Focused one-cycle electromagnetic pulses

We describe several families of exact unbounded solutions of Maxwell's equations in vacuum. These solutions depict one- (or 11/2-) cycle electromagnetic pulses whose fields are of either transverse magnetic or transverse electric character and are confined to toroidal wave packets that converge to a focus and then diverge in a manner that is expected from familiar rules of diffraction. These ''focused doughnut'' pulses constitute a subset of the ''modified power spectrum'' pulse solutions discovered by Ziolkowski [Phys. Rev. A 39, 2005 (1989)]. We derive the total energy, the energy spectrum, tie ability to accelerate an electron, and other properties of these focused doughnut pulse solutions.