Conservation of the Spin and Orbital Angular Momenta in Electromagnetism

Authors

Konstantin Y. Bliokh, CEMS, RIKEN
Justin Dressel, Chapman UniversityFollow
Franco Nori, CEMS, RIKEN

Document Type

Article

Publication Date

9-24-2014

Abstract

We review and re-examine the description and separation of the spin and orbital angular momenta (AM) of an electromagnetic field in free space. While the spin and orbital AM of light are not separately meaningful physical quantities in orthodox quantum mechanics or classical field theory, these quantities are routinely measured and used for applications in optics. A meaningful quantum description of the spin and orbital AM of light was recently provided by several authors, which describes separately conserved and measurable integral values of these quantities. However, the electromagnetic field theory still lacks corresponding locally conserved spin and orbital AM currents. In this paper, we construct these missing spin and orbital AM densities and fluxes that satisfy the proper continuity equations. We show that these are physically measurable and conserved quantities. These are, however, not Lorentz-covariant, so only make sense in the single laboratory reference frame of the measurement probe. The fluxes we derive improve the canonical (nonconserved) spin and orbital AM fluxes, and include a 'spin–orbit' term that describes the spin–orbit interaction effects observed in nonparaxial optical fields. We also consider both standard and dual-symmetric versions of the electromagnetic field theory. Applying the general theory to nonparaxial optical vortex beams validates our results and allows us to discriminate between earlier approaches to the problem. Our treatment yields the complete and consistent description of the spin and orbital AM of free Maxwell fields in both quantum-mechanical and field-theory approaches.

Comments

This article was originally published in New Journal of Physics, volume 16, in 2014. DOI: 10.1088/1367-2630/16/9/093037

Recommended Citation

Bliokh, K.Y., Dressel, J., Nori, F., 2014. Conservation of the spin and orbital angular momenta in electromagnetism. New Journal of Physics 16, 093037. doi:10.1088/1367-2630/16/9/093037

Peer Reviewed

1

Copyright

IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.