Asymptotic behaviour of the spectra of systems of Maxwell equations in periodic composite media with high contrast

Kirill Cherednichenko, Shane Cooper

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)583-605
JournalMathematika
Volume64
Issue number2
Early online date23 Apr 2018
DOIs
Publication statusPublished - 2018

Keywords

  • Electromagnetism, Composites, Maxwell Equations, Spectrum, Homogenisation, Asymptotics

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