Fig. 1. (a) Scheme of a double-pass laser amplifier: , , and are the equivalent fluences of the input and output energy in the forward propagating direction in gain media 1 and 2, respectively. Similarly, , , and are the equivalent fluences of the input and output energy in the backward propagating direction in gain media 1 and 2, respectively. The temporal lengths and calculated from the geometry of the amplifier determine the time delay between each input. (b) The front part of the amplified input pulse is reflected on the mirror and is overlapped with the rear part of the input pulse in gain media 1 and 2, according to and .

Fig. 2. (a) Numerical F–N equation can be used to calculate the amplification during the whole duration of the input pulse according to the temporal sequence. , , and are the input and output fluences, effective pump and spontaneous emission, respectively. (b) Temporal profile of the flash-lamp pulse whose effective pump energy is J. (c) Variation of the stored energy in the gain medium pumped by a flash lamp: the spontaneous emission shows an exponential attenuation described by the fluorescence lifetime ( ) of the laser-active ions. The solid green line was obtained by considering spontaneous emission, while the green dashed line without.

Fig. 3. Simulation parameters: the input pulse width, given by its FWHM : 2 ns to 280  s (red) and the input pulse injection time, : s to s (dashed).

Fig. 4. The extraction efficiency as a function of the input pulse width, where s (blue), s (orange), s (red), s (green) and s (purple) (a) without considering spontaneous emission, while (b) with considering. (c), (d) Trend of the stored energy in Nd:YAG rod1 and Nd:YAG rod2 during the amplification, where and ns–280  s. (e) Optimal pulse width and injection time of the input pulse resulting in the maximum extraction efficiency. (f) Normalized input and output pulse shapes at the optimal input conditions in (e).