  The modeling and simulation of electromagnetic wave propagation is often
accompanied by a restriction to bounded domains which requires the introduction
of artificial boundaries. The corresponding boundary conditions should be
chosen in order to minimize parasitic reflections. In this paper, we
investigate a new type of transparent boundary condition for a discontinuous
Galerkin Trefftz finite element method. The choice of a particular basis
consisting of polynomial plane waves allows us to split the electromagnetic
field into components with a well specified direction of propagation. The
reflections at the artificial boundaries are then reduced by penalizing
components of the field incoming into the space-time domain of interest. We
formally introduce this concept, discuss its realization within the
discontinuous Galerkin framework, and demonstrate the performance of the
resulting approximations by numerical tests. A comparison with first order
absorbing boundary conditions, that are frequently used in practice, is made.
For a proper choice of basis functions, we observe spectral convergence in our
numerical test and an overall dissipative behavior for which we also give some
theoretical explanation.
