Bouchitté, GuySchweizer, Ben2008-07-162008-07-162008-07-16Schweizer, Ben; Bouchitté, Guy: Homogenization of Maxwell's Equations in a Split Ring Geometry. - In: Multiscale Model. Simul. Volume 8, Issue 3, pp. 717-750 (2010)1540-3459http://hdl.handle.net/2003/2574310.17877/DE290R-15319We analyze the time harmonic Maxwell’s equations in a complex geometry. The scatterer Omega subset R^3 contains a periodic pattern of small wire structures of high conductivity, the single element has the shape of a split ring. We rigorously derive effective equations for the scatterer and provide formulas for the effective permittivity and permeability. The latter turns out to be frequency dependent and has a negative real part for appropriate parameter values. This magnetic activity is the key feature of a left-handed meta-material.enSociety for Industrial and Applied MathematicsPreprints der Fakultät für Mathematik;2008-16510preprint