Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Effective parameters of metamaterials: a rigorous homogenization theory via Whitney interpolation

Not Accessible

Your library or personal account may give you access

Abstract

A rigorous homogenization theory of metamaterials—artificial periodic structures judiciously designed to control the propagation of electromagnetic (EM) waves—is developed. The theory is an amalgamation of two concepts: Smith and Pendry’s physical insight into field averaging and the mathematical framework of Whitney-like interpolation. All coarse-grained fields are unambiguously defined and satisfy Maxwell’s equations exactly. Fields with tangential and normal continuity across boundaries are associated with two different kinds of interpolation, which reveals the physical and mathematical origin of “artificial magnetism.” The new approach is illustrated with several examples and agrees well with the established results (e.g., the Maxwell–Garnett formula and the zero cell-size limit) within the range of applicability of the latter. The sources of approximation error and the respective suitable error indicators are clearly identified, along with systematic routes for improving the accuracy further. The proposed methodology should be applicable in areas beyond metamaterials and EM waves (e.g., in acoustics and elasticity).

© 2011 Optical Society of America

Full Article  |  PDF Article
More Like This
Nonlocal homogenization of metamaterials by dual interpolation of fields

Igor Tsukerman
J. Opt. Soc. Am. B 28(12) 2956-2965 (2011)

Homogenization of nonlocal wire metamaterial via a renormalization approach

A. I. Căbuz, A. Nicolet, F. Zolla, D. Felbacq, and G. Bouchitté
J. Opt. Soc. Am. B 28(5) 1275-1282 (2011)

Homogenization of metamaterials by field averaging (invited paper)

David R. Smith and John B. Pendry
J. Opt. Soc. Am. B 23(3) 391-403 (2006)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (9)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (25)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved