# Temporally Programmable Hybrid MOPA Laser with Arbitrary Pulse Shape and Frequency Doubling
## 3 MOPA Laser with Arbitrary Pulse Shape
### Arbitrary Pulse Shape Output for the MOPA System  
To further boost the output power and obtain the desired output pulse shapes, another two Nd:YVO\({}_{4}\) amplifiers were cascaded after the first Nd:YVO\({}_{4}\) amplifier. The output power of 7.3 W was scaled up to 21 W and 41.4 W by the two amplifiers, respectively. With the help of a beam propagation  
Figure 4: (**a**) Pulse shape transfer function from experiment and simulation. (**b**) Output pulse shape from experiment and simulation with the same input pulse shape.  
Figure 5: Compensation of the pulse distortion. (**a**) Input pulse shape (three pulses); (**b**) output pulse shape with amplified power.  
analyzer (Spiricon M2-200-FW-SCOR, Ophir, Israel), the beam quality was measured to be very good. The M\({}^{2}\) factor were 1.150 and 1.113, respectively, at horizontal and vertical directions. Due to the setup of the amplifiers, the ASE and parasitic oscillation was not significantly observed at the output of the whole system, both from the pulse shape and the spectrum. The optical signal-to-noise ratio (OSNR) was as high as 42 dB. The spectral line-width (3 dB) was so narrow that it exceeded the resolution of the optical spectrum analyzer (Agilent 86142B, Palo Alto, CA, USA). Many times, the resolution was measured to be less than 0.060 nm. Therefore, we concluded that the spectral linewidth was narrower than 0.06 nm.  
The pulse shapes were recorded for each amplifier as shown in Figure 6. The pulse shape distorted after each amplifier resulting from different gains for the leading and trailing edge. The leading edge first consumes the inversion population resulting in a smaller gain for the falling edge and then pulse distortion.  
Several desired pulse shapes were obtained after the third amplifier through the same method. The initial pulse gain for the MOPA system was calculated as 34.7 dB. As shown in Figure 7, four common pulse shapes, including multiple-step, parabolic, Gaussian, and flat-top pulses, were introduced. The corresponding input pulses are shown in the insets.  
To enhance the peak power, the repetition rate was set to be 40 kHz, and the pulse duration was 40 ns. The output power was 38.3 W, corresponding to the pulse energy of 0.96 mJ, with the input power of 13.5 mW. Using the same method, square, parabolic, and Gaussian pulses were obtained for the MOPA system, as shown in Figure 8. The highest peak power of 41.6 kW, much larger than that in [9], was achieved by the Gaussian pulse.  
Limited by the rising time and falling time of the arbitrary waveform generator (AWG), the leading edge and falling edge of the pulses could not be controlled very precisely, especially for the square pulses with fast leading edges and falling edges. In addition, the control of the null point of the EOM and the inadequate sampling rate of the AWG led to the small mismatch of the targeted pulse shape.  
Figure 6: Pulse evolution for each amplifier.  
Figure 8: Desired pulse shapes for the 1064 nm and 532 nm at a PRF of 40 kHz. Target is for 1064 nm. (**a**) Square; (**b**) Parabolic; (**c**) Gaussian. (Input pulse shape is given in the inset).  
Figure 7: Desired pulse shapes for the 1064 nm and 532 nm at a PRF of 100 kHz. Target is for 1064 nm. (**a**) Multiple-step; (**b**) Parabolic; (**c**) Gaussian; (**d**) Square. (Input pulse shape is given in the inset).