We demonstrate pulse shortening of 1-ps Yb:YAG thin-disk regenerative amplifier to 500 fs by cross-polarized wave generation (XPW) in a 6 mm BaF2 crystal. The process is self-compressed and has 8.5% conversion efficiency corresponding to 18 µJ energy. Our theoretical and experimental investigation shows that the factor of 3 spectral broadening and pulse shortening in ps-XPW-generation only happens in unsaturated regime. We demonstrate that the initial spectral chirp affects the spectral broadening and pulse shortening of XPW pulses.