A high-order corrected description of ultra-short and tightly focused laser pulses, and their electron acceleration in vacuum

Field expressions are derived for ultra-short, tightly focused laser pulses up to the second-order temporal correction and seventh-order spatial correction. To evaluate the importance of these corrections, we simulate these fields and investigate the final energy of the accelerated electrons. We vary the order of the corrected expressions, the pulse duration, and the beam waist. We find that electron capture is still an important and generic phenomenon in ultra-short, tightly focused laser pulses. While small differences in the electron acceleration are obtained for various orders of the corrected field equations relative to the paraxial field equations, there is no qualitative difference in the behavior of the electron. Furthermore, the temporal and spatial corrections are found to be correlated.