Non-paraxial effect of ultrashort pulsed Bessel beams on their propagation

The propagation of ultrashort pulsed Bessel beams in free space within and beyond the paraxial approximation is studied. It is shown that the nonparaxial effect does not affect their spatial pulse profile, which retains the Bessel shape unchanged upon propagation, whereas it affects their temporal pulse form if the spatial parameter becomes relatively large. The condition, under which the paraxial approximation is valid, is found to be ＜ min/2c, where min denotes the minimum frequency of the pulse spectrum and cis the velocity of light.