Speed-of-light limitations in passive linear media

Aaron Welters, Yehuda Avniel, and Steven G. Johnson
Phys. Rev. A 90, 023847 – Published 26 August 2014

Abstract

We prove that well-known speed-of-light restrictions on electromagnetic energy velocity can be extended to a new level of generality, encompassing even nonlocal chiral media in periodic geometries, while at the same time weakening the underlying assumptions to only passivity and linearity of the medium (either with a transparency window or with dissipation). As was also shown by other authors under more limiting assumptions, passivity alone is sufficient to guarantee causality and positivity of the energy density (with no thermodynamic assumptions). Our proof is general enough to include a very broad range of material properties, including anisotropy, bianisotropy (chirality), nonlocality, dispersion, periodicity, and even delta functions or similar generalized functions. We also show that the “dynamical energy density” used by some previous authors in dissipative media reduces to the standard Brillouin formula for dispersive energy density in a transparency window. The results in this paper are proved by exploiting deep results from linear-response theory, harmonic analysis, and functional analysis that had previously not been brought together in the context of electrodynamics.

  • Figure
  • Received 1 May 2014

DOI:https://doi.org/10.1103/PhysRevA.90.023847

©2014 American Physical Society

Authors & Affiliations

Aaron Welters*, Yehuda Avniel, and Steven G. Johnson

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *awelters@math.mit.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 90, Iss. 2 — August 2014

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×