## 3 Experimental Setup  
In the experiment, a MOPA system that consisted of a ps mode-locked oscillator, a four-pass traveling-wave amplifier, and a double-pass traveling-wave Nd:YVO\({}_{4}\) amplifier was adopted to obtain the high pulse energy output at 1064 nm, presented in Figure 1.  
In the present system, the amplifier is seeded with a self-developed semiconductor saturable absorption mirror (SESAM) mode-locked Nd:YVO\({}_{4}\) oscillator capable of generating 16.3 ps pulses at a repetition rate of 30 MHz with a single pulse energy [16] of 0.115 \(\upmu\)J. Picosecond pulse sequence from the seed was injected into the pulse picker through two high-reflection mirrors, M1 and M2. The function of the pulse picker is to select the desired repetition rate for traveling amplifier by eliminating the pulse leakage of the seed sequence. The size of the RTP (Rubidium Titanyl Phosphate) crystals used in the pulse picker is 5 \(\times\) 5 \(\times\) 7 mm\({}^{3}\).  
The laser pulse is injected into the four-pass amplifier by the M3. In the four-pass amplifier, the gain medium is 0.3 at.% doped Nd:YVO\({}_{4}\) with a size of 4 \(\times\) 4 \(\times\) 12 mm\({}^{3}\) and double-end-wedged cut at 2\({}^{\circ}\). Both sides of the Nd:YVO\({}_{4}\) have anti-reflective (AR) coating at the 1064 nm and 888 nm wavelength. A 60 W, 888 nm fiber-coupled laser diode (p2-060-0888-3-A-R01-S0119 made by Nlight) with a numerical aperture of 0.22 and a diameter of 400 \(\upmu\)m is used as the pump source. The coupling ratio of the pump beam is 1:2 into the Nd:YVO\({}_{4}\) crystal.  
To further amplify the output power, one stage traveling-wave Nd:YVO\({}_{4}\) amplifier is adopted. Through a focus lens M5 and two high-reflection mirrors, M4, M6, the pulses were injected into the  
Figure 1: Schematic diagram of the 500-kHz level high energy double-pass Nd:YVO\({}_{4}\) picosecond amplifier experimental setup.  
double-pass traveling-wave amplifier. A Nd:YVO\({}_{4}\) crystal with the dimensions of 4 \(\times\) 4 \(\times\) 20 mm\({}^{3}\) is selected as gain medium with 0.3 at.% Nd\({}^{3+}\)-doped and double-end-wedged cut at 2\({}^{\circ}\) to inhibit the production of ASE. Both end facets of the laser crystal were anti-reflection (AR) coated at 1064 nm and 808 nm. A 60 W, 808 nm fiber-coupled laser diode (SN: 1038266-W4312 made by Nlight) with the numerical aperture of 0.22 and the diameter of 400 \(\upmu\)m was used as the pump source of the amplifier, the line width is \(\pm\)3 nm. Reflected by M0, the laser passes the gain medium two times with the coupling ratio of 1:4. The folding angle of the light path was about 5\({}^{\circ}\).  
In the system, The plane mirrors M1, M2, M4, M6 and M8 were HR coated at 1064 nm and 808 nm; M3 was a focus lens with anti-reflective (AR) coating at the 1064 nm wavelength of size \(\upvarphi\)12.7 \(\times\) 6 (f = 200 mm), M5 and M7 were focus lens with antireflective (AR) coating at the 1064 nm and 808 nm wavelength of size \(\upvarphi\)12.7 \(\times\) 4 (f = 150 mm).The arm length between M4-M5 and M5-M6 was carefully optimized to be 75 mm and 45 mm; the arm length between M0 and M6 was 265 mm; the arm length between M0 and M8 was 327 mm. The offset in x, y axis is 0.3 mm and the fabrication tolerance is \(\pm\)0.01 mm. In order to reduce the thermal effects and improve laser beam quality at high power, the temperature of the water was maintained at 19 \({}^{\circ}\)C.