## 3 Results and Discussion  
When the absorbed pump power is 73.8 W, maximum regenerative amplified output power 19.6 W was generated at 99.6 kHz in center wavelength of 1064.06 nm and spectral width of 0.14 nm. Here, the un-picked seed pulses are amplified to 150 mW when switching off the high voltage of the PC. The pump source spectrum is shifted to the long wavelength with the increase of the power. As shown in Figure 2, the central wavelength of the pump source is 887.66 nm with spectral width of 1.84 nm when operating at 73.8 W.  
The curve of output power varies with pump absorbed power is shown in Figure 3. It can be seen from the figure that the output power increases gradually with the increase of the pump power. The highest output power achieved is 19.6W while the absorbed power of medium is 73.8 W.  
As shown in Figure 4, different regenerative amplification time corresponding to different output pulse energy. The output energy is relatively stable, about 196 \(\upmu\)J, when the regeneration amplification time ranges from 180 ns to 225 ns. The stable pulse train, unstable multi-period pulse train trace and a single pulse profile of the regenerative amplified output are shown in Figure 5 (a-c), respectively. Stable pulse train is obtained with the regenerative amplification time of 195 ns at repetition rate of 99.6 kHz, as shown in Figure 5 (a). As the regenerative amplification time continues to increase, along with the phen  
Figure 1: Design scheme of the fiber laser pumped regenerative amplifier. the output pulse train becomes no longer stable with repetition rate jitter from about 20 kHz to 50 kHz, as illustrated in Figure 5 (b). Figure 4: The output energy as a function of regeneration amplification time in operation. Figure 3: The output power as a function of absorbed power in operation. Figure 2: The spectral intensity distribution as a function of absorbed pump power. After regenerative regeneration, spectrum distribution of the injected seed is slightly changed, as depicted in Figure 6. Solid line is the spectral intensity distribution curve of seed source with center wavelength 1064.06 nm and the spectral width 0.2 nm. Broken line is corresponding to the regenerative amplified output spectral intensity with center wavelength 1064.07 nm and spectral width 0.14 nm. Results shows that gain narrowing tends to compress the optical spectrum. The autocorrelation signal shows that the output pulse duration is 36 ps, as illustrated in Figure 7. Compared with the pulse duration 20 ps of the injected picosecond seed source, the output pulse duration is broadened widely. According to the Fourier transform limited pulse, time-bandwidth product (TBWP) must be equal to or greater than the constant \(\kappa\)[13,14]:  
\[\Delta t\cdot\Delta\
u\geq\kappa \tag{1}\]  
where \(\Delta t\) is the full width at half maximum (FWHM) of pulse envelope intensity, \(\Delta\
u\) is the FWHM of Fourier transform spectroscopy. The TBWP for a Gauss pulse is \(\kappa=2\ln 2\) / \(\pi=0.441\). The TBWP of the fiber picosecond seed source is 1.06, and the regenerative amplified output pulse TBWP is 1.34. Figure 5: Oscilloscope traces of (**a**) the pulse train at 195 ns regeneration amplification time; (**b**) the pulse train of unstable multi-period phenomenon; (**c**) a single pulse shape at 195 ns regeneration amplification time. Figure 6: Spectral intensity distribution of the injected seed (solid line) and regenerative amplified output (broken line). In our experiment, on the one hand, the reason for pulse duration being broader is gain narrowing, and the other is chirp phenomenon. Figure 8 represents the beam characteristics of the output, which indicates nearly diffraction limited beam quality. The result giving a beam quality of \(M_{x}^{2}=1.20\), \(M_{y}^{2}=1.19\) in both directions perpendicular to the axis of propagation. The beam diameter in \(\mathbf{x}\) direction is 1.5 mm and \(\mathbf{y}\) direction is 1.3 mm.