## 4 SRSI for Temporal Profile Characterization
### Tg-Srsi
How can we simplify the optical setup to achieve such a device? There are three key points for the successful characterization of sub-nanojoule femtosecond pulses using an optical setup that is smaller than a palm. (1) Use the TG process, with its sensitivity to higher energy levels, to generate the reference pulse. (2) Use a nonlinear medium with relatively higher third-order nonlinearity. (3) Most importantly, use a symmetric focusing and collimation pair of \begin{table}
\begin{tabular}{c c c c} \hline
**Geometry** & **PG (XPW)** & **SD** & **TG** \\ \hline Sensitivity (multi-shot) & \(\sim\)100 nJ & \(\sim\)1000 nJ & \(\sim\)10 nJ \\ Sensitivity (single shot) & \(\sim\)1 uJ & \(\sim\)10 uJ & \(\sim\)0.1 uJ \\ Advantages & Self-phase-matching & Deep UV capability & Background free; Sensitive; \\ Disadvantages & Require polarizers & Non-self-phase-matching & Three beams \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of XPW, SD, and TG processes [31]. Figure 17: (**a**) Measured spectral interferometry obtained using TG-SRSI. (**b**,**d**) Measured SHG-FROG and TG-FROG time-frequency traces, respectively. (**c**) Reconstructed spectra (solid lines) and spectral phases (dash-dotted lines) obtained using TG-SRSI (black lines), SHG-FROG (red lines), and TG-FROG (blue lines), respectively [61]. parabolic mirrors with a tight focal length to make the focal intensity in the nonlinear medium as high as possible. The use of a symmetric pair of parabolic mirrors will simplify the setup and make it easy to align. The enhanced TG-SRSI setup is shown in Figure 18a. The input unknown pulse is reflected by a special coated mirror (M1), of which three-fourths of its front surface has a high reflectivity coating and the remaining area is not coated, as shown in the inset \"a\" of Figure 18a. The input unknown laser beam can be regarded as four beams, \(E_{1}(\omega)\), \(E_{2}(\omega)\), \(E_{3}(\omega)\) and \(E_{4}(\omega)\), which are reflected from areas 1, 2, 3 and 4 of M1, respectively. The first three beams are identical incident beams that generate the TG reference beam, and \(E_{4}(\omega)\), which is dramatically attenuated by the uncoated glass surface, is used as the testing pulse to be calculated. An off-axis parabolic aluminum mirror (PM1), with an effective focal length of only 25.4 mm, focuses the four beams. When \(E_{1}(\omega)\), \(E_{2}(\omega)\), and \(E_{3}(\omega)\) are focused by PM1 into a nonlinear 0.15-mm-thick YAG plate (P2) simultaneously, a TG reference pulse \(E_{\text{ref}}(\omega)\) is generated owing to the TG nonlinear process. Beam \(E_{4}(\omega)\), the input unknown pulse denoted as \(E_{\text{unk}}(\omega)\), is attenuated by the uncoated area of M1 when the incident angle of the p-polarized unknown pulse on M1 is \(\sim\)45\({}^{\circ}\). A 0.5-mm-thick fused silica plate (P1) is inserted in the propagation path of \(E_{\text{unk}}(\omega)\) to introduce a time delay \(\tau\) between \(E_{\text{unk}}(\omega)\) and \(E_{\text{ref}}(\omega)\). P1 can attenuate \(E_{\text{unk}}(\omega)\) to a certain value when its coating film has a different reflective ratio. After P2, another off-axis parabolic aluminum mirror (PM2), with the same 25.4-mm effective focal length as PM1, symmetrically collimates the beam. Beams \(E_{\text{unk}}(\omega)\) and \(E_{\text{ref}}(\omega)\) are automatically in the same direction owing to the BOXCARS beam geometry of the TG process [60; 62]. Both the symmetric parabolic mirrors pair and the BOXCARS geometry make the setup easy to align. \(E_{\text{unk}}(\omega)\) and \(E_{\text{ref}}(\omega)\), with a time delay \(\tau\) between them, are filtered out and guided into a spectrometer by a lens (L) and a high reflectivity mirror (M2). Figure 19 presents the results of measuring 0.48, 0.60, and 0.71 nJ pulses with the enhanced TG-SRSI. The reconstructed spectra and the spectra directly measured by the spectrometer match very well, as seen in Figure 19a.