Homogenization of Dielectric Photonic Quasi Crystals

Abstract : We adapt two-scale convergence to the homogenization of photonic quasi-periodic structures such as Penrose tilings. This convergence relies upon the irrational nature of a parameter characterizing a quasi-crystalline phase through its associated cut-and-projection matrix of permittivity: We generate quasi crystals by considering a periodic structure in an upper-dimensional space. We apply this tool to the homogenization of the vector Maxwell system.
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https://hal.archives-ouvertes.fr/hal-00544537
Contributor : Sébastien Guenneau <>
Submitted on : Wednesday, December 8, 2010 - 1:09:37 PM
Last modification on : Friday, April 19, 2019 - 11:38:34 AM

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Guy Bouchitté, Sébastien Guenneau, Frédéric Zolla. Homogenization of Dielectric Photonic Quasi Crystals. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2010, 8 (5), pp.1862-1881. ⟨10.1137/090770333⟩. ⟨hal-00544537⟩

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