Spatio-temporal modification of femtosecond focal spot under tight focusing condition

The focusing property of a focal spot of a femtosecond laser pulse is presented under tight focusing conditions (below f-number of 1). The spatial and temporal intensity distributions of a focused electric field are calculated by vector diffraction integrals and coherent superposition method. The validity of the calculation method is examined by comparing the intensity distribution obtained under a high f-number condition to that obtained with the fast Fourier transform method that assumes the scalar paraxial approximation. The spatial and temporal modifications under tight focusing conditions are described for a focused femtosecond laser pulse. The calculation results show that a peak intensity of about 2.5×10²⁴ W/cm² can be achievable by tightly focusing a 12-fs, 10 PW laser pulse with a f/0.5 parabolic optic. The precise information on intensity distributions of a femtosecond focal spot obtained under a tight focusing condition will be crucial in assessing a focused intensity and in describing the motion of charged particles under an extremely strong electric field in ultra-relativistic and/or relativistic laser matter-interaction studies.