Effective Maxwell's equations in general periodic microstructures. Issue 13 (3rd October 2018)

• Record Type: Journal Article
• Authors: Schweizer, B.; Urban, M.
• Is Part Of: Applicable analysis. Volume 97:Issue 13(2018)
• Page Start: 2210
• Page End: 2230
• Publication Date: 2018-10-03
• Subjects: Maxwell's equations -- homogenisation -- diffraction -- periodic structure -- meta-material; 35Q61 -- 35B27 -- 78M40 -- 78A45; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1359563
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We study the time harmonic Maxwell equations in a meta-material consisting of perfect conductors and void space. The meta-material is assumed to be periodic with period ; we study the behaviour of solutions in the limit and derive an effective system. In geometries with a non-trivial topology, the limit system implies that certain components of the effective fields vanish. We identify the corresponding effective system and can predict, from topological properties of the meta-material, whether or not it permits the propagation of waves.