# Investigation of Spatial Chirp Induced by Misalignments in a Parallel Grating Pair Pulse Stretcher
## 3 Spatial Chirp Induced by the Misalignments and its Adjustment
### Spatial Chirp Analysis with the Ray Tracing Simulation Method
Then, the values of the rest two misalignments \(\varphi_{\rm h}\) and \(\varphi_{\rm v}\) are set intentionally to achieve the opposite off-axis deviations, so that their effects can counteract the effects due to the other three misalignments and the overall off-axis deviation becomes zero. This simulation configuration is rational because making the input pulses and the output pulses coaxial are the basic steps in the practical adjustment of the stretcher. Figure 4 schematically shows the spatial chirp induced by different misalignments, in which the simulation parameters are identical to those in Table 1. It can be observed that when the off-axis deviation is zero, their line dispersions still exist, resulting in an evident spatial chirp of the output pulses. Figure 4d,e shows the spot profiles of a stretched Gaussian pulse with a diameter of 2 mm when the view screens are 0.5 and 3.0 m away from the first grating G1, respectively. Since the spatial chirp is mainly from the angular dispersion, which cannot be directly observed, we used a view screen in the far field (3.0 m) to observe the line dispersion of the stretched pulses, which is clearer compared to the screen in the near field (0.5 m), as shown in Figure 4d,e. The spatial chirp can lead to an elliptical profile of the pulse spot, in which the direction can be used to distinguish the spatial chirp type. However, for the pulses with a relatively large \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Misalignments**} & \multicolumn{2}{c}{**Off-Axis Deviation (mm) of \(\lambda_{2}\)**} & \multicolumn{2}{c}{**Line Dispersion (mm) Between**} \\ \cline{3-6}  & & **(800 nm)** & & \(\lambda_{1}\) **(775 nm) and \(\lambda_{3}\) (825 nm)** \\ \cline{3-6}  & & **Horizontal Direction** & **Vertical Direction** & **Horizontal Direction** & **Vertical Direction** \\ \hline \multirow{3}{*}{Grating} & \(\theta_{\rm h}=-0.2^{\circ}\) & 64.07 & 0 & \(-0.57\) & 0 \\  & \(\theta_{\rm v}=-0.1^{\circ}\) & 0 & 27.55 & 0 & 0 \\  & \(\theta_{\rm r}=0.1^{\circ}\) & 0 & \(-15.20\) & 0 & 1.17 \\ \hline \multirow{3}{*}{Mirror} & \(\varphi_{\rm h}=-0.424^{\circ}\) & \(-64.28\) & 0 & 1.56 & 0 \\  & \(\varphi_{\rm v}=-0.078^{\circ}\) & 0 & \(-12.34\) & 0 & 0.18 \\ \hline \multicolumn{6}{c}{The five misalignments exist simultaneously} & \(-0.05\) & \(-0.02\) & 0.94 & 1.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The spatial characteristics of the stretched pulses caused by the misalignments when the view screen is 3.0 m away from the first grating G1 of the stretcher. Figure 3: The line dispersion between \(\lambda_{1}\) (775 nm) and \(\lambda_{3}\) (825 nm) induced by each individual misalignment. **(a,b)** The horizontal tilt error and the vertical tilt error of M; (c,e) the horizontal tilt error, the vertical tilt error, and the rotation error of G2. H-Disp: the line dispersion in the horizontal direction; V-Disp: the line dispersion in the vertical dispersion. diameter, the spatial chirp cannot be distinguished easily by the naked eye, as shown in Figure 4f,g, which is the same as Figure 4d,e, except the pulse diameter is 5 mm.