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Nonlinear compression has become an obligatory technique along with the development of ultrafast lasers in generating ultrashort pulses with narrow pulse widths and high peak power. In particular, techniques of nonlinear compression have experienced a rapid progress as ytterbium (Yb)-doped lasers with pulse widths in the range from hundreds of femtoseconds to a few picoseconds have become mainstream laser tools for both scientific and industrial applications. Here, we report a simple and stable nonlinear pulse compression technique with high efficiency through cascaded filamentation in air followed by dispersion compensation. Pulses at a center wavelength of 1040 nm with millijoule pulse energy and 160 fs pulse width from a high-power Yb:CaAlGdO4 regenerative amplifier are compressed to 32 fs, with only 2.4% loss from the filamentation process. The compressed pulse has a stable output power with a root-mean-square variation of 0.2% over 1 hour.
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