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Percolation effects in the checkerboard Babinet series of metamaterial structures
Author(s) -
Kempa K.
Publication year - 2010
Publication title -
physica status solidi (rrl) – rapid research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 68
eISSN - 1862-6270
pISSN - 1862-6254
DOI - 10.1002/pssr.201004266
Subject(s) - checkerboard , percolation (cognitive psychology) , series (stratigraphy) , metamaterial , percolation threshold , physics , optics , mathematics , geometry , quantum mechanics , geology , paleontology , neuroscience , electrical resistivity and conductivity , biology
The proposed checkerboard Babinet series consists of pairs of Babinet complementary metamaterial structures, with the checkerboard pattern being the self‐complementary structure. In this work, formulas are derived for the effective dielectric function and transmittance of all structures in the series, and it is shown that the evolution of the structures from holes to islands is a topological analog of the percolation problem, and that the highly singular checkerboard pattern represents the percolation threshold. The results are in agreement with the percolation theory of Bergman and Imry. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)