Nonlinear focus is an important parameter for the filamentation phenomena since it denotes the beginning of the filamentation stage when the initial power is near or larger than the filamentation threshold P-TH [Opt. Lett. 19, 862 (1994); Phys. Rev. A 78, 033826 (2008)]. We combine the pulse's dispersion length with the Dawes and Marburger's formula and achieve a new formula that can predict the nonlinear focus very well regardless of the dispersion being important or not. We also find that there exists a threshold, P-ML, for the initial peak power with which the nonlinear focus has a maximum length due to the competition between Kerr self-focusing and the dispersion. (C) 2016 Optical Society of America.
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