## 1 Introduction
First, for the same average signal power, the signal peak power can be significantly higher, resulting in a higher SHG power (proportional to the signal power squared). Second, for the same average power, the thermal load on both the fiber and the non-linear crystal are the same. Stated differently, the SHG efficiency is enhanced, but the thermal load is unchanged. Conversely, the same SHG conversion efficiency can be achieved with a lower average power and, therefore, a lower thermal load. These features can be advantageous to other applications such as remote pulsed Raman spectroscopy [20], metal laser cutting [21], and gas tracing [22], especially when the pulses are sufficiently long to maintain a similar behavior as in the CW mode. Although conversion efficiencies of 68% [23] and 60% [24] have been demonstrated in pulsed mode operation in a PPLN crystal. The conversion efficiencies are high due to the short pulse duration, in the order of 100 ps [23] and 560 ps [24], while the second-harmonic pulse energies were relatively low, in the range of sub-\(\upmu\)[23] to tens of \(\upmu\)[24]. On the other hand, for a given drive current, operating a laser in the QCW mode generally allows it to be driven above its CW rating and to obtain peak powers that are greater than the maximum CW power. This approach has proven useful to increase the conversion efficiency in other non-linear crystals like LBO [25]. In general, short fundamental pulses (nanoseconds) produce high conversion efficiencies thanks to their very high peak powers, but low second-harmonic pulse energies due to their low pulse energy. Longer fundamental pulses yield the opposite benefits, namely lower efficiencies but higher second-harmonic pulse energies. In spite of this benefit, the use of longer pulses has not been fully exploited in a MgO:PPLN crystal. To the best of our knowledge, the highest pulse energy reported so far is limited to 440 \(\upmu\)l in a 20-mm MgO:PPLN crystal (double the length used in the work reported here), with no details on the development of QCW opereration [26]. In light of the foregoing, here we investigate the frequency doubling of a QCW single-frequency fiber amplifier in a 10-mm MgO:PPLN crystal. We report the generation of \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & **Fundamental** & **Pulse Energy** & **Output Power** & **Peak Power at** & **Conversion** & **Crystal** & **Configuration** & **Operation** \\  & **Power (W)** & **at 1064 nm** & **at 532 nm (W)** & **532 nm (W)** & **Efficiency (\%)** & **Length (mm)** & **Mode** \\ \hline
[14] & 25 & - & 7.5 & - & 30 & 25 & single-pass & CW \\
[15] & 7.6 & - & 5 & - & 66 & - & multi-pass & CW \\
[18] & 20 & - & 1.1 & - & 9 & 10 & single-pass & CW \\
[23] & 0.2 & - & 0.135 & - & 68 & 10 & single-pass & pulsed \\
[24] & 0.069 & 10 & 0.04 & - & 60 & 5 & single-pass & Pulsed \\
[26] & - & - & - & 8.8 & 34 & 20 & single-pass & QCW \\ This work & 0.428 & 4280 & 0.067 & 6.7 & 20 & 10 & single-pass & QCW \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Selected work on the second-harmonic generation using periodically poled Mg-doped lithium niobate (MgO:PPLN) crystals. output peak powers at 1064 nm up to twice as high as the maximum power achievable under the CW pumping, and output pulse energies at 532 nm close to 700 \(\upmu\)J. To the best of our knowledge, this is the highest pulse energy achieved in a PPLN crystal. Moreover, QCW operation reduces the number of pump diodes required for the fundamental laser, hence contributing to further reducing the size of the fiber amplifier.