Acceleration of electrons by tightly focused azimuthally polarized ultrashort pulses in a vacuum

Using the complex sink-source model (CSSM) and the Hertz potential method (HPM), the electromagnetic field expressions of tightly focused ultrashort azimuthally polarized pulses can be obtained. By numerically solving the relativistic Newton-Lorentz equation, the acceleration and confinement of electrons by the sub-cycle and few-cycle azimuthally polarized ultrashort pulses in vacuum are studied. Considering the radiation reaction force, it is found that electrons with an initial kinetic energy of less than 1MeV can be accelerated to hundreds of MeV and can be confined in the range of less than 1 micron for hundreds of femtoseconds in the direction perpendicular to the pulse propagation (transverse direction) by the pulses. With the increase of the beam waist and the intensity of the pulse, the electrons can obtain the exit kinetic energy exceeding 1GeV. When electrons are accelerated by the few-cycle pulses, the confined time of the electrons in the transverse direction is three times longer than that of the sub-cycle pulse. When the initial velocity of the electron points to a point in front of the focus, the electron can obtain the maximum exit kinetic energy. The change of the angular frequency corresponding to the spectral peak of the electromagnetic radiation from the electron acceleration with the electric field amplitude parameter E₀ of the pulse is studied. The phenomena of redshift and blueshift of the spectrum peak frequency of the electron radiation with the E₀ are found. These studies provide the methods to confine the movement of electrons in certain directions and accelerate electrons in the same time.