## 2 Experimental Principle and Setup  
Q-switch is the core component of the regenerative amplifier that is used in the pulse picker for mode-locked sequence. To date, both acousto- and electro-optic switches have been used to realize the pulse selection function in regenerative amplifiers [19; 25; 26]. However, due to the slow switching speed (with rise time up to 100 nanoseconds) and limited diffraction efficiency (usually less than 90%), the acousto-optic switch is difficult to generate regenerative pulses without the leakage of mode-locked seed. In contrast to the acousto-optic switch, the electro-optic switch has faster switching speed (rise time \(<\)10 ns) and excellent switching effect, which is widely adopted in regenerative amplifiers. Nowadays, the commonly used electro-optic crystals include \(\beta\)-BaB\({}_{2}\)O\({}_{4}\) (BBO), KH\({}_{2}\)PO\({}_{4}\) (KDP), KD\({}_{2}\)PO\({}_{4}\) (KD * P), RbTiOPO\({}_{4}\) (RTP), and LiNbO\({}_{3}\) (Lithium niobate) etc. To meet different experimental conditions (such as half- or quarter-wavelength voltage, acceptable input beam diameter, and available crystal size), both longitudinal and transverse electrode configuration Pockels cells are manufactured. However, so far there is not one kind of electro-optic crystal or configuration the can provide a general solution under different operating wavelengths, repetition rates, spot diameters, and output powers. At present, BBO crystal Pockels cells with minimal piezoelectric ringing and low acoustic noise, have emerged in high repetition rate (\(>\)100 kHz) pulse picking applications [14; 15; 16; 17; 19]. Nevertheless, with the increase of repetition rate, it is difficult to realize fast switching within the effective duty cycle due to the long fall time of the high voltage. To solve the problem, double BBO crystal Pockels cell is adopted in our experiment to reduce the load of the high voltage driving supply by reducing the quarter-wavelength voltage. The value of the quarter-wavelength voltage \(V_{\lambda/4}\) of BBO crystal is given by [27; 28]:  
\[V_{\lambda/4}=\frac{\lambda d}{4n_{0}^{3}d_{2}L} \tag{1}\]  
where laser wavelength \(\lambda\) = 1064 nm, the crystal section thickness \(d\) = 3 mm, the refractive index of the crystal \(n_{0}\) = 1.66, the effective electro-optic coefficient \(d_{2}\) = 2.2 pm/V, and the crystal length \(L\) = 40 mm. The calculated value of the quarter-wavelength voltage is just 2000 V, which is almost half that of the previous reports. The lower quarter-wavelength voltage of Pockels cell means faster switching speed, and makes it possible for higher repetition rate operation. The experimental setup of the picosecond amplifier is shown in Figure 1, which consists of a picosecond seed source, two optical isolators, a BBO pulse picker, a regenerative amplifier, and one stage traveling-wave amplifier. Figure 1: Diagram of the non-leakage 100-kHz Nd:YVO\({}_{4}\) picosecond regenerative amplifier. The inset is the illustration of the setup. In the present system, the amplifier is seeded with a self-developed semiconductor saturable absorption mirror (SESAM) mode-locked oscillator capable of generating 11.5 ps pulses at a repetition rate of 80 MHz with a single pulse energy of 1 nJ. Picosecond pulse sequence from the seed is 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 regenerative amplifier by eliminating the pulse leakage of the seed sequence. The half-wave plate HWP1 is set to let most of the seed light to \(p\)-polarization and the rest \(s\)-polarization reflected into the photodetector (PD) as feedback signal. After passing through the first stage optical isolator composed of a polarization beam splitter PBS1, a Faraday rotator FR1, and a HWP2, the seed enters into the double BBO crystal Pockels cell PC1 (PCB3S-1342; EKSMA Optics, Vilnius, Lithuania). The size of the two BBO crystals are 3 \(\times\) 3 \(\times\) 20 mm\({}^{3}\).