Ultra-short and ultra-intense laser is one of the hottest research spot of laser technology and strong field physics, due to its challenging and the frontier application research. As the key specification of ultrafast ultrahigh intensity laser pulse, the contrast ratio is very influential on the effect of laser-matter interaction. To perform the laser-matter interaction experiments at a high power level, the contrast is required to be as high as 1010 to prevent preplasma dynamics. To solve these problems, one has proposed many methods to improve the contrast of ultrafast laser, such as using the saturable absorbers, double chirped pulse amplification, plasma mirrors and the cross-polarized wave (XPW) generation. The XPW technology can not only enhance the contrast of the pulse by 3-4 orders of magnitude without introducing any space dispersion, but also extend the output spectrum to support shorter pulse duration. The XPW is a nonlinear filter technique in third-order nonlinear crystal with anisotropic susceptibility. Because of its simple and all-solid-state structure, the XPW technique has become one of the most effective methods to enhance the temporal pulse contrast and deliver shorter pulse duration in the field of high peak-power ultrafast lasers. This method has been used in many large laser facilities under construction or upgrades, such as the Apollon and ELI, the contrast ratio as high as 1010 has been achieved. It is known that the conversion efficiency and spectral characteristics of XPW have a strong dependence on the spatial and temporal magnitudes of the input driving pulse. In our experiment, it is found that the various changes of the driven pulse properties have different influences on the characteristics of XPW pulses. The relationship between the linear dispersion of driven pulse and temporal property of XPW is investigated theoretically. In addition, an experiment on verifying the theory is conducted by taking advantage of a programmable acousto-optic dispersion filter. The experimental results fit well to the theoretical results while some new phenomena emerge when the intensity in the BaF2 crystal reaches a saturation threshold. The spectral broadening capability of XPW becomes stronger and exceeds a theoretical upper limit. The pulse width can also be compressed to shorter than the theoretical limit. It is found that there are significant differences in spectral shape and conversion efficiency between the XPW signals by applying the opposite linear chirps to the driving pulse. A further analysis and theoretical explanation of these new phenomena are also presented.