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.
- Electromagnetism, Composites, Maxwell Equations, Spectrum, Homogenisation, Asymptotics