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Abstract
We analyse the behaviour of the spectrum of the system of Maxwell equations of electromagnetism, with rapidly oscillating periodic coeﬃcients, subject to periodic boundary conditions on a “macroscopic” domain (0,T)3,T > 0. We consider the case when the contrast between the values of the coeﬃcients in diﬀerent parts of their periodicity cell increases as the period of oscillations η goes to zero. We show that the limit of the spectrum as η → 0 contains the spectrum of a “homogenised” system of equations that is solved by the limits of sequences of eigenfunctions of the original problem. We investigate the behaviour of this system and demonstrate phenomena not present in the scalar theory for polarised waves.
Original language  English 

Pages (fromto)  583605 
Journal  Mathematika 
Volume  64 
Issue number  2 
Early online date  23 Apr 2018 
DOIs  
Publication status  Published  2018 
Keywords
 Electromagnetism, Composites, Maxwell Equations, Spectrum, Homogenisation, Asymptotics
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Dive into the research topics of 'Asymptotic behaviour of the spectra of systems of Maxwell equations in periodic composite media with high contrast'. Together they form a unique fingerprint.Projects
 2 Finished

Fellowship for Shane Cooper  Intradisciplinary Mathematics
Cooper, S.
Engineering and Physical Sciences Research Council
1/04/15 → 30/06/17
Project: Research council

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council