Abstract
There have been numerous observations of seif-trapping of ultrashort laser pulses in filaments.1-3 The observation of non- linear optical phenomena associated with the filamentation, such as pulse spectral distortion and conical emission,3 suggest that the pulse has maintained its longitudinal localization and has collapsed transversely. The nonlinear effects cannot be solely explained by a "moving focus": the energy density is the same in the pancake-shaped volume of the original pulse (a few cm diameter, 30 μ height) than uniformly distributed (as it would be in a moving focus) in a 100-μm, 30-m-long filament. It should be noted that (by causality) the leading edge of the femtosecond pulse can only contribute to a moving focus, since the focus is moving toward the source. The diameter of the self-guided channel should result from a balance between self-focusing as a result of the third-order susceptibility of air (n2 = 3 × 10−19 cm2/W) and the self-defocus- ing as a result of free carrier produced by field ionization of air. With the highest intensity on axis, the laser pulse creates its own "hollow waveguide," with the internal light being guided by the higher index on the wall. The theory of the hollow waveguide4 applied to this problem shows that, for the lowest order mode, the loss factor corresponds to an attenuation length of only 10-20 cm, in contradiction with experimental observations of filaments over tens of meters.
© 1996 Optical Society of America
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