Speed-of-light limitations in passive linear media
Name
PhysRevA.90.023847.pdf
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330.55 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Welters, Aaron
Johnson, Steven G.
Avniel, Yehuda B.
Date Issued
August 2014
Journal
Physical Review A
Publisher
American Physical Society
Citation
Welters, Aaron, Yehuda Aviel, and Steven G. Johnson. "Speed-of-light limitations in passive linear media." Phys. Rev. A 90, 023847 (August 2014). © 2014 American Physical Society
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.90.023847
