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

Cherednichenko, Kirill; Cooper, Shane

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 where 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 “homogenized” 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 polarized waves.

Citation

Cherednichenko, K., & Cooper, S. (2018). Asymptotic behaviour of the spectra of systems of Maxwell equations in periodic composite media with high contrast. Mathematika, 64(2), 583-605. https://doi.org/10.1112/s0025579318000062

• Journal Article Type: Article
• Acceptance Date: Dec 16, 2017
• Online Publication Date: Apr 23, 2018
• Publication Date: Apr 23, 2018
• Deposit Date: Dec 17, 2017
• Publicly Available Date: Dec 18, 2017
• Journal: Mathematika
• Print ISSN: 0025-5793
• Electronic ISSN: 2041-7942
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 64
• Issue: 2
• Pages: 583-605
• DOI: https://doi.org/10.1112/s0025579318000062