  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 $(0,T)^d, T>0.$ 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 $\eta$ goes to zero. We show that the limit of the spectrum as
$\eta\to0$ 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.
