# Investigation of Spatial Chirp Induced by Misalignments in a Parallel Grating Pair Pulse Stretcher
## 4 Experimental results  
### Spatial Chirp Measurement of the Stretched Pulse  
For pulses with a large diameter, their spatial chirp may not be distinguished easily by the naked eye according to the spot profiles, as shown in Figure 4f,g. The initial diameter of the fs pulses output from our laser source is about 11 mm. After being stretched by the stretcher, we have changed its diameter to be about 5.5 mm with a 1/2 beam shrinker, which is still too large to observe its spatial chirp. Here, we use an imaging spectrometer (Horiba, iHR550) to detect the spatial chirp of the output pulses in real-time. The CCD detector (Horiba, Syncer-1024x256) attached to the imaging spectrometer can achieve the spectrum corresponding to a line of the light spot in the vertical direction. Figure 6a,d  
Figure 5: The flow chart to accurately calibrate the misalignments of the stretcher.  
shows the spatial-spectrum of a stretched pulse with an evident vertical chirp and a pulse with little vertical chirp, respectively, both of which are obtained in one single pulse. According to Figure 6b,c, we can find that, for a pulse with a large vertical chirp, both the spatial profiles corresponding to different wavelengths and the spectrum profiles corresponding to different positions have an obvious shift. However, for a well-adjusted stretcher with little vertical chirp, both the spatial profiles and the spectrum profiles have a good overlap, as shown in Figure 6e,f. Therefore, we can use the above phenomenon to evaluate the vertical chirp of the pulses. In Figure 6c,f, we can find that the spectrum band width for the spatially chirped pulse is narrower than the unchirped pulse. This is reasonable because the spectrum for the spatially chirped pulse disperses in spatial, and only part of the spectrum enters into the slit of the spectrometer. Therefore, a narrower spectrum band width can also be regarded as evidence for the existence of spatial chirp. However, it is not convenient to evaluate the FWHM of spectrums because the spectrum profile in our experiment is not an ideal Gaussian profile. Thus, we prefer to use the spatial profile to analyze the spatial chirp here, which possesses a relative ideal Gaussian profile and is easy to identify its spatial center. To detect the horizontal chirp of a pulse, we just need to move the slit of the imaging spectrometer in the horizontal direction and observe whether there is a shift among their spectrum profiles, which are similar to those shown in Figure 6c,f.  
Although the spatial chirp induced by each misalignment obeys \"linear superposition\", we do not know their individual contribution to the overall effect, thus cannot give an accurate evaluation for each misalignment. Furthermore, misalignments cannot only cause spatial dispersion but also high order temporal dispersion [14; 19]. When the grating pair structure acts as a pulse compressor, one can measure the spatial dispersion and the pulse duration simultaneously to obtain a more precise alignment procedure [22]. For our pulse stretcher, only the second order temporal dispersion (linear temporal chirp) is concerned, and the spatial chirp measurement is sufficient to achieve a satisfied adjustment accuracy.  
Figure 6: The vertical chirp of the stretched pulses measured with an imaging spectrometer. (**a**) The spectrum corresponding to a vertical line of the light spot with a large vertical chirp; (**b**) the spatial profiles corresponding to three different wavelengths in (**a**), in which the centers show an obvious shift in vertical direction; (**c**) the spectrum corresponding to three different positions in (**a**), in which profiles also have an obvious shift; (**d,e**) the spatial-spectrum of an output pulse when the stretcher is well adjusted, which show little shift both in the spatial profiles and spectrum profiles, indicating the pulse has little vertical chirp.