## 3 Results and Discussion
However, above the lasing threshold, the pulse photon density achieves large values, and significantly depletes the population of level 2 (Figure 9b), which is accompanied by an increase of the level 1 pop  
Figure 8: Numerically calculated dependence of the output power on time for a 2 (m) long fiber with the facet reflectivity for signal wave at \(z=L\) switched between 0.04 and 0.2 and \(T_{tr}=200\) (ns): (**a**) At pump power of 1.2 (W); (**b**) At pump power of 1.5 (W); (**c**) At pump power of 2 (W); (**d**) At pump power of 8 (W). the steady state after the depletion is very slow, taking more than 1 ms. This slow recovery process can be sped up by increasing the pump power, as can be observed by comparing the results shown in Figure 9b,d. The effect of photon density reduction accompanied by slow recovery of the energy level populations puts a limit on the maximum repetition rate of a stable pulse train generated by a Q-switched laser. Namely, before the next pulse can be generated, the photon density of the signal wave has to return nearly to the steady state equilibrium. Otherwise, there is no guarantee that the generated pulse train will be stable and have no jitter. A value of the photon intensity before the onset of the switching pulse, which is significantly lower than in the steady state, would translate into a longer time needed to build up the signal power within the cavity, and hence, could result in a larger pulse delay for the second pulse than for the first. Figure 10 shows numerically calculated dependence of the pulse output power on time for a 2 m long fiber, with the facet reflectivity for signal wave at \(z=L\) switched between 0.04 and 0.2 at four selected values of the transition time \(T_{tr}\): 100 ns (a), 50 ns (b), 400 ns (c) and 600 ns (d). The pump power used in these simulations was 8 W. One can observe that reducing the transition time below 200 ns has no significant impact on the pulse appearance. The only effect observed is a small change of the pulse position. It is interesting to note that the 200 ns switching time is sufficient to obtain optimal performance in a cavity with round trip time of approximately 40 ns, and 5 fold change of the facet reflectivity during switching. A significant reduction of the peak pulse power occurs, however, when the transition time is increased to 400 ns; a further reduction of the peak pulse power takes place by  
Figure 9: Numerically calculated dependence of the energy level populations on time for a 2 (m) long fiber with the facet reflectivity for signal wave at \(z=L\) switched between 0.04 and 0.2 and 0.2 and \(T_{tr}=200\) (ns): (a) At pump power of 1.2 (W); (b) At pump power of 1.5 (W); (c) At pump power of 2 (W); (d) At pump power of 8 (W). increasing the transition time to 600 ns. However, we note that even with a 600 ns switching pulse transition time, a high peak power, and a fairly narrow Q-switched pulse, can still be generated. In Figure 11, a study of the impact of the fiber length on the pulse shape is performed. These results show that the fiber length has a major impact on both the pulse width and pulse peak power. By reducing the fiber length, one reduces the pulse round trip time, and thus allows for a faster buildup of power within the fiber laser cavity. This results in the generation of shorter pulses, which is also accompanied by a higher value of the peak power. Thus, one has to be cautious when reducing the fiber length whilst trying to reduce the pulse duration, because the peak power increases concurrently, and high photon density within the fiber laser cavity may damage the fiber. Finally, a numerical simulation is performed for calculation of a train of 5 Q-switched pulses. These results demonstrate the importance of the spontaneous emission, even if the fiber laser operates above the threshold before and after switching.