Journal
OPTICS COMMUNICATIONS
Volume 271, Issue 2, Pages 470-474Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.optcom.2006.10.056
Keywords
Bergman-Milton bounds; Maxwell Garnett estimates; Hashin-Shtrikman bounds; metamaterials
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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. (c) 2006 Elsevier B.V. All rights reserved.
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