# High-Quality, InN-Based, Saturable Absorbers for Ultrafast Laser Development
## 2 Material Characterization  
InN epitaxial layers were deposited by plasma-assisted molecular beam epitaxy (MBE) on a commercial GaN-on-sapphire template. The growth temperature was 450 \({}^{\circ}\)C, and the growth rate was 290 nm/h. During the deposition, the In/N flux ratio was 1.2. The indium (In) flux was interrupted along the growth every 10 min to consume the excess In on the sample surface and prevent the accumulation of In droplets there as well [22]. Two samples with different InN thicknesses were investigated: samples S1 and S2, with InN thicknesses of 360 nm and 780 nm, respectively. The thickness of the GaN-on-sapphire template was 4 \(\upmu\)m/350 \(\upmu\)m in both samples. Previously reported 1 \(\upmu\)m-thick InN samples [26] with higher residual doping (samples S0 and S0\({}^{\prime}\)) were included in this analysis for comparison purposes. For the reference samples, the growth rate was 280 nm/h, and growth interruptions under nitrogen performed every 5 min. An optical transmittance spectrum of the samples under study is shown in the inset of Figure 1. The linear transmission at the operation wavelength of the laser (1560 nm) was 23%, 9%, 16%, and 3% for samples S0, S0\({}^{\prime}\), S1, and S2, respectively. Hence, the linear absorption coefficients were estimated at \(\alpha_{0}=1.4\times 10^{4}\) cm\({}^{-1}\) for S0, \(\alpha_{0}=2\times 10^{4}\) cm\({}^{-1}\) for S0\({}^{\prime}\), and \(\alpha_{0}=4\times 10^{4}\) cm\({}^{-1}\) for samples S1 and S2. Furthermore, we have calculated the semiconductor bandgap energy from Tauc's plots [31; 32]. The obtained results, shown in Figure 1, evidence a redshift for samples S1 and S2, whose bandgap energies have been fitted to 0.69 eV and 0.67 eV, respectively, in comparison to 0.8 eV and 0.77 eV in the reference samples S0 and S0\({}^{\prime}\), respectively. From the bandgap energies, the carrier concentration is estimated below \(10^{18}\) cm\({}^{3}\) for S1 and S2, 4-5 \(\times 10^{18}\) cm\({}^{3}\) for S0\({}^{\prime}\), and higher than \(10^{19}\) cm\({}^{3}\) for S0 [33]. The smaller bandgap energy in S1 and S2 can be attributed to the reduction of the Burstein-Moss effect, due to a lower carrier concentration, and therefore to an improvement of the crystal quality because of a higher control of the growth conditions related to the time intervals of N deposition [34]. The nonlinear transmission of the SAs was measured by the open-aperture Z-scan technique [35], depicted in Figure 2a, which allows for determination of the intensity-dependent, nonlinear absorption properties (\(\alpha_{2}\)) for each sample. The SAs are excited by an ultrafast, mode-locked fiber laser with a pulse width of 250 fs, beam waist (\(w_{0}\)) of 8.5 \(\upmu\)m, and a Rayleigh distance (\(z_{R}\)) of 223.2 \(\upmu\)m (characterized by the knife-edge technique [36; 37]), operating at 1560 nm with a repetition rate of 5.6 MHz. The transmitted signal is monitored by a Ge photodiode (Detector B, Thorlabs SM05 PD6A) as the sample moves gradually along the propagation direction on a motorized translation stage. A power meter detects the output power of the reference beam in Detector A (Thorlabs PM100 USB), in order to control possible oscillations of the laser. The laser beam has a maximum peak power of 40 kW, which corresponds to an energy fluence of 7 mJ/cm\({}^{2}\) incident on the sample surface. Figure 1: [PERSON]’s plot for direct electronic transitions, i.e., representation of (\(\alpha\)E)\({}^{2}\) versus energy (E), for samples S0 (**black line**), S0 (**green line**), S1 (**blue line**), and S2 (**red line**). The vertical dashed line indicates the operation wavelength of the laser. The inset shows the transmission of each sample as a function of the incident wavelength. Figure 2: (**a**) Schematic description of the setup for Z-scan measurements. (**b**) Normalized nonlinear transmission change as a function of the focal distance for the case of maximum incident pulse energy (40 kW).