  We provide a functional framework and a numerical algorithm to compute the
Bloch variety for Maxwell's equations when the electric permittivity is
frequency dependent. We incorporate the idea of a mixed formulation for
Maxwell's equations to obtain a quadratic eigenvalue for the wave-vector in
terms of the frequency. We reformulate this problem as a larger linear
eigenvalue problem and prove that this results in the need to compute
eigenvalues of a compact operator. Using finite elements, we provide
preliminary numerical examples of the scheme for both frequency independent and
frequency dependent permittivity.
