Exact closed-form solutions to Maxwell's equations are used to investigatethe acceleration of electrons in vacuum driven by ultrashort and nonparaxialradially polarized laser pulses. We show that the threshold power above whichsignificant acceleration takes place is greatly reduced by using a tighterfocus. Moreover, electrons accelerated by tightly focused single-cycle laserpulses may reach around 80% of the theoretical energy gain limit, about twicethe value previously reported with few-cycle paraxial pulses. Our resultsdemonstrate that the direct acceleration of electrons in vacuum is well withinreach of the current laser technology.
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