  We study the systematic numerical approximation of Maxwell's equations in
dispersive media. Two discretization strategies are considered, one based on a
traditional leapfrog time integration method and the other based on convolution
quadrature. The two schemes are proven to be equivalent and to preserve the
underlying energy-dissipation structure of the problem. The second approach,
however, is independent of the number of internal states and allows to handle
rather general dispersive materials. Using ideas of fast-and-oblivious
convolution quadrature, the method can be implemented efficiently.
