Spatiotemporal evolution of focused single-cycle electromagnetic pulses

We analyze exact solutions of Maxwell's equations that are capable of descr ibing focused single-cycle electromagnetic pulses. These finite energy solu tions are a subset of Ziollcowski's ''modified power spectrum'' pulse solut ions [Phys. Rev A 39, 2005 (1989)]. They display substantial temporal resha ping, time reversal, and polarity reversals as they pass through the focus. The temporal profiles at the focus and in the far field are related by a H ilbert transform in time. These results are explained in terms of the Gouy phase shift of focused beams. We also show that these pulse solutions are n atural spatiotemporal modes of an open resonator and propose methods for th eir practical realization.