On the Bergman-Milton bounds for the homogenization of dielectric composite materials

Andrew J. Duncan, Tom G. Mackay, Akhlesh Lakhtakia

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


The Bergman-Milton bounds provide limits on the effective permittivity of a composite material comprising two isotropic dielectric materials. These provide tight bounds for composites arising from many conventional materials. We reconsider the Bergman-Milton bounds in light of the recent emergence of metamaterials, in which unconventional parameter regimes for relative permittivities are encountered. Specifically, it is demonstrated that: (a) for nondissipative materials the bounds may be unlimited if the constituent materials have relative permittivities of opposite signs; (b) for weakly dissipative materials characterized by relative permittivities with real parts of opposite signs, the bounds may be exceedingly large.

Original languageEnglish (US)
Pages (from-to)470-474
Number of pages5
JournalOptics Communications
Issue number2
StatePublished - Mar 15 2007

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Physical and Theoretical Chemistry
  • Electrical and Electronic Engineering


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