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

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

doi:10.1016/j.optcom.2006.10.056

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

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

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Abstract

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.

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Andrew J. Duncan, Tom G. Mackay, Akhlesh Lakhtakia. 2005-12-01. On the Bergman-Milton bounds for the homogenization of dielectric composite materials. https://doi.org/10.1016/j.optcom.2006.10.056

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