A Convolution Quadrature Method for Maxwell's Equations in Dispersive Media

We study the systematic numerical approximation of Maxwell's equations in dispersive media. Two discretization strategies are considered, one based on the 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 in principle allows to handle rather general dispersive materials. Using ideas of fast-and-oblivious convolution quadrature, the method can be implemented efficiently.