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Limit‐Periodic Dielectric Media

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1 Author(s)
Redheffer, Raymond ; University of California, Low Angeles 24, California

Your organization might have access to this article on the publisher's site. To check, click on this link:http://dx.doi.org/+10.1063/1.1722217 

A stratified dielectric sheet with dielectric constant Є(x), permeability μ(x) and thickness d is uniformly contracted to yield a sheet with parameters Є(nx), μ(nx), d/n. Now n of these contracted panels are stacked up to yield again a sheet of thickness d. What can be said of the limiting medium obtained in this way, as n→∞ ? If the symbol [] denotes ``mean value of,'' the results of this paper may be summarized as follows: At perpendicular polarization, the limiting medium acts like a homogeneous medium with dielectric constant, permeability and thickness given respectively by [Є][μ]-12[1/μ]-12, [μ]12[1/μ]-12, d[μ]12[1/μ]12. At parallel polarization the parameters are, respectively, [Є]12[1/Є]-12, [μ][Є]-12[1/Є]-12, d[Є]12[1/Є]12. The relevance of these results to topics of current interest is indicated. The analysis is not based on the equivalent-circuit analogues which are sometimes used to study artificial dielectrics, but is developed without approximati on from Maxwell's equations.

Published in:

Journal of Applied Physics  (Volume:27 ,  Issue: 10 )