  We consider a Maxwell system on $\mathbb{R}^3$ with periodic and highly
oscillating coefficients. It is known that the solutions converge in the
weak-$\ast$ topology of $L^\infty(0,T;\,L^2(\mathbb{R}^3))$ to the solution of
a similar problem with constant coefficients given as the $H$-limits of the
electric permittivity and the magnetic permeability respectively, i.e. the
limit in the sense of the homogenization of linear elliptic equations with
varying coefficients. However, it is not true that the elliptic corrector also
provides a corrector for the solution of the Maxwell system, i.e. an
approximation of the solutions in the strong topology of $L^2$. We shall prove
that the oscillations in the space variable also produce oscillations in the
time variable. We get a corrector consisting of adding to the elliptic
corrector the sum of infinitely plane waves in the fast variable. Note that
related results have been previously proved for the wave equation. Our proof is
based on the two-scale convergence theory for almost periodic functions. One of
the novelties is to show how this contains the classical Block decomposition.
