Speedoflight limitations in passive linear media
Abstract
We prove that wellknown speedoflight 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 linearresponse theory, harmonic analysis, and functional analysis that had previously not been brought together in the context of electrodynamics.
 Publication:

Physical Review A
 Pub Date:
 August 2014
 DOI:
 10.1103/PhysRevA.90.023847
 arXiv:
 arXiv:1405.0238
 Bibcode:
 2014PhRvA..90b3847W
 Keywords:

 42.25.Bs;
 41.20.Jb;
 42.70.Qs;
 Wave propagation transmission and absorption;
 Electromagnetic wave propagation;
 radiowave propagation;
 Photonic bandgap materials;
 Physics  Optics;
 Mathematical Physics
 EPrint:
 19 pages, 1 figure