# Saturable Absorption Dynamics of Highly Stacked 2D Materials for Ultrafast Pulsed Laser Production
## 4 Topological Insulator SAs
### Highly Stacked Bi\({}_{2}\)Te\({}_{3}\) SAs
The insertion losses of the isolator, coupler, and WDM were measured to be 1.2, 0.8 and 0.5 dB, respectively, at 1950 nm. The period of the laser pulses was measured as 35.8 ns, which corresponds to a repetition rate of 27.9 MHz, being compatible with the fundamental frequency of the ring cavity. A strong signal peak with a peak-to-background ratio of 76 dB was observed at the repetition rate of 27.9 MHz in the electronic spectrum analysis. The optical spectrum measurement showed that the output pulses has a center wavelength of 1935 nm and a 3 dB bandwidth of 5.64 nm (Figure 12). If it is a transform-limited case, the pulse-widthwould be 698 fs. Kelly sidebands were clearly observed in the spectrum [67] in which the first-order Kelly sideband was at a distance 8.2 nm from the center wavelength. Using the experimentally measured total cavity dispersion value of 0.458 ps\({}^{2}\), the position of the first-order Kelly sideband was theoretically calculated as 9.117 nm relative to the center wavelength, assuming the transform-limited case. Figure 12b shows the theoretical plot of a relative Kelly sideband position as a function of the temporal width of transform-limited pulses for various Kelly sideband orders. Small difference between experimental and theoretical values of its relative position indicates that the output pulses are slightly chirped. For a straightforward measurement of temporal width of output pulses, an autocorrelation analysis was performed using a second harmonic generation (SHG)-based autocorrelator. Since the power of the output pulses (average power of 1 mW) was not high enough to induce SHG, an amplification process was taken before autocorrelation analysis. To avoid any temporal and spectral distortion of laser pulses during the amplification process, the amplification gain was carefully adjusted, attaining the average power of 20 mW. Comparing with the original optical spectrum (Figure 12a), the amplified spectrum has almost the same spectral shape  
Figure 11: (**a**) The laser schematic. (**b**) Measured SEM image of the mechanically exfoliated, thick Bi\({}_{2}\)Te\({}_{3}\) layer. (**c**) Bi\({}_{2}\)Te\({}_{3}\) layer depth measurement result using an alpha step profiler. Reprinted with permission from [66]. Figure 12: (**a**) Measured optical spectrum of output pulses. (**b**) Theoretically calculated Kelly sideband position relative to the center wavelength (\(\Delta\lambda\)) as a function of the temporal width of transform-limited pulses for various Kelly sideband orders (m). Reprinted with permission from [66]. (Figure 13a). The autocorrelation trace showed the pulse width of 795 fs and the time bandwidth product of 0.35, confirming slightly chirped output pulses (Figure 13b). It should be noted that TIs have semimetal electronic band structures at the surface, being linearly dispersed across the Fermi energy level, similarly to graphene, while they have sizable band gaps at the interior region. This fact indicates the promising SA potential of TIs for the development of advanced midinfrared laser technologies, as exemplified by Bi\({}_{2}\)Te\({}_{3}\).