New electromagnetic directed energy pulse train (EDEPT) solutions of Maxwell's equations have been obtained. One particular solution, the modified power spectrum (MPS) pulse, will be described in detail. This pulse can be tailored to give directed energy transfer in space in such a manner that theoretically it beats the diffraction limit. These EDEPT solutions are not physically pathological and can be reconstructed from causal Green's functions. They represent fields that recover their initial amplitudes along the direction of propagation out to extremely large distances from their initial location. Moreover, these fields appear to be launchable from finite aperture antennas.