## 4 SRSI for Temporal Profile Characterization
### Tg-Srsi
For TG-SRSI measurements, the TG signal and the test beam are collinearly self-combined and pass through an iris (H2). For TG-FROG and SHG-FROG measurements, only the TG and the SHG signal, respectively, is selected by the iris. The selected signals are focused by a focal lens (L) onto a plane mirror (M4) before entering a spectrometer to acquire the original data. Using the FASI setup with the TG-SRSI, TG-FROG, and SHG-FROG methods, we independently characterized an \(\sim\)40 fs pulse at 800 nm from a Ti/sapphire laser system. In this setup, TG-SRSI is fast, TG-FROG is suitable for complex pulses and a wide spectral range, and SHG-FROG is energy-sensitive. The results obtained by these three methods are shown in Figure 17, where they are compared to prove the reliability of the FASI method. The original spectral interferometry and two-dimensional frequency-time spectrogram obtained using TG-SRSI, SHG-FROG, and TG-FROG are shown in Figure 17a,b,d, respectively. The spectral interferometry data were obtained in single-shot when the delay between the TG signal and the test beam was \(\sim\)1.3 ps. Thus, for many laser systems, our FASI device can run in real-time or single-shot condition when in TG-SRSI mode. The SHG-FROG and TG-FROG data were collected by using the motorized stage to scan for 256 steps at 2 fs per step. Figure 17c shows the reconstructed spectra and spectral phases obtained by the three methods. The reconstructed spectrum of TG-SRSI showed the best fidelity, owing to the analytical calculation. The reconstructed spectral phases of the three methods overlapped each other well. These results clearly prove the ability to combine FROG and SRSI in a single setup by using the TG effect. This combination also promises that the FASI device will be reliable and consistent with the three methods. In addition, this device can be extended to the UV and MIR spectral range because the TG effect is not limited by the phase-matching requirement. Weak femtosecond pulses (sub- to several nanojoules) generated by oscillators or non-collinear optical parametric amplifiers are widely used to explore ultrafast phenomena in biology and chemistry. Accurate and complete temporal characterization of such pulses is vitally important in these applications. SHG-FROG is used in the FASI setup for energy-sensitive pulse characterization because SRSI is based on a third-order nonlinear process, which usually needs pulses at the microjoule level as  
Figure 16: (**a**) Experimental setup for FASI; H1, black plate with four equal-sized holes, as shown in (**b**); MS, mirror set composed of an L-shaped mirror and a movable quarter mirror, as shown in (**c**); M1, plane mirror, which is five-sixths silver coated and can be moved up for SRSI measurement (**d**) or down for FROG measurement (**e**); M2–M4, silver-coated plane mirrors; PM, silver-coated parabolic reflector; P, 500-\(\upmu\)m-thick fused silica plate or 50-\(\upmu\)m-thick BBO crystal; H2, iris; L, lens. The red spots in (**c**–**e**) are the locations of the four incident beams on the mirrors [61]. input. However, for SHG to be efficient in real use requires a phase-matching process, which limits the spectral range. Can SRSI be used to characterize sub-nanojoule femtosecond pulses? The answer is yes, as outlined below. To extend the use of the SRSI method for weak-pulse characterization, we explored the TG-SRSI technique because the TG process is relatively sensitive to higher energy compared to the SD and XPW processes [31], as shown in Table 1. Femtosecond pulses of <100 nJ had been successfully characterized on the basis of a reflective objective design using TG-SRSI [62]. However, that energy level is still far from sub-nanojoule level, so TG-SRSI cannot be used to characterize femtosecond pulses from oscillators. How can the TG-SRSI method be improved to measure a sub-nanojoule femtosecond pulse? In addition, a relatively compact device with a high performance level like that of a sensor would be powerful in the application of TG-SRSI.