Energy–momentum tensor for the electromagnetic field in a dielectric

Crenshaw, Michael E.; Bahder, Thomas B.

doi:10.1016/j.optcom.2011.01.055

Cited by 13 publications

(43 citation statements)

References 20 publications

(11 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, one can investigate optical forces acting on the medium or on a small material probe in the medium [7][8][9][10]. On the other hand, one may wonder about the momentum carried by the wave per se and characterizing wave parameters such as the velocity of its propagation (phase or group) or wave vector [11][12][13][14][15][16][17][18][19]. In this work we mostly stick with the second approach.…”

Section: Introduction and Overview 1abraham And Minkowski Momentamentioning

confidence: 99%

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

2017

View full text Add to dashboard Cite

We examine the momentum and angular momentum (AM) properties of monochromatic optical fields in dispersive and inhomogeneous isotropic media, using the Abraham-and Minkowski-type approaches, as well as the kinetic (Poynting-like) and canonical (with separate spin and orbital degrees of freedom) pictures. While the kinetic Abraham-Poynting momentum describes the energy flux and the group velocity of the wave, the Minkowski-type quantities, with proper dispersion corrections, describe the actual momentum and AM carried by the wave. The kinetic Minkowski-type momentum and AM densities agree with phenomenological results derived by Philbin. Using the canonical spinorbital decomposition, previously used for free-space fields, we find the corresponding canonical momentum, spin and orbital AM of light in a dispersive inhomogeneous medium. These acquire a very natural form analogous to the Brillouin energy density and are valid for arbitrary structured fields. The general theory is applied to a non-trivial example of a surface plasmon-polariton (SPP) wave at a metal-vacuum interface. We show that the integral momentum of the SPP per particle corresponds to the SPP wave vector, and hence exceeds the momentum of a photon in the vacuum. We also provide the first accurate calculation of the transverse spin and orbital AM of the SPP. While the intrinsic orbital AM vanishes, the transverse spin can change its sign depending on the SPP frequency. Importantly, we present both macroscopic and microscopic calculations, thereby proving the validity of the general phenomenological results. The microscopic theory also predicts a transverse magnetization in the metal (i.e. a magnetic moment for the SPP) as well as the corresponding direct magnetization current, which provides the difference between the Abraham and Minkowski momenta.

show abstract

Section: Introduction and Overview 1abraham And Minkowski Momentamentioning

confidence: 99%

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

2017

View full text Add to dashboard Cite

show abstract

“…In a previous work, we considered a dielectric medium with an index of refraction that was time-independent and spatially uniform, and the dielectric was covered with a thin gradient-index antireflection coating [5]. We found that the total energy and the Gordon momentum were conserved quantities (constant in time).…”

Section: Discussionmentioning

confidence: 96%

Electromagnetic energy, momentum, and angular momentum in an inhomogeneous linear dielectric

Crenshaw

Bahder

2012

Optics Communications

Self Cite

View full text Add to dashboard Cite

In a previous work, Optics Communications 284 (2011) 2460-2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy-momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy-momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.

show abstract

“…We multiply Poynting's theorem, Eq. (3.5), by n and use a vector identity to commute the index of refraction with the divergence operator to obtain [17] n c…”

Section: Total Energy-momentum Tensormentioning

confidence: 99%

“…That much was obvious from the conservation of the Gordon form of momentum in Refs. [13] and [17], also in Eq. (2.17).…”

Section: The Linear Index Of Refractionmentioning

confidence: 99%

“…In this article, we carefully define a thermodynamically closed continuum electrodynamic system with complete equations of motion containing a stationary simple linear medium illuminated by a plane quasimonochromatic electromagnetic pulse through a gradient-index antireflection coating and identify the conserved total energy and the conserved total momentum, thereby extending our previous work [17][18][19] on dielectrics to a medium with both magnetic and dielectric properties. Assuming the validity of the macroscopic Maxwell-Heaviside equations, the total momentum in a simple linear medium is found using the law of conservation of linear momentum.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Electromagnetic momentum and the energy–momentum tensor in a linear medium with magnetic and dielectric properties

Crenshaw

2014

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

In a continuum setting, the energy-momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The welldefined total energy and the well-defined total momentum in a thermodynamically closed system with complete equations of motion are used to construct the total energy-momentum tensor for a stationary simple linear material with both magnetic and dielectric properties illuminated by a quasimonochromatic pulse of light through a gradient-index antireflection coating. The perplexing issues surrounding the Abraham and Minkowski momentums are bypassed by working entirely with conservation principles, the total energy, and the total momentum. We derive electromagnetic continuity equations and equations of motion for the macroscopic fields based on the material fourdivergence of the traceless, symmetric total energy-momentum tensor. We identify contradictions between the macroscopic Maxwell equations and the continuum form of the conservation principles. We resolve the contradictions, which are the actual fundamental issues underlying the AbrahamMinkowski controversy, by constructing a unified version of continuum electrodynamics that is based on establishing consistency between the three-dimensional Maxwell equations for macroscopic fields, the electromagnetic continuity equations, the four-divergence of the total energy-momentum tensor, and a four-dimensional tensor formulation of electrodynamics for macroscopic fields in a simple linear medium.

show abstract

Energy–momentum tensor for the electromagnetic field in a dielectric

Cited by 13 publications

References 20 publications

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

Electromagnetic energy, momentum, and angular momentum in an inhomogeneous linear dielectric

Electromagnetic momentum and the energy–momentum tensor in a linear medium with magnetic and dielectric properties

Contact Info

Product

Resources

About