We present the simulations and experimental results on white light generation in the filamentation of high-power femtosecond laser pulse in atmospheric air. We have shown that the strong spatio-temporal localization of the light field in the filament, which provides supercontinuum generation, is sustained due to the dynamic transformation of the field on the whole transverse scale of the beam, including its periphery. Because of the correct consideration of the low-intensity large-scale background of the radiation and high-intensity small-scale filament we obtained the quantitative agreement between the simulated and experimentally obtained conical emission angles of a 250 fs 800 nm 10 mJ pulse. It has been found that the sources of the supercontinuum blue wing are in the rings surrounding the filament as well as at the back of the pulse, where the shock wave formation enhanced by self-steepening takes place. We demonstrated that the conversion efficiency of initially narrow laser pulse spectrum into the supercontinuum depends on the length of filament with high intensity gradients and can be increased by introducing initial chirp into the pulse.
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