Generation of extremely strong accelerating electric field by focusing radially polarized THz pulses with a paraboloid ring

Efficient acceleration of electrically charged particles by focused electromagnetic pulses requires a strong accelerating electric field as well as a sufficiently large interaction region. Single-cycle terahertz pulses are promising candidates for such applications due to their advantageous wavelength and available peak electric field at the MV/cm level. We propose and characterize a focusing optics for a possible electron vacuum accelerator. This consists of a reflaxicon for beam shaping and a ring-like segment of an on-axis parabolic mirror for tight focusing of the radially polarized THz pulse in order to reach a strong accelerating electric field. The electric field distribution in the focal region was determined by the Stratton-Chu vector diffraction method. Semi-analytical and purely analytical formulae were also derived, simplifying the computation procedure. By focusing radially polarized single-cycle terahertz pulses with 3 mJ pulse energy, calculations predict accelerating electric field component in the order of 100 MV/cm, well suitable for particle acceleration.