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

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

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32 Citations (Scopus)


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 ranges 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 languageUndefined/Unknown
Pages (from-to)470-474
Number of pages5
JournalOptics Communications
Early online date15 Nov 2006
Publication statusE-pub ahead of print - 15 Nov 2006


  • physics
  • optics

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