Two inovative techniques for the simulation of the effect of a lossy dielectric half-space are derived and analysed. The first is an adapted impedance surface condition imposed at the interface to replace the dielectric medium. This condition, when coupled with Maxwell's equations yields a stable system which can be written in a variational form. It allows us to take into acccount both the polarization and the angle of incidence of the out-going waves. The second technique is a generalization of the Bérenger perfectly matched layers: the dielectric is now replaced by a short length layer in which the waves are governed by a modification of Maxwell's equations. For this model, the two reflection coefficients are the same as for the true dielectric while the damping inside the layer is enforced.