While the key parameters of the most practically significant scenarios of laser-induced filamentation are known to obey, to a reasonable approximation, a set of physically transparent scaling laws in their behavior as functions of laser pulse widths, propagation paths, and beam-focusing geometries 30 , 31 , 32 , any scaling with respect to the ratio P / P cr of the laser peak power, P , to the critical power of self-focusing, P cr , is inherently limited as this ratio controls the number of filaments that a high- P laser beam breaks up into and defines the limits of the single-filamentation regime 30 , 31 , 32 , 33 .
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