# Temporally Programmable Hybrid MOPA Laser with Arbitrary Pulse Shape and Frequency Doubling
## 1 Introduction  
In the fields of optical sensing and Lidar applications, a long pulse duration, a good pulse shape, as well as a narrow spectral linewidth are required to achieve high precision measurements [1; 2; 3; 4; 5]. Master oscillator power amplifier (MOPA) systems seeded by a modulated semiconductor diode is a cost-effective approach to obtaining the above parameters. However, the gain saturation effect of amplifiers would cause pulse shape distortion and would shorten the pulse duration in the case of deep saturation. To obtain the required laser parameters for the above-mentioned applications, the negative influence of pulse distortion from MOPA systems should be eliminated. Therefore, the inverse problem on how to obtain the desirable output waveform by actively controlling the input pulse shape and compensating the gain saturation effect should be solved. The general compensating method was firstly proposed by [PERSON] in 1986 in his book Lasers [6]. The key of the method is to get the function \(G(t)\) describing the change of the input waveform, which is directly related to the gain characteristics of the amplifier. Many researchers have reported works on the pre-compensation of pulse distortion in master oscillator fiber power amplifier (MOFPA) systems [7; 8; 9; 10; 11]. Although it is easy to obtain \(G(t)\) and control the pulse shape in fiber amplifiers, the peak power is limited by the nonlinear effect in the fiber [5; 12], especially for the case of narrow spectral linewidth. To overcome the shortage of fiber amplifiers, solid-state amplifiers are introduced in this paper. From the literature investigation, for solid-sate amplifiers, few have proposed a way of obtaining \(G(t)\) and arbitrary output waveforms accurately in theory. Few works have demonstrated compensation of pulse distortion in solid-state amplifiers by experiment. With the help of a complicated computational system Laser Performance Operations Model (LPOM), a square pulse for a huge laser system wasachieved by the group of National Ignition Facility (NIF) [13]. However, the detailed information of the software is not provided by the group. Other software packages for the simulation of the output from an amplification chain include Miro [14] and GLAD [15]. However, they are not easy to access for a high price. In 2015, [PERSON] et al. [16] demonstrated an experimental method of shaping the input pulse of a solid-state MOPA system by introducing a device made up of two polarizers, one Pockels cell and one half-wave plate. However, the shaping ability is restricted to providing arbitrary input pulse, and the device could not compensate the pulse distortion in the case of an arbitrary saturation degree. Although a square pulse shape is demonstrated in the experiment, the difference between the desired pulse shape and the measured one is large due to the non-linear edge of the input pulse. Gain characteristics and pulse shape transfer function are not deduced theoretically for their MOPA system in that paper either. Table 1 shows the detailed information of progress in temporal compensation for saturated amplifiers. Our previous work [17] emphasizes the demonstration of an arbitrary burst envelope for an MOPA laser operating in burst mode, which could be used in chirped amplification. In this study, we obtained arbitrary nanosecond pulse shapes in a solid-state MOPA system made up of three Neodymium doped yttrium vanadate (Nd:YVO\({}_{4}\)) amplifiers. The theoretical method is similar to that in [17]. The pulse distortion was experimentally compensated without a feedback loop. Several particular desired pulse shapes were demonstrated, with a high peak power level and a narrow spectral linewidth. The MOPA laser, compared with the fiber laser, achieved a higher pulse energy and peak power by introducing more solid-state amplifiers, without the limit of a nonlinear effect. Moreover, second harmonic generation (SHG) was demonstrated after the MOPA source, resulting in arbitrary waveforms of the green laser.