## 4 SRSI for Temporal Profile Characterization
### Tg-Srsi
This typically occurs when the femtosecond pulses (especially pulses with few cycles) to be characterized have a large chirp [35; 37]. Because of the two requirements of SRSI, it will not work correctly under these conditions. The SRSI method will work well only for femtosecond pulses with small chirp, which will provide a broadened spectrum of the generated reference signal. Thus, all independent methods for femtosecond pulse characterization have their own advantages and disadvantages when their properties are compared. The application of each method and its corresponding setup has a limited spectral or temporal range. The disadvantages and the advantages of FROG and SRSI are complementary. FROG is energy-sensitive and capable of characterizing pulses with large chirp, even complex pulses, while SRSI is a fast method with a simple setup. Furthermore, SD and TG processes can be used with both methods. Therefore, if the two methods are combined using the SD or the TG process, a method with the most advantages and a wider application range is obtained. We call this method FASI (Frequency-resolved optical gating And Self-referenced spectral Interferometry) [61]. The experimental setup used to prove the capability of the FASI method in practical use is shown in Figure 16a. A variable neutral density filter is used to continuously change the incident pulse energy before entering the setup. A black plate (H1) with four equal-sized holes is used to separate the incident beam into four 2.5-mm-diameter beams. The four holes are arranged in a rectangle and form BOXCARS geometry. The four beams are introduced into a mirror set (MS) comprising an L-shaped mirror and a separate square mirror, which fits into the L-shaped mirror, as shown in Figure 16c. The square mirror, connected to a motorized stage (M-122, PI), introduces scanned or fixed delay for FROG or SRSI, respectively. The mirror set reflects the four beams to a specially designed mirror (M1), of which five-sixths of its area is silver-coated and one-sixth of the left part is not coated, as shown in Figure 16d,e. M1 is fixed on a manual stage that can be moved vertically. For TG-FROG measurements, M1 is moved down and all four beams are reflected by silver-coated part of the mirror, as shown in Figure 16e. For SHG-FROG or TG-FROG measurements, only two or three beams, respectively, are  
Figure 15: (**a**) Measured spectra of the TG signal (blue dash-dotted line), the testing pulse (black solid line), and the reconstructed spectrum of the testing pulse (red dotted line); reconstructed spectral phase obtained by TG-SRSI with (black dashed line) and without (magenta dash-dot-dotted line) the 1-mm-thick fused silica plate located at the Brewster angle; and calculated spectral phase without the glass plate (cyan dashed line). (**b**) Reconstructed temporal profile of the testing pulse with (black and gray solid lines) and without (magenta dash-dot-dotted line) the 1-mm thick glass plate, where the pulses were 10.6 and 15.1 fs, respectively; FTL temporal profile of the testing pulse (blue dashed line) and the TG signal (red dotted line), where the testing pulses were 9.6 and 6.8 fs, respectively [60]. needed. For TG-SRSI measurements, M1 is moved up, and the beam reflected by the quarter mirror (Figure 16c) is reflected again by the uncoated part of M1 (Figure 16d). M1 reflects all the beams onto M2 at a reflective angle of ~50\({}^{\circ}\). Using the Fresnel equation, the reflectivity of the uncoated part of M1 is calculated to be <0.3% for horizontally polarized light. Thus, the testing-pulse energy will be reduced to result in perfect spectral interference. M2 reflects the beams onto a silver-coated parabolic reflector (PM), with a focal length of 150 mm, which focuses all the beams onto a 500-\(\upmu\)m-thick fused silica plate (P) to generate the TG signal. For SHG-FROG measurements, the upper two beams on M1 are blocked and the glass plate is replaced by a 50-\(\upmu\)m-thick beta barium borate (BBO) crystal.