  Exact closed-form solutions to Maxwell's equations are used to investigate
the acceleration of electrons in vacuum driven by ultrashort and nonparaxial
radially polarized laser pulses. We show that the threshold power above which
significant acceleration takes place is greatly reduced by using a tighter
focus. Moreover, electrons accelerated by tightly focused single-cycle laser
pulses may reach around 80% of the theoretical energy gain limit, about twice
the value previously reported with few-cycle paraxial pulses. Our results
demonstrate that the direct acceleration of electrons in vacuum is well within
reach of the current laser technology.
