## 4 SRSI for Temporal Profile Characterization
### Tg-Srsi
The figure shows that all three spectral phases coincide. These results prove that TG-SRSI used in our simple setup can accurately characterize femtosecond pulses. Figure 13: (**a**) Principle of TG-SRSI. (**b**) Experimental setup; H1: black plate; P1 and P2: fused silica plates; M1: plane mirror three-fourths silver-coated; PM: parabolic mirror; H2: iris; L: lens; M2: plane mirror [60]. Figure 14d shows the reconstructed temporal profiles of the testing pulse after adding 0, 500, and \(-500\) fs\({}^{2}\) GDDs to the incident pulse. The resulting pulse durations (hereafter referred to as mean FWHM) were 37.5, 42.1 and 42.6 fs, respectively, when the testing-pulse and the TG reference signal had the Fourier-transform-limited (FTL) pulse durations of 36.8 and 27.0 fs, respectively. Moreover, the temporal profile of the 37.5 fs testing pulse had a 50 dB dynamic range. In the TG-SRSI method, the nonlinear medium is an arbitrarily selected transparent plate. In principle, the TG-SRSI method can be used to characterize femtosecond pulses at other wavelengths by replacing the spectrometer with one suitable for the test pulse. To check the potential of the TG-SRSI method and our setup, a sub-10 fs pulse with a center wavelength of approximately 1.8 \(\upmu\)m was tested using the setup shown in Figure 13b, where only the spectrometer was changed (NIR256-2.1, Ocean Optics, Dunedin, FL, USA). Figure 15 shows the results of the characterization experiment. The spectrum of the laser beam, measured directly by the spectrometer, was close in shape to that of the TG-SRSI-reconstructed spectrum, as seen in Figure 15a; the corresponding reconstructed spectral phase is also shown. Placing a 1-mm-thick fused silica plate at the Brewster angle before the setup for dispersion compensation obtained the shortest pulse of 10.6 fs, as shown in Figure 15b on linear and logarithmic scales. Because the spectral range of the NIR256-2.1 spectrometer is limited, a signal longer than 2.1 \(\upmu\)m cannot be measured. It is not clear why the intensity of the longer-wavelength TG signal is always weak. The FTL pulse duration of the TG signal was 6.8 fs, which is much shorter than that of the testing pulse at 9.6 fs, as shown in Figure 15b. To investigate the reliability of the measurement, the 1-mm-thick fused silica plate was removed, inducing \(-55\) fs\({}^{2}\) and 250 fs\({}^{3}\) dispersions at this wavelength to the pulse. Therefore, the pulse was broadened to 15.1 fs because of the uncompensated dispersion. The reconstructed spectral phase coincided with the calculated spectral phase, as seen in  
Figure 14: **(a)** Original measured spectral interferogram obtained using the TG-SRSI method. **(b)** Measured spectra of the TG signal (green dash-dotted line) and the testing pulse (red dash-dot-dotted line), the reconstructed spectrum of the testing pulse (solid black line), and the spectral phase obtained by TG-SRSI (gray dotted line) and Wizzler (blue dashed line). **(c)** Spectral phase obtained by TG-SRSI (solid lines), Wizzler (dotted lines), and calculation (dash-dotted line) when GDDs of 500 fs\({}^{2}\) (up and red line) and \(-500\) fs\({}^{2}\) (down and blue line) were introduced into the testing pulse. **(d)** Reconstructed temporal profile of the testing pulse after adding 0 fs\({}^{2}\) (thick and thin black solid lines), 500 fs\({}^{2}\) (magenta dash-dotted line), and \(-500\) fs\({}^{2}\) (blue dotted line), and the FTL temporal profiles of the testing pulse (red dotted line) and the TG signal (black dash-dot-dotted line). Figure 15a. This result clearly proves that the TG-SRSI method is capable of working and yielding reliable results in the mid-IR spectral region. Although SRSI works well in characterizing femtosecond pulses, its one drawback is the requirement that a broadened reference spectrum be generated by the third-order nonlinear process, which may result in the generation of a reference pulse with a narrower spectrum than that of the testing pulse.