Trouble with the Lorentz Law of Force: Response to Critics

In a recent paper [arXiv:1205.0096], we questioned the validity of the Lorentz law of force in the presence of material media that contain electric and/or magnetic dipoles. A number of authors have criticized our methods and conclusions. This paper is an attempt at answering the critics and elaborating the relevant issues in some detail.Comment: 13 pages, 4 figures, 40 reference

Fourier Optics in the Classroom

Borrowing methods and formulas from Prof. Goodman's classic Introduction to Fourier Optics textbook [1], I have developed a software package [2] that has been used in both industrial research and classroom teaching [3]. This paper briefly describes a few optical system simulations that have been used over the past 30 years to convey the power and the beauty of Fourier Optics to our students at the University of Arizona's College of Optical Sciences.Comment: 2 pages, 5 figures, 3 references, Published in the Proceedings of the Optical Society of America's Imaging & Applied Optics Congress, Orlando, Florida (June 2018

Optical Angular Momentum in Classical Electrodynamics

Invoking Maxwell's classical equations in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of the EM angular momentum. The energy and the angular momentum of an EM field will be shown to have an intimate relationship; a source radiating EM angular momentum will, of necessity, pick up an equal but opposite amount of mechanical angular momentum; and the spin and orbital angular momenta of the EM field, when absorbed by a small particle, will be seen to elicit different responses from the particle.Comment: 15 pages, 3 figures, 43 equations, 34 reference

Momentum of the Electromagnetic Field in Transparent Dielectric Media

We present arguments in favor of the proposition that the momentum of light inside a transparent dielectric medium is the arithmetic average of the Minkowski and Abraham momenta. Using the Lorentz transformation of the fields (and of the coordinates) from a stationary to a moving reference frame, we show the consistent transformation of electromagnetic energy and momentum between the two frames. We also examine the momentum of static (i.e., time-independent) electromagnetic fields, and show that the close connection that exists between the Poynting vector and the momentum density extends all the way across the frequency spectrum to this zero-frequency limit. In the specific example presented in this paper, the static field inside a non-absorbing dielectric material turns out to have the Minkowski momentum.Comment: 10 pages, 5 figures, 29 equations, 15 reference

Comment on "Observation of a push force on the end face of a nanometer silica filament exerted by outgoing light," Phys. Rev. Lett. 101, 243601 (2008)

In a recent paper, W. She, J. Yu and R. Feng reported the slight deformations observed upon transmission of a light pulse through a fairly short length of a silica glass nano-fiber. Relating the shape and magnitude of these deformations to the momentum of the light pulse both inside and outside the fiber, these authors concluded that, within the fiber, the photons carry the Abraham momentum. In my view, the authors' claim that they have resolved the Abraham-Minkowski controversy surrounding the momentum of photons inside dielectric media is premature. A correct interpretation of the experiments of She et al requires precise calculations that would properly account not only for the electromagnetic momentum (both inside and outside the fiber) but also for the Lorentz force exerted on the fiber by the light pulse in its entire path through this nano-waveguide.Comment: 2 pages, 4 reference

Angular Momentum Exchange Between Light and Material Media Deduced from the Doppler Shift

Electromagnetic waves carry energy as well as linear and angular momenta. When a light pulse is reflected from, transmitted through, or absorbed by a material medium, energy and momentum (both linear and angular) are generally exchanged, while the total amount of each entity remains intact. The extent of such exchanges between light and matter can be deduced, among other methods, with the aid of the Doppler shift phenomenon. The main focus of the present paper is on the transfer of angular momentum from a monochromatic light pulse to spinning objects such as a mirror, an absorptive dielectric, or a birefringent plate. The fact that individual photons of frequency omega carry energy in the amount of h_bar*omega, where h_bar is Planck's reduced constant, enables one to relate the Doppler shift to the amount of energy exchanged. Under certain circumstances, the knowledge of exchanged energy leads directly to a determination of the momentum transferred from the photon to the material body, or vice versa.Comment: 8 pages, 7 figures, 7 equations, 14 reference

Force, Torque, Linear Momentum, and Angular Momentum in Classical Electrodynamics

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 consistent with Maxwell's equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetized medium, the Einstein-Laub (E-L) formulation of EM force and torque does not invoke hidden entities under such circumstances. Moreover, total force/torque exerted by EM fields on any given object turns out to be independent of whether the density of force/torque is evaluated using the law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions inside matter. Such differences in distribution are occasionally measurable, and could serve as a guide in deciding which formulation, if either, corresponds to physical reality.Comment: 15 pages, 35 equations, 75 references. Significant overlap with arXiv:1312.3262, which is the conference proceedings version of this paper. The conference paper, entitled "The Force Law of Classical Electrodynamics: Lorentz versus Einstein and Laub," was published in the Proceedings of SPIE 8810, 88100K-1:18 (2013). arXiv admin note: text overlap with arXiv:1409.479