# High-Quality, InN-Based, Saturable Absorbers for Ultrafast Laser Development
## 3 Pulsed Laser Operation
In order to better understand the saturable absorber properties of the proposed InN materials, those properties have been compared to the best performance in our previous work (sample S0\({}^{\prime}\)) [29]. Inserting sample S1, an ultrafast, mode-locking generation was obtained for an intracavity pump power higher than 35 mW. The maximum output power of the laser cavity (minimum attenuation) was 31.6 mW, which corresponded to a peak power and pulse energy of 25.5 kW and 5.6 nJ, respectively, at an intracavity pump power of 73.7 mW. Figure 4a,b shows the autocorrelation trace and the optical spectrum, which yields a pulse duration of 156.3 fs in the autocorrelation trace (fitted to a Gaussian pulse shape and measured as the full width at half-maximum (FWHM) of the optical pulse, i.e., \(\tau_{\text{pulse}}\)\(=\)\(\tau_{\text{AC}}\times 0.648=156.3\) fs, where \(\tau_{\text{AC}}\) = 221 fs is the pulse duration of the autocorrelation function), and there is a 3 dB spectral bandwidth of 26.4 nm at 1564 nm. A 0.648 constant has been applied to transform the autocorrelation (AC) temporal width to the pulse profile, as in reference [44]. Figure 4: (**a**) Mode-locked autocorrelation trace for reference sample (S0\({}^{\prime}\)) and modified saturable absorbers (SAs) (S1 and S2) with a Gaussian fitting function, i.e., the pulse duration of the autocorrelation function (\(\tau_{\text{AC}}\)) = 235 fs for S0\({}^{\prime}\), \(\tau_{\text{AC}}\) = 221 fs for S1, and \(\tau_{\text{AC}}\) = 190 fs for S2. (**b**) Optical spectrum of each sample centered in 1560 nm and fitted to a Gaussian function (22.6 nm for reference sample S0\({}^{\prime}\), 25.4 nm for S1, and 40 nm for S2), with a pump power of 70 mW within the laser cavity. This corresponds to a time-bandwidth product (TBP; measured as \(\Delta\tau\)-\(\Delta\upsilon\), where \(\tau\) is the pulse duration and \(\upsilon\) the optical frequency) of 0.49. This implies that the pulse is not in the transform-limited situation, i.e., the optical pulses are slightly chirped. No Kelly sidebands have been observed in the optical spectrum, which denotes the weak intracavity nonlinearity and dispersion of the fiber laser [42]. By using S2, a readily highly stable pulsed laser was obtained when the intracavity pump power was higher than 38.5 mW. In the case of maximum pump power (70 mW), the output pulse had an optical power of 30 mW, developing a peak power of 28.2 kW and a 5.4 nJ pulse energy. Concerning the pulse duration of the autocorrelation function, it was estimated at 134.4 fs with a Gaussian fit (\(\tau_{\text{pulse}}\)= \(\tau_{\text{AC}}\times 0.648=134.4\) fs where \(\tau_{\text{AC}}\) = 190 fs), and the optical bandwidth at 3 dB decay was 40 nm, centered at a wavelength of 1569 nm. In this case, a more chirped pulse was obtained with TBP = 0.62. Therefore, a reduction of the temporal duration was obtained for samples S1 and S2 concerning reference sample S0\({}^{\prime}\) (166.2 fs), while the optical bandwidth increased from 22.6 nm (S0\({}^{\prime}\)) to 40 nm (S2). Also, Figure 4b shows a redshift of the central wavelength in S1 (1564 nm) and S2 (1569 nm) for the reference sample S0\({}^{\prime}\) (1560 nm), which can be explained by the enhancement of the saturable absorption coefficient, and thus to the reduction of the carrier concentration by means of the higher control of the growth conditions during the fabrication process.