# Directly Measuring the Pulse Front Distortion of High-Peak-Power Femtosecond Lasers
## 1 Introduction  
In the past decade, significant advances in extreme high-field laser physics have been realized, benefiting from the rapid development of high-peak-power lasers. As examples, take the acceleration of high-energy particle beams, and high-order harmonic and X-ray generation [1; 2; 3]. A crucial factor for the success of these laser-matter interaction studies is the laser intensity at focus. Focused intensity as high as \(10^{22}\) W/cm\({}^{2}\) has been realized in several multi-hundred terawatt (TW) and petawatt (PW) femtosecond lasers [4; 5; 6; 7], and \(10^{23}\) W/cm\({}^{2}\) will probably be realized in 10 PW-level lasers in the near future [8; 9]. In a typical high-peak-power femtosecond laser system, the lens-based telescopes are generally employed, which generate pulse front distortion (PFD) because of the dispersion effect of large spectral bandwidth [10; 11; 12]. In addition, the beam size of femtosecond lasers is increasing correspondingly along with the rapid development of laser peak power, and meanwhile PFD is increasing with the square of laser beam size. Moreover, PFD can broaden the effective pulse duration at the far field and consequently reduce the laser's focused intensity [13; 14]. Therefore, the PFD in high-peak-power femtosecond lasers should be carefully measured and compensated for [15; 16], in order to guarantee optimum performance. PFD can be avoided by using all-reflective or achromatic telescopes [17; 18]. However, spherical mirrors have remarkable astigmatism; off-axis parabolic mirrors are expensive and difficult to align; and achromatic lenses are limited by size availability. Therefore, most of existing high-peak-power laser systems are still equipped with lens-based telescopes. In order to measure the PFD, some methods based on the Michelson and Mach-Zehnder interferometers were proposed [19; 20; 21; 22; 23]. Nevertheless, the vast majority of them need to introduce or generate an ideal reference pulse without PFD, which willincrease the complexity and difficulty in measurement. Especially for high-peak-power femtosecond lasers, the required large-size optical components in measurement may be also a limitation. In 2016, we proposed a novel measurement scheme for the PFD of large-aperture ultra-short laser pulses, which can work without any difficulty for the desired reference pulses, and meanwhile can decrease the size requirements of the optical components in measurement [24]. However, a perfect axisymmtric quadratic curve assumption of PFD is a prerequisite in this method. Based on the measured results, we can only deduce the assumed quadratic curve of PFD, and the PFD at an arbitrary position of the pulse under investigation cannot be directly measured. Moreover, owning to the thermal lens focusing [25; 26] and the long optical paths of high-peak-power femtosecond laser systems, the output pulses are hard to be strictly collimated, and therefore their PFD values are general not strict quadratic curves. In this work, our previously proposed self-reference cross correlator was improved to measure the PFD values of high-peak-power femtosecond lasers directly, which is induced by the chromatic aberration of lenses. After improvement, the quadratic curve assumption of PFD is not needed in measurement. Moreover, this improved self-reference cross correlator can not only achieve the global PFD, but also directly measure the PFD at any position of the pulse. The disadvantage of this new self-reference cross correlator is that the single-shot measurement of the global PFD is not available, as it is obtained based on a scanning measurement of the PFD at different positions. This new self-reference cross correlator was applied to a 200 TW/27 fs laser [27], and the experimentally measured PFD values are in good agreement with the theoretical curve. In addition, the temporal intensity distribution of this 200 TW laser in the focal region was also theoretically investigated.