2 Experimental setup

2.1 The ns pulsed seed

The experimental setup has a typical MOPA configuration comprising a ns pulsed seed (Figure 1) and four-stage amplifiers. All fiber-based components in the system utilize the PM fiber. In the ns pulsed seed, a CW linearly polarized single frequency laser based on the ultra-short cavity^{[Reference Xu, Yang, Zhang, Wei, Qian, Chen, Zhang, Shen, Peng and Qiu34]} is modulated by an electrical–optical intensity modulator (EOIM) to generate the ns pulses. The CW single frequency laser emits an output power of 42 mW at the center wavelength of 1064 nm, with a nominal linewidth of 20 kHz. The EOIM has a response bandwidth beyond 10 GHz and a handling power range within 100 mW, driven by an arbitrary function generator (AFG). The pulse width and the repetition frequency of the drive signal are set to 4 ns and 10 MHz, respectively. After the EOIM, the generated pulses with an average power of 0.48 mW are injected into a low power amplifier. The low power amplifier utilizes a 1-m-long single-mode double cladding PM Yb-doped fiber (YDF) with core/inner cladding diameters of $6/125~\unicode[STIX]{x03BC}\text{m}$ , pumped by a laser diode (LD) emitting the wavelength of 974 nm through a wavelength division multiplexer (WDM). After a PM bandpass filter (BPF) and a PM isolator (ISO), the amplified ns pulses are launched into an AOM to remove the leakage among the pulses and improve the pulse extinction ratio. The AOM has a rise/fall time of 30 ns and a handling power capacity of 5 W. After the AOM, a coupler with a coupling ratio of 5:95 is used to split the laser beam into two parts. The part from the 5% port is used to monitor the properties of the ns pulses in real time. The part from the 95% port is finally injected into the following amplifiers as the seed, with an average output power of 2 mW.

The pulse sequence of the ns pulsed seed is shown in Figure 2(a), captured by a digital oscilloscope at its highest sampling rate of 5 GS/s. The profile of the pulse sequence reveals good stability and high extinction ratio of the ns pulsed seed. The full width at half maximum (FWHM) of the ns pulsed seed is read to be ${\sim}$ 4.4 ns, a little wider than the pulse width of the electrical drive signal imposed on the EOIM.

Figure 2. (a) The pulse sequence of the ns pulsed seed and (b) the pulse profile of the ns pulsed seed.

The spectral linewidth of the ns pulses is collaboratively measured by a Fabry–Pérot interferometer and a digital oscilloscope. The free spectral range and resolution of the Fabry–Pérot interferometer are 4 GHz and 10 MHz, respectively. As shown in Figure 3, the spectral linewidth is measured to be ${\sim}$ 36.2 MHz, due to the spectral broadening induced by the intensity modulation.

2.2 The power amplifier stages

As shown in Figure 4, following the ns pulsed seed, there are three pre-amplifiers and a main amplifier. The 1st pre-amplifier and 2nd pre-amplifier employ the same components as the low power amplifier used in the pulsed seed, with the only difference that the 1st pre-amplifier is counter-pumped through the WDM but the 2nd pre-amplifier is co-pumped. After the 1st pre-amplifier and 2nd pre-amplifier, the average power of the ns pulses is boosted to be 23.6 mW and 184.9 mW, respectively. The 3rd pre-amplifier adopts a 2.5 m-long PM double cladding Yb-doped fiber with core/inner cladding diameters of $15/130~\unicode[STIX]{x03BC}\text{m}$ , pumped by a 25 W LD with 976 nm emitting wavelength. The absorption coefficient of the active fiber is ${\sim}$ 5.5 dB at 976 nm pump wavelength, and the core/cladding NAs are 0.078 and 0.46, respectively. The average power of the ns pulses is amplified to be ${\sim}$ 10 W, and then injected into the main amplifier after a PM ISO and a PM tapper with a beam splitting ratio of $0.1\%:99.9\%$ . Through the backward 0.1% port of the tapper, the backward power of the main amplifier is monitored to judge whether the SBS occurs or not.

Figure 3. The scanning spectrum of the ns pulsed seed.

Figure 4. The experimental setup of the power amplifier stages.

In the main amplifier, a 3 m-long high concentration PM LMA double cladding Yb-doped fiber with core/inner cladding diameters of $30/250~\unicode[STIX]{x03BC}\text{m}$ is employed, pumped by six 976 nm LDs of ${\sim}$ 100 W power via a ( $6+1$ ) $\times$ 1 signal/pump combiner. The core/inner cladding NAs are 0.073 and ${>}$ 0.46, respectively, and the absorption coefficient is as high as ${\sim}$ 13.6 dB at the 976 nm wavelength due to high doping concentration. After the active fiber, a 1.15 m-long passive fiber matched with the active fiber in size is followed to deliver the laser power, so the total fiber length of the main amplifier is ${\sim}$ 4.15 m. Meantime, a pump stripper made from the high-index gel is arranged on the passive fiber to remove the cladding light, including the residual pump light and the cladding signal light. The output port of the passive fiber is cleaved with an oblique angle of $8^{\circ }$ , in order to prevent the end feedback and end damage.

3 Results and discussion

The dependence of the average output power and backward power on the pump power is shown in Figure 5. It is noted that the average output power scales linearly with the pump power increased, with a fitted slope efficiency of ${\sim}$ 80.3%. When the pump power is 575 W, a maximal output power of 466 W is obtained without power roll-over observed. The corresponding pulse energy is calculated to be ${\sim}46.6~\unicode[STIX]{x03BC}\text{J}$ at the repetition frequency of 10 MHz. The backward power also increases with an approximately linear trend, indicating the absence of the SBS in the main amplifier. The absence of the SBS mainly benefits from the large mode area and the short fiber length of the main amplifier and the narrow pulse duration of ${\sim}$ 4 ns that is much shorter than the phonon lifetime of the SBS with a typical value of 10 ns^{[Reference Agrawal35]}. Nonetheless, with the output power increasing, the increasing slope of the backward power gradually becomes bigger, which could be attributed to the onset of the amplified spontaneous emission (ASE), as shown in Figure 6.

Figure 5. The dependence of the average output power and backward power on the pump power in the main amplifier.

The Figure 6 shows the output spectra of the 3rd pre-amplifier and the main amplifier at the maximal output power. It is noted that, at the maximal output power, a little ASE is observed. It was reported that^{[Reference Huang, Zhang, Wang and Zhou36]}, the ASE contributes more to the backward power than the forward power, so the backward power increases faster once the occurrence of the ASE. However, the signal to noise ratio is as high as 46.8 dB, so the ASE content could be neglected. It is also noted that the SRS effect does not occur at the maximal output power.

Figure 6. The output spectra of the 3rd pre-amplifier and the main amplifier at the maximal output power.

During the amplification process, the stability and the extinction ratio of the ns pulses are well maintained, as shown in Figure 7(a). What is shown in Figure 7(b) is the Fourier transform spectrum of the time trace of the pulse sequence at the maximal output power. It is revealed that the Fourier transform spectrum has regular harmonics, indicating the good stability of the pulse sequence. However, due to the effect of gain saturation, the amplification of the front edge of the ns pulses is stronger than their back edge, as shown in Figure 8. As a concomitant result, the FWHM of the ns pulses is condensed a little to be ${\sim}$ 4 ns at the maximal output power.

Figure 7. (a) The pulse sequence of the main amplifier at the maximal output power and (b) the corresponding Fourier transform spectrum.

Figure 8. The pulse profiles of the seed, the 3rd pre-amplifier and the main amplifier at the maximal output power.

The peak power of the ns pulses can be calculated as^{[Reference Su, Zhou, Xiao, Wang and Xu21]}

(1) $$\begin{eqnarray}\displaystyle P_{\text{peak}} & = & \displaystyle \left(\left.\int _{t_{1}}^{t_{2}}I\,\text{d}t\right/\int _{T_{0}}^{T_{0}+T}I\,\text{d}t\right)\frac{T}{\unicode[STIX]{x0394}t}P_{\text{ave}}\nonumber\\ \displaystyle & = & \displaystyle \left(\left.\int _{t_{1}}^{t_{2}}I\,\text{d}t\right/\int _{T_{0}}^{T_{0}+T}I\,\text{d}t\right)\frac{P_{\text{ave}}}{\unicode[STIX]{x0394}t\cdot f_{R}},\end{eqnarray}$$

where $I$ is the normalized intensity of the ns pulses, and $T$ is pulse period. $P_{\text{ave}}$ is the average power, and $f_{R}$ is the repetition frequency. $\unicode[STIX]{x0394}t$ is the minimum time interval around the pulse peak, which is determined by the time difference between $t_{1}$ and $t_{2}$ , with a value of 0.2 ns according to the minimal sampling interval of the digital oscilloscope (corresponding to the maximal sampling rate of 5 GS/s). As a result, the peak power is calculated to be 8.8 kW.

The peak SBS threshold can be estimated according to the formula $P_{\text{SBS-peak }}=21A_{\text{eff}}(1+\unicode[STIX]{x0394}\unicode[STIX]{x1D708}_{L}/\unicode[STIX]{x0394}\unicode[STIX]{x1D708}_{B})\text{ln}(G)/g_{B}L_{\text{overlap}}$ , where $g_{B}\approx 3\times 10^{-11}~\text{m}/\text{W}$ is the peak SBS gain coefficient^{[Reference Agrawal35]}, $A_{\text{eff}}$ is the effective mode area, $\unicode[STIX]{x0394}\unicode[STIX]{x1D708}_{L}$ is the linewidth of the signal laser (has a value of 179.8 MHz as shown in Figure 9) , $\unicode[STIX]{x0394}\unicode[STIX]{x1D708}_{B}\approx 40~\text{MHz}$ is the linewidth of the SBS gain spectrum^{[Reference Rothenberg, Thielen, Wickham and Asman37]}, $G\approx 466/10=46.6$ is the linear amplification factor of the main amplifier and $L_{\text{overlap}}$ is the interaction fiber length^{[Reference Su, Zhou, Wang, Lü and Xu38]}:

(2) $$\begin{eqnarray}\displaystyle & & \displaystyle L_{\text{overlap}}=\nonumber\\ \displaystyle & & \displaystyle \left\{\begin{array}{@{}l@{}}\min \left(L,\displaystyle \frac{ct_{p}}{2n}\right),\hspace{116.39996pt}L\leqslant Tc/2n,\\ \left(\left\langle \displaystyle \frac{2nL}{cT}\right\rangle -1\right)\times \displaystyle \frac{ct_{p}}{2n}\\[12.0pt] \,+\min \left[\!\displaystyle \frac{ct_{p}}{2n},L-\displaystyle \frac{1}{2}\left(\left\langle \displaystyle \frac{2nL}{cT}\right\rangle -1\right)\!\left(\displaystyle \frac{Tc}{n}\right)\!\right],\,\,L>Tc/2n,\end{array}\right.\hspace{-10.00002pt}\nonumber\\ \displaystyle & & \displaystyle\end{eqnarray}$$

where $c\approx 3\times 10^{8}~\text{m}/\text{s}$ is the optical velocity in vacuum, $L$ is the fiber length, $t_{p}$ is the pulse duration, $n\approx 1.45$ is the optical refractive index of the fiber core and $T$ is the pulse period. As a result, the calculated peak SBS threshold is ${\sim}$ 10.95 kW, which is a little higher than present peak power. The peak SRS threshold can be estimated to be ${\sim}$ 27.2 kW according to the formula $P_{\text{SRS-peak}}=16A_{\text{eff}}/g_{R}L_{\text{eff}}$ ^{[Reference Agrawal35]}, where $g_{R}\approx 1\times 10^{-13}~\text{m}/\text{W}$ is the Raman gain coefficient, $A_{\text{eff}}$ is the effective mode area and $L_{\text{eff}}$ is the effective fiber length. This estimated value is far higher than present output peak power, so the SRS could not be the limitation factor for further power scaling but the SBS threshold may be reached firstly as the output power increases a little further.

Figure 9 shows the scanning spectra of the 3rd pre-amplifier and the main amplifier at the maximal output power. Due to nonlinear effect such as self-phase modulation (SPM), the linewidth of the maximal output power is broadened to be ${\sim}$ 203.6 MHz, with an increase of ${\sim}$ 23.8 MHz compared with the 3rd pre-amplifier. There is an empirical formula, $\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D714}=0.86\unicode[STIX]{x0394}\unicode[STIX]{x1D714}_{0}\unicode[STIX]{x1D719}_{\text{max}}$ , which can be used to estimate the broadened linewidth of the main amplifier. The $\unicode[STIX]{x0394}\unicode[STIX]{x1D714}_{0}$ is the initial spectral linewidth, i.e., the linewidth of the 3rd pre-amplifier. $\unicode[STIX]{x1D719}_{\text{max}}=\unicode[STIX]{x1D6FE}P_{\text{peak}}L_{\text{eff}}$ is the maximal phase shift in the main amplifier, where $P_{\text{peak}}$ is the peak power, $\unicode[STIX]{x1D6FE}=n_{2}\unicode[STIX]{x1D714}_{0}/cA_{\text{eff}}$ is the nonlinear parameter, and $n_{\text{2}}$ has a value of $2.6\times 10^{-20}$ ^{[Reference Agrawal35]}. By the calculation, $\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D714}=1.09\unicode[STIX]{x0394}\unicode[STIX]{x1D714}_{0}$ , so the broadened linewidth of the main amplifier is about 195.3 MHz in theory, which is close to the experimental result.

Figure 9. The scanning spectra of (a) the 3rd pre-amplifier and (b) the main amplifier at the maximal output power.

To evaluate the polarization property of the pulse laser, the polarization degree (PD) during the power scaling process is measured based on the system consisting of a collimator, a $\unicode[STIX]{x1D706}/4$ waveplate and a polarization beam splitter. The PD is defined as $P_{1}/(P_{2}+P_{2})$ , where $P_{1}$ is the power of the main polarization state and $P_{2}$ is the power of another orthogonal state. As shown in Figure 10, the PD is maintained around 90% in the whole power scaling process. At the maximal output power, the PD is ${\sim}$ 90%, which is not high enough and may be attributed to the unavoidable offset at the splicing points. Meanwhile, the degradation of PD is accumulated as the number of the splicing points increases in the whole chain. The PD may be improved further if we monitor and optimize it in real time before constructing each stage amplifier. The slight instability of PD during the amplification may be attributed to the birefringence perturbation induced by the change of the thermal load and the cooling situation with the pump power increased.

Figure 10. The polarization degree (PD) during the power scaling process of the main amplifier.

Based on the collimated beam, the beam quality is also measured. At the output power of 442 W, the $M^{2}$ is measured to be 1.32 by a beam quality analyzer, indicating a near-diffraction-limited beam quality, as shown in Figure 11(a). When reaching the maximal output power of 466 W with the pump limited, the $M^{2}$ degrades to be 1.78 rapidly. It is inferred that the degradation of beam quality is induced by the MI^{[Reference Eidam, Wirth, Jauregui, Stutzki, Jansen, Otto, Schmidt, Schreiber, Limpert and Tunnermann39]}.

Figure 11. The beam quality at the output power of (a) 442 W and (b) the maximal power.

Because the response frequency of the CCD in the beam quality analyzer is too slow to respond the dynamic change of the beam profile when the MI occurs, a beam profile analyzer with relatively higher response frequency is used to capture the MI-induced beam degradation. As shown in Figure 12, at the maximal output power, the beam profile varies over time, which is a typical feature of the MI^{[Reference Eidam, Wirth, Jauregui, Stutzki, Jansen, Otto, Schmidt, Schreiber, Limpert and Tunnermann39, Reference Tao, Ma, Wang, Zhou and Liu40]}. Nonetheless, in spite of the MI, the increasing trend of the output power does not change obviously due to the relatively large mode area of the active fiber which can sufficiently confine multiple modes, as demonstrated above. Remaining the rest of the system unchanged, the MI threshold may be improved further by changing the pump direction if the backward signal/pump combiner is available^{[Reference Tao, Ma, Wang, Zhou and Liu41, Reference Shi, Su, Zhang, Yang, Wang, Zhou, Xu and Lu42]}.

Figure 12. The six random samples of beam profile at the maximal output power captured by a beam profile analyzer with a sampling frequency of 30 Hz.