## 4 SRSI for Temporal Profile Characterization
### _Sd-Srsi_  
Although XPW is used in the SRSI method with success, the polarizer limits the spectral range and usually induces dispersion of the incident pulse. This limitation is the same as that which occurs when the XPW effect is used in pulse cleaning, where the polarizer limits the improvement of the temporal contrast because of its extinction ratio. Recently, a reflective polarizer was used in the XPW-SRSI method to solve this problem [31]. In 2010, we used the SD process, which does not require a polarizer, to obtain greater improvement in the temporal contrast [51]. As with pulse cleaning, the limitation caused by a polarizer can be eliminated if the SD effect is used in the SRSI method, because a polarizer is not used. The SD process is a non-collinear four-wave-mixing parametric process and not a self-phase-matched process. A relatively thin nonlinear medium should be chosen to satisfy the broadband phase-matching of the SD process. The two-dimensional phase-matching patterns of SD processes at 800 nm in a 0.1-mm-thick fused silica glass plate and at 400 nm in a 0.1-mm-thick CaF\({}_{2}\) plate are shown in Figure 7a,b, respectively. The phase-matched spectral range is wider than nearly one octave at 800 nm, which can support the characterization of sub-5 fs laser pulses. Experiments were performed to show the principle with the center wavelength of the pulse at 800 and 400 nm. In the experimental setups shown in Figure 8, beamsplitter BS2 is used to separate a test pulse. The generated SD reference pulse is collinearly combined with the test pulse by another beamsplitter. Figures 9 and 10 show the results obtained using the setups displayed in Figure 8 at 800 and 400 nm, respectively. Figure 9a,b show the original data obtained in the experiment using SD-SRSI and SD-FROG, respectively, for a pulse at 800 nm. Figure 9c shows the resulting spectra and spectral phases  
Figure 6: Typical results obtained by Wizzler. (**a**) Spectrum interferogram. (**b**) Reconstructed spectrum (black line) and spectral phase (red line). Figure 7: Two-dimensional phase-mismatch pattern plotted against the crossing angle and the probe wavelength when the pump wavelength was fixed at (**a**) 800 nm in a 0.1-mm-thick fused silica glass plate or (**b**) 400 nm in a 0.1-mm-thick CaF\({}_{2}\) plate. The black solid line corresponds to zero phase mismatch [43]. of the test pulse obtained by SD-SRSI and SD-FROG, where the reconstructed spectrum obtained by SD-SRSI agrees well with the spectrum measured directly by the spectrometer; even the fine spectral modulation overlaps. Figure 9d shows that the reconstructed pulse profiles for both methods closely overlap, with a pulse duration of \(\sim\)55 fs for both closed temporal profiles. Figure 8: Experimental setup for SD-SRSI used to characterize a pulse at (**a**) 800 nm [VND, variable neutral density filter; BS1, BS2, and BS3, 50:50 1-mm-thick beamsplitters; SM1: spherical mirror with a radius of curvature \(R=-700\) mm; FS: 0.1-mm-thick fused silica glass plate; ND: neutral density filter; SM2: spherical mirror with a radius of curvature \(R=-1000\) mm; EPP-2000-HR: high-resolution spectrometer (\(\sim\)0.15 nm resolution around 800 nm)] and at (**b**) 400 nm [BS1, BS2, and BS3, 50:50 0.5-mm-thick beamsplitters; SM: spherical mirror with a radius of curvature \(R=-300\) mm; CaF\({}_{2}\): 0.1-mm-thick CaF\({}_{2}\) plate; USB 4000: spectrometer (\(\sim\)1.5 nm resolution at 400 nm)] [43]. Figure 9: (**a**) Spectra of the incident pulse (red dotted line), the SD1 signal (blue line), and the interference between them (black line) measured by a high-resolution spectrometer. (**b**) Two-dimensional SD-FROG trace of the incident pulse. (**c**) Reconstructed spectrum (blue solid line) and spectral phase (blue dash-dotted line) obtained by SD-SRSI and reconstructed spectrum (black solid line) and spectral phase (black dash-dotted line) obtained by SD-FROG. The red dotted line is the spectrum of the incident pulse measured by the spectrometer.