  In this work we discuss the numerical discretization of the time-dependent
Maxwell's equations using a fully explicit leap-frog type discontinuous
Galerkin method. We present a sufficient condition for the stability, for cases
of typical boundary conditions, either perfect electric, perfect magnetic or
first order Silver-M\"uller. The bounds of the stability region point out the
influence of not only the mesh size but also the dependence on the choice of
the numerical flux and the degree of the polynomials used in the construction
of the finite element space, making possible to balance accuracy and
computational efficiency. In the model we consider heterogeneous anisotropic
permittivity tensors which arise naturally in many applications of interest.
Numerical results supporting the analysis are provided.
