The collapse distance of femtosecond pulses in air

The conventional semi-empirical formula for collapse distance [Phys. Rev. 179, 862 (1969), Prog. Quant. Electr. 4, 35 (1975)] has been widely used in many applications. However, it is not applicable when the dispersion length is smaller than or has similar order-of-magnitude as the collapse distance. For the "enough short" pulses, there exists a threshold for the initial peak power, with which the collapse distance has a maximum value due to the competition between the Kerr self-focusing and the group velocity dispersion. New semi-empirical formulas are obtained for the collapse distance of the pulse with the initial power being less or larger than the threshold, and they can match the numerical simulations gracefully.