Optimization of the pulse width and injection time in a double-pass laser amplifier

We have optimized the input pulse width and injection time to achieve the highest possible output pulse energy in a double-pass laser amplifier. For this purpose, we have extended the modified Frantz-Nodvik equation by simultaneously including both spontaneous emission and pump energy variation. The maximum achieved fluence of the output pulse was 2.4 J/$cm^2$. An input pulse energy of 1 J could be maximally amplified to output pulse energy of 12.17 J, where the optimal values of the pulse width and injection time of the input pulse were 168 {\mu}s and 10 {\mu}s, respectively, with the effective pump energy being 8.84 J.