## 4 SRSI for Temporal Profile Characterization
### Tg-Srsi  
XPW-SRSI is limited by the polarizer and SD-SRSI is limited by the phase-matching or angular chirp of the SD signal. How can these problems be solved? The TG effect is also a frequency-conserved third-order nonlinear process that has been used in ultrashort TG spectroscopy and TG-FROG pulse characterization. The TG process is self-phase-matching and does not require a polarizer. Moreover, the TG signal has no spatial or angular chirp, as shown in Figure 12, in which all the spectra have nearly the same profile, indicating negligible angular dispersion in the generated TG signal. Furthermore, there was no obvious angular dispersion when the crossing angle increased from 2\({}^{\circ}\) to 6\({}^{\circ}\) during the TG process in a 500-um-thick fused silica plate. These properties make TG suitable for use with the SRSI method, and the polarizer and angular chirp limitations of XPW-SRSI and SD-SRSI, respectively, are avoided. The principle of TG-SRSI is shown in Figure 13a. The unknown pulse to be characterized is separated into four beams, one of  
Figure 11: SD spectra measured at three different positions on the beam, C0, C5, and C-5, shown in the inset. C0 is the center of the beam and C5 and C-5 are about 5 mm from C0, with C-5 closer to the incident beams [55]. Figure 12: TG signal spectra at seven different points on the beam, shown in the inset. L: left; R: right; U: up; D: down; the number corresponds to the distance from the center point, e.g., L2U2 is 2 mm left and 2 mm up from the center point [60]. which is energy-attenuated, time-delayed, and then used as the testing beam. It and the other three beams are focused onto a thin transparent plate in a BOXCARS beam geometry and the three beams overlap in time and space. The TG signal is generated in the same direction as the testing beam so the optical setup of this system is alignment-free. A simple experimental setup based on the principle of TG is composed of only a few optical components, as shown in Figure 13b. A black plate (H1) with four equal-sized holes separates the incident beam into four beams. A 500-\(\upmu\)m-thick fused silica plate (P1) is placed in the path of the testing beam to induce a suitable delay between it and the other three beams. The delay can be adjusted by simply rotating P1. A specially designed plane mirror (M1), three-fourths of which is coated with protective silver, is used to attenuate the testing beam. The reflectivity of the uncoated part of M1 is calculated to be about 0.6% for horizontally polarized light and an incident angle of 45\({}^{\circ}\). A silver-coated parabolic mirror (PM) focuses the four beams onto a second 500-\(\upmu\)m-thick fused silica plate (P2) to generate the TG signal. To avoid any distortion by other third-order nonlinear processes, the incident pulse energy is sufficiently low, which makes the efficiency of the TG signal <1%. An iris (H2) selects the combined TG signal and testing beam, which is then focused into a spectrometer (AvaSpec UL3648-USB2, Avantes, Apeldoorn, The Netherlands). A spectral interferogram is obtained when the delay between the TG signal and the testing pulse is ~1000 fs. Thus, the temporal profile of the testing pulse can be obtained in real-time or in a single shot. The original measured spectral interferogram obtained using the TG-SRSI setup is shown in Figure 14a. Figure 14b shows that the flat spectral phase, reconstructed on the basis of the spectral interferogram, overlapped well with the spectral phase obtained by Wizzler. To prove further the reliability of the TG-SRSI technique and setup, precise 500 fs\({}^{2}\) and \(-\)500 fs\({}^{2}\) group delay dispersions (GDDs), induced by a Dazzler ultrafast pulse shaper (FASTLITE), were added directly to the incident pulse. Figure 14c shows the chirped spectral phases of the testing pulse with the \(\pm\)500 fs\({}^{2}\) GDDs added as measured by TG-SRSI and Wizzler, and the calculated spectral phase obtained by adding \(\pm\)500 fs\({}^{2}\) GDD onto the flat phase in Figure 14b.