The paper analyzes the discontinuous Galerkin approximation of Maxwell's equations written in first-order form and with non-homogeneous magnetic permeability and electric permittivity. Although the Sobolev smoothness index of the solution may be smaller than 1/2 , it is shown that the approximation is spectrally correct. The convergence proof is based on a duality argument. One essential idea is that the smoothness index of the dual solution is always larger than 1/2 irrespective of the regularity of the material properties. Discrete involutions also play a key role in the analysis.