Group velocity in lossy periodic structured media

P. Y. Chen, R. C. McPhedran, C. M. de Sterke, C. G. Poulton, A. A. Asatryan, L. C. Botten, M. J. Steel

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


In lossless periodic media, the concept of group velocity is fundamental to the study of propagation dynamics. When spatially averaged, the group velocity is numerically equivalent to energy velocity, defined as the ratio of energy flux to energy density of modal fields. However, in lossy media, energy velocity diverges from group velocity. Here, we define a modal field velocity which remains equal to the complex modal group velocity in homogeneous and periodicmedia. The definition extends to the more general situation of modal fields that exhibit spatial or temporal decay due to lossy elements or Bragg reflection effects. Our simple expression relies on a generalization of the concepts of energy flux and density. Numerical examples, such as a two-dimensional square array of silver rods in vacuum, are provided to confirm the result. Examples demonstrate how the dispersion relation of the periodic structure, the properties of its modes, and their group velocities change markedly in lossy media.

Original languageEnglish
Article number053825
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number5
StatePublished - 6 Dec 2010
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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