## 3 Experimental Results
### Second-Harmonic Generation Using an Efficient Nonlinear Crystal  
The frequency conversion efficiency of CW 1064 nm in PPLN crystals has been shown to saturate when the output power generated at 532 nm exceeds 3 W [10; 16; 17; 18; 27]. Therefore, our second-harmonic generation is performed only in the QCW mode. To frequency-double the signal at 1064 nm, the laser beam coming out of the amplifier was collimated, then focused into the non-linear crystal using a lens with a focal length of either 100 mm or 150 mm to achieve different beam waist diameters, namely of \(\sim\)52 um and \(\sim\)80 um, respectively. The nonlinear crystal used was a z-cut, type-0 ee-e 10 mm-long, 1 mm-thick, and 10 mm-wide MgO:PPLN bulk crystal (Covesion, UK) with five periodically poled gratings with periods of 6.83 um, 6.86 um, 6.90 um, 6.93 um, and 6.96 um. The following results were obtained with the first grating because it was designed to operate at the lowest phase-matching temperatures, namely 35 \({}^{\circ}\)C at 1064 nm. The oven then did not have to be operated at high temperatures. Both the input and output facets of the crystal were coated to reduce their power reflectivity at 532 nm and 1064 nm to less than 1%. To achieve efficient SHG, the phase-matching temperature proprieties were studied by determining the phase-matching temperature and acceptance bandwidth for each grating. Figure 3: Measured characteristics of the single-stage fiber amplifier output signal at 1064 nm using either 3 m of fiber pumped continuously or 1.5 m pumped in the QCW regime. (**a**) Output power in the case of CW pumping (solid curves) and QCW pumping (dashed curves). The onset of SBS was reached at an output power of 25 W and 42.8 W, respectively. (**b**) Normalized optical spectrum in the forward direction under QCW pumping at an output peak power of 42.8 W.  
The measured temperature tuning curve of the single-pass SHG is shown in Figure 4a. The \(\mathrm{sinc^{2}}\) fit to the experimental data shows a full-width at half maximum (FWHM) bandwidth of 3.8 \(\pm\) 0.4 \({}^{\circ}\)C at a phase-matching temperature of 36 \({}^{\circ}\)C evaluated at 4 W. This value is slightly larger than the calculated value of the temperature acceptance bandwidth, namely 2.28 \({}^{\circ}\)C, using eq. 44 in [28]. This discrepancy may be due to the non-uniformity of the grating period along the length of the crystal, or to uncertainties on the Sellmeier coefficients used to perform the fit [29]. No change in the phase-matching temperature was observed when increasing the fundamental power. The power conversion efficiency for second-harmonic generation is proportional to the focusing parameter \(\xi\) = L/b, where L is the length of the nonlinear crystal and b is the confocal parameter [30]. The confocal parameter is defined as \(\mathrm{b}=2\pi\mathrm{m}_{\omega}/\lambda_{\omega}\mathrm{w}^{2}\), where \(\mathrm{n}_{\omega}\), \(\lambda_{\omega}\), and \(\mathrm{w}\) are the refractive index, wavelength, and beam waist radius, respectively, of the fundamental beam. For this crystal length, the calculated optimum focusing parameter is \(\xi\) \(\approx\) 2.84, which would require a relatively small beam waist diameter of \(\sim\)32 \(\upmu\)m. For peak powers greater than 40 W, this spot size would exceed the damage threshold of the crystal in the CW mode (500 kW/cm\({}^{2}\)) and may approach the damage threshold in the QCW mode (no data are reported for the crystal damage in the \(\upmu\)s regime). Therefore, we limited our experiments to larger focused beam diameters, namely \(\sim\)80 \(\upmu\)m and \(\sim\)52 \(\upmu\)m, corresponding to an L/b of \(\sim\)0.47 and \(\sim\)1.12, respectively. For a 52-\(\upmu\)m beam diameter, the conversion efficiency was consequently halved compared to what it would have been if operated at the optimal focusing parameter. The output peak powers and conversion efficiency measured with respect to the peak power at 1064 nm (duty cycle of 1%) at these beam diameters are presented in Figure 4b.