2 Experimental setup

Our experimental setup includes three main parts: the all PM fiber mode-locked laser, slab laser amplifier and ultraviolet generator.

2.1 All PM fiber mode-locked laser

The all PM fiber mode-locked laser contains a passively mode-locked oscillator, a fiber pre-amplifier and a fiber-based pulse picker (shown in Figure 1). The laser oscillator is based on a Fabry–Perot (FP) cavity configuration. The total cavity length is about 3.3 m, which consists of a piece of 100 cm PM Yb-doped gain fiber (Nufern, PM-YSF-6/125-HI), pumped by a 976 nm power laser diode (LD) via a PM wavelength division multiplexer (WDM). A SESAM directly butt-coupled to the PM fiber is used as one end reflector of the FP cavity for self-started passive mode-locking of the fiber laser. It has a modulation depth of 31%, a relaxation time of 4 ps and a saturation fluence of $40~\unicode[STIX]{x03BC}\text{J}/\text{cm}^{2}$ (Batop, SAM-1064-57-4ps). A PM fiber Bragg grating (FBG) is used as one reflector of the FP cavity, and the FBG has a reflection peak wavelength of 1063.9 nm with $-3$  dB bandwidth of 0.5 nm, which is designed to match the gain spectrum of Nd: $\text{YVO}_{4}$ crystal. It is worth noting that this FBG is also optimized for low noise operation^{[Reference Chen, Song, Jung, Hu, Wang and Kim13]}. The laser consists of a total PM fiber length of ${\sim}3.3~\text{m}$ , which results in a laser repetition rate of ${\sim}30~\text{MHz}$ . The mode-locked pulses are directed out by a 50 : 50 optical PM coupler. After outputting from the oscillator laser, 10% of the laser is directed out by a 90 : 10 optical PM coupler for producing a delayed gate signal for latter pulse picking. The remaining 90% of the laser is coupled into the PM fiber laser pre-amplifier, which consists of a PM WDM, a 1.2 m PM Yb-doped gain fiber (the same type as used in the oscillator laser) and a 976 nm power LD. A fiber isolator (ISO) is installed between the seed laser and the pre-amplifier to isolate the returning light. The pulse picker used in our experiment consists of three components, including a photonics detector (PD, Thorlabs, PDA36A), a signal generator (SG, SRS, DG645) and a fiber-based acoustic optical modulator (AOM, AA Opto-Electronic, MT250-IR6-Fio-PM0). Irradiated by the 10% seed pulses, the PD generates a synchronous radio frequency (RF) signal which is equal to the repetition rate of the seed pulses. Triggered by this RF signal, the SG could produce a delay gate signal with a lower frequency which can be an integral fraction of the repetition rate. Then this delay gate signal will be sent to the AOM as the trigger signal for pulse picking. As a consequence, the repetition rate of the picked pulses could be adjusted by setting the SG. At last the picked pulses are collimated by a fiber collimator.

Figure 2. Configuration of the ultraviolet picosecond pulse laser system.

2.2 Slab laser amplifier and ultraviolet generator

Due to the fact that the Nd: $\text{YVO}_{4}$ crystal has a large emission cross-section and polarized emission attributed to its natural birefringence, we choose it as the gain medium in latter solid-state amplification stages. Besides, the Nd: $\text{YVO}_{4}$ crystal also shows much more price advantages over the Yb-based crystal and enough gain bandwidth for ${\sim}10~\text{ps}$ pulse amplification as well. The structure of solid-state slab laser amplifier is shown in Figure 2(a). In order to compensate the energy loss by the former pulse picker, two end-pumped double-pass Nd: $\text{YVO}_{4}$ pre-amplifiers are employed for energy amplification before the slab amplifier. An optical isolator is used to protect the all PM fiber mode-locked laser against returning light from these two amplifiers. The slab amplifier mainly consists of a LD stack, two beam shapers, a pair of plane mirrors and an Nd: $\text{YVO}_{4}$ slab crystal. The LD stack emits pump light at center wavelength of 808 nm and the beam is shaped by a coupling system which consists of a planar waveguide, a spherical lens and several cylindrical lenses. Through the coupling system, a $14~\text{mm}\times 1~\text{mm}$ homogeneous pump line is measured on the pump end of the slab Nd: $\text{YVO}_{4}$ crystal, which is nearly Gaussian distribution in the vertical direction and homogeneous in the horizontal direction. A 0.3% doped Nd: $\text{YVO}_{4}$ crystal is used as the gain medium of the slab amplifier. The crystal has a dimension of $10~\text{mm}\times 14~\text{mm}\times 1~\text{mm}$ . The two large faces ( $10~\text{mm}\times 14~\text{mm}$ ) of the slab crystal are contacted by two heat sinks, which are cooled by circulating water at the temperature of $25\,^{\circ }\text{C}$ . The two transmitting faces ( $14~\text{mm}\times 1~\text{mm}$ ) are antireflective coated. There are two types of mirrors in our system. M1 is the dichroic mirror which has high transmission at 808 nm and high reflection at 1064 nm. M2 has high reflection at 1064 nm.

Before coupling into the slab amplifier, the seed beam is shaped by beam shaper-1 which consists of two cylindrical lenses and a spherical lens. In the horizontal direction, the beam shaper-1 is used to compress the seed beam to be line-like for mode matching between the seed beam and the pump light. In the vertical direction, the spherical lens is used to focus the seed beam (which is Gaussian distribution). Meanwhile the spherical lens increases the divergence angle of the seed beam. As a result, the beam diameter will be wider for every passage through the crystal which ensures that the optical power density is always similar. The beam shaper-2 is used to restore the amplified laser beam to Gaussian distribution in both the horizontal and vertical directions.

The ultraviolet generator shown in Figure 2(b) consists of two commercial LBO crystals without additional heating. In LBO1, the 532 nm pulses are generated from 1064 nm pulses of the slab amplifier by doubling-frequency generation (DFG). The 355 nm pulses are produced in LBO2 from 532 nm and 1064 nm pulses, through sum frequency generation (SFG). A prism is used to separate 355 nm, 532 nm and 1064 nm pulses.

The output spectra of the all PM fiber mode-locked laser are recorded by an optical spectrum analyzer (Yokogawa-AQ6370B) with the resolution of 0.02 nm. Its RF spectrum is measured by a high speed photo-detector (Thorlabs DET10A/M) which is connected to an oscilloscope (Iwatsu, 400 MHz). The pulse duration is measured by an optical autocorrelator (APE, PulseCheck).

Figure 3. Output characteristics of the all PM fiber pulse seed source. (a) Spectrum profiles, the inset shows the long term stability of the seed pulses (in the 10% output port) in 2 h. (b) Autocorrelation trace and its Gaussian fitting.

3 Experimental results and discussions

When the pump power is 75 mW, the oscillator laser is self-started mode-locking with the output power of 2 mW. As the pump power increases to 130 mW, 5 mW output power is achieved. Then the output power is amplified to 75 mW with 400 mW pump power of the fiber pre-amplifier. Thanks to the all-fiber construction, we realize a low repetition rate of 30.7 MHz with a compact size, which is difficult to a solid-state mode-locking laser. The fiber-based pulse picker reduces the repetition rate to 500 kHz with diffraction efficiency of ${\sim}50\%$ , according to the output power of 0.6 mW. Figure 3(a) shows the output optical spectrum profiles of the oscillator, pre-amplifier and pulse picker. Due to the normal dispersion and self-phase modulation (SPM) effect in the pre-amplifier and pulse picker, the full width at half-maximum (FWHM) spectral width is broadened to ${\sim}0.75~\text{nm}$ , which is acceptable for the Nd: $\text{YVO}_{4}$ amplifier. Figure 3(b) shows the autocorrelation (AC) trace. The black solid line represents our experimental data, and the red dotted line is its Gaussian fitting. The FWHM duration of the fitted curve in Figure 3(b) is $1.414\times 9.09~\text{ps}$ . In addition, the stability of mode-locking can be greatly improved by using all PM fiber construction, as shown in Figure 1. In our experiment, the mode-locking state e.g., the spectrum profile would not be affected by slight mechanical stress and air-wobbling because of the insensitivity of the PM fiber to external perturbations, which is an accepted advantage of the mode-locked laser with all PM fiber format. Besides, because the stability of amplified pulses significantly follows from the stability of seed pulses, we measure the output powers of the seed pulses (in the 10% output port), at the frequency of 1 time per second in a long time of 2 h. We plot the measured data in the inset of Figure 3(a) and the calculated root mean square (RMS) power fluctuations are only ${\sim}0.12\%$ . We believe that the seed fiber laser with this high stability will be beneficial to a robust and stable laser system.

Figure 4. Output characteristics of the all slab amplifier. (a) Measured (dots) and calculated (line) output power of the slab amplifier. (b) Long term stability of the slab amplifier in 2 h. (c) Beam radius and profile. (d) Autocorrelation trace and its Gaussian fitting.

The seed beam is amplified to ${\sim}90~\text{mW}$ by two end-pumped double-pass Nd: $\text{YVO}_{4}$ pre-amplifiers. In our design, the seed beam will pass through the slab crystal 10 times. At the pump power of 125 W emitted by the LD stack, the output power of the slab amplifier is 3.5 W. As the pump power increases up to 260 W, 19.8 W output power is achieved. The corresponding pulse energy is about $40~\unicode[STIX]{x03BC}\text{J}$ , at the repetition rate of 500 kHz. Figure 4(a) shows the measured (dots) and calculated (line) output power. The slope efficiency is ${\sim}12\%$ . This low slope efficiency is due to the low output power of the seed beam. However, the corresponding single-pass amplification factor is about 1.71, which is in line with the general performance of the slab amplifier. With a more powerful seed beam ( ${>}1~\text{W}$ ), the output power and the extraction efficiency can be further improved. This high power seed beam can be achieved by optimizing the pre-amplifiers or cascading more amplifiers. We also measure the output powers of the slab amplifier in 2 h. The measured data is shown in Figure 4(b), and the corresponding RMS power fluctuations are only ${\sim}0.94\%$ . It is evident that this high stability from the whole system benefits from the stable and robust all PM mode-locked fiber laser. Figure 4(c) shows the standard position-beam-radius measurements by a laser beam profiler, which indicates that beam quality is $M_{x}^{2}=1.35$ or $M_{y}^{2}=1.31$ in the orthogonal directions. Better beam quality makes it easier to focus the laser beam to a smaller point for higher optical power density, which is significant in material processing systems. The measured autocorrelation trace of the slab amplifier output is shown in Figure 4(d). The FWHM of the pulse duration is 10.89 ps (by Gaussian fitting), which is a bit wider than the seed pulse. Because the negligible dispersion induced by the small slab crystal cannot broaden these narrowband picosecond pulses with the variational duration as large as ${\sim}1.8~\text{ps}$ , and the Nd: $\text{YVO}_{4}$ crystal only provides ${\sim}1~\text{nm}$ gain bandwidth at 1064 nm (comparable to the seed pulse after pulse picker), we attribute this temporal broadening to slight spectral mismatch and the finite gain bandwidth of Nd: $\text{YVO}_{4}$ crystal. Then the amplified picosecond pulses are coupled in the ultraviolet generator without focusing. The ultraviolet generator outputs 7.5 W UV pulses at the central wavelength of 355 nm. The optical–optical efficiency and the corresponding pulse energy are 37.5% and $15~\unicode[STIX]{x03BC}\text{J}$ , respectively. By assuming that the pulse duration is 10 ps, the peak power reaches 1.5 MW.

In order to test this laser system, we carry out an experiment of material processing on polycrystalline diamond samples. The material processing by picosecond pulses can be generally considered as strong evaporation, the critical condition for evaporation can be written as^{[Reference Chichkov, Momma, Nolte, von Alvensleben and Tünnermann3]}

(1) $$\begin{eqnarray}\displaystyle F_{A} & = & \displaystyle \frac{4P_{0}}{\unicode[STIX]{x1D70B}t_{0}f_{r}d^{2}}\geqslant F_{th}e^{\unicode[STIX]{x1D6FC}z},\end{eqnarray}$$

(2) $$\begin{eqnarray}\displaystyle F_{th} & = & \displaystyle \unicode[STIX]{x1D70C}\unicode[STIX]{x1D714}/\unicode[STIX]{x1D6FC},\end{eqnarray}$$

where $F_{A}$ is the power density of a single laser pulse, $P_{0}$ is the average power output, $t_{0}$ is the pulse width, $f_{r}$ is the repetition rate, $d$ is focused spot diameter, $\unicode[STIX]{x1D6FC}$ is the wavelength-related material absorption coefficient and $z$ is the direction perpendicular to the target surface. $F_{th}$ is the threshold laser fluence for evaporation, which is determined by the density $\unicode[STIX]{x1D70C}$ and the specific (per unit mass) heat of evaporation  $\unicode[STIX]{x1D714}$ .

Figure 5. SEM images of laser-cut grooves on the diamond surface by 355 nm picosecond pulses with (a) $P_{0}=1~\text{W}$ at the repetition rate of 500 kHz (the corresponding pulse energy is $2~\unicode[STIX]{x03BC}\text{J}$ ) and (b) $P_{0}=1~\text{W}$ at the repetition rate of 10 MHz (the corresponding pulse energy is $0.1~\unicode[STIX]{x03BC}\text{J}$ ), respectively.

According to Equation (1), we need to increase the power density up to the threshold laser fluence for evaporation, in order to achieve a high processing performance. Thanks to the high output beam quality, the UV picosecond beam can be focused to $d=10~\unicode[STIX]{x03BC}\text{m}$ by a lens with the focal length of 40 mm. The polycrystalline diamond samples are irradiated normal to the target surface in open air and scanned at a rate of $600~\text{mm}/\text{s}$ by moving a motorized stage during laser irradiation. For comparison, the repetition rate $f_{r}$ of the UV beam is set to be 500 kHz or 10 MHz, with the same average power $P_{0}=1~\text{W}$ . The scanning electron microscope (SEM) observations (shown in Figure 5(a)) show that the former processing result is satisfactory both in efficiency and quality. Meanwhile with the similar average power but the much lower pulse energy, the latter processing result is unsatisfactory, for both the rough surface and the narrow width of the laser-cut grooves, as shown in Figure 5(b). This can be explained that with $f_{r}=500~\text{kHz}$ (the pulse energy is 20 times higher than $f_{r}=10~\text{MHz}$ ) the pulse power density is high enough to realize evaporation process in the entire area irradiated by the focal spot. As a result, the width of the laser-cut grooves is similar to the diameter of the focal spot. In contrast, the width of the laser-cut grooves is much shorter than the diameter of the focal spot, with $f_{r}=10~\text{MHz}$ .