum as we derived for a mode propagating in a dispersive optical waveguides is the 'true' conserved momentum. This total momentum can be expressed as PTot = -U Die/(vg) + neff (U/c). It has three contributions: (1) the Abraham momentum; (2) the momentum from the Abraham force, which equals to the difference between the Abraham momentum and the Minkowski momentum; and (3) the momentum from the dipole force which can be expressed as -UDie/vg. The last two contributions constitute the mechanical momentum. Compared with FDTD-Lorentz-force method, the presently derived total momentum formula provides a better method in terms of analyzing the permanent transfer of optical momentum to a waveguide.