Propagation properties of ultrashort pulsed Bessel-Gauss beams in free space

Using a complex analytical signal representation, the free-space propagation properties of ultrashort pulsed Bessel-Gauss beams whose waist width is independent of frequency are studied. It is found that within the diffraction-free range the transversal intensity distribution of ultrashort pulsed Bessel-Gauss beams remains nearly unchanged, and the on-axis temporal pulse forms broaden along the propagation. Beyond this range, there is a remarkable spreading of the transversal intensity. With the increase of the propagation distance, the on-axis blue shift increases firstly, then gradually decreases after reaching its maximum, and finally approaches an asymptotic value. For example, for a single-cycle ultrashort pulsed Bessel-Gauss beam, the on-axis blue shift increases and reaches a maximu