## 1 Introduction  
Over the past decade, there has been significant development of high power ultrashort pulse lasers with high repetition rate [1; 2; 3], with applications including nonlinear optical frequency conversion, precise material processing, satellite ranging, and high-intensity physics [4; 5; 6; 7]. Specifically, in ultrashort lasers in the order of picoseconds, their pulse width is smaller than the electron-phonon coupling time of most materials, heat conduction can be decreased substantially during the process of interaction. This decrease is beneficial to fine processing, biological medicine, and historical relic cleaning [8; 9; 10; 11]. Currently, mode-locking is the main approach to obtain the pulse width around \(\sim\)10 ps. However, the pulse energy of the directly generated mode-locked lasers is very low such that it restricts their applications. To solve this problem, different types of laser amplifiers are utilized, in which a regenerative amplifier is considered to be the most effective method for strong amplification of the mode-locked pulses [1; 2; 12; 13]. In most cases, increasing the repetition rate and power can improve the efficiency of laser processing and laser ranging. Therefore, it is not only necessary to increase the single pulse energy but also the repetition rate of the current regenerative amplified lasers. Determined by the parameters of Pockels cell and regenerative cavity, repetition rates from hundreds to mega-Hz have been obtained with output power up to 100 watts. For instance, Nd:YVO\({}_{4}\) picosecond regenerative amplifiers with a repetition rate up to 850 kHz have been demonstrated [14; 15]; other broadband gain materials such as Yb:CaF\({}_{2}\), Yb:CaIGO, Yb:YVO\({}_{4}\), and Nd:LuVO\({}_{4}\) show up to 1.43 MHz repetition rate [16; 17; 18]. Currently, [PERSON] et al. [19] reported the record high repetition rate of 2 MHz for a picosecond regenerative amplifier in Yb:YAG. In general, when the repetition rate is up to 100 kHz, it is very difficult for the Pockels cell to realize the fast and complete switching due to the limitations of high voltage driving supply. This will lead to the leakage of the directly amplified seed pulses in the output that not only introduce optical noise but also increase unnecessary pump power consumption. Especially after traveling-wave amplification, the existence of pulse leakage will further reduce the master-slave pulse ratio of the output and influence the performance of the laser system in applications. For example, in nonmetallic brittle materials processing (viz. artificial crystal, ceramics, and solar panels), the amplified leaking pulses easily cause breakage of the samples because of the excessive heat load; meanwhile, the presence of leaked pulses also results in the reduction of accuracy in laser satellite ranging and laser communication due to the introduction of stray signals. Therefore, it is necessary to eliminate the pulse leakage of regenerative amplifiers used in some specific industrial areas. Nd:YVO\({}_{4}\) crystals as a gain material with sufficient gain bandwidth and a high emission cross section are widely adopted in end-pumping picosecond regenerative amplifiers. Nowadays, fiber coupled high-power laser diode (LD) are an appropriate pumping source for the regenerative amplifier due to their highly compact size and relatively low cost. The pumping of Nd:YVO\({}_{4}\) with 888 nm LD induces less thermal stress gradient along the crystal compared with 808 nm that makes it possible for long time operation of the laser with higher stability [20; 21]. Table 1 presents the physical parameters of Nd:YVO\({}_{4}\) crystal pumped by 808 nm and 888 nm wavelengths [22; 23]. As the data show, the lower fractional thermal loading in 888 nm pump compared with 808 nm wavelength results in the heat reduction and optical efficiency growth.