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 ele ctromagnetic pulses whose fields are of either transverse magnetic or transverse electric character and are confined to toroidal wave packet s that converge to a focus and then diverge in a manner that is expect ed from familiar rules of diffraction. These ''focused doughnut'' puls es constitute a subset of the ''modified power spectrum'' pulse soluti ons discovered by Ziolkowski [Phys. Rev. A 39, 2005 (1989)]. We derive the total energy, the energy spectrum, tie ability to accelerate an e lectron, and other properties of these focused doughnut pulse solution s.