### Picosecond Gain Dynamics of Excimers  
The additional (formerly not considered) issue leading to reduced gain and intensity contrast for the signal pulse is connected to the gain dynamics of _KrF_, _XeCl_, and _XeF_, which was studied earlier, extensively, from the point of view of energy extraction only [15; 46; 50]. In Figure 5a-c, the logarithm of the gain is shown versus the delay between a saturating and a probe pulse for _KrF_, _XeCl_, and _XeF_. In Figure 5a, the gain of _KrF_ is followed over the first 300 ps after passage of the saturating pulse. After the initial drop, the gain recovers with a \(\tau=57\) ps time, constant to 25% of its initial value. Figure 5: Logarithm of the gain in _KrF_ (**a**), in _XeCl_ (**b**) and in _XeF_ (**c**), versus the delay between the saturating and the probe pulse, followed over a 300 ps time window (based on [15; 46]). For comparison, the result of the same measurements for _XeCl_ and _XeF_ shows that, with _XeCl_, there is also a gain recovery with a similar time constant (\(\tau\) = 53 ps), but with a much larger amplitude (65%). Compared to the previous two cases for _XeF_, the gain recovers with larger time constant (\(\tau\) = 85 ps) and with an even larger amplitude (85%). When these measurements were repeated with pump and probe beams of parallel and orthogonal polarization, the difference of the gain in the first picosecond is revealed to be a molecular reorientation effect [46]. From these results, a molecular reorientation time of \(T/4\) = 1.1 ps and 0.7 ps is obtained for _XeCl_ and _KrF_, respectively. In all cases, the recovery of the gain is the evidence of leftover optical energy in the active medium; meaning that some part of the energy of the excited molecules is not accessible by subpicosecond pulses, only by pulses of sufficiently longer durations than the corresponding recovery time. The observed gain recovery was attributed to rotational relaxation in the B state and to C \(\rightarrow\) B relaxation, with possible contribution of the incomplete relaxation (therefore, transient population) of the X state. The latter assumption was expected to be valid, mainly for _XeCl_ and _XeF_, where the slightly bound X state can be populated by the short and intense saturating pulse; thus, its reabsorption also contributes to the limited energy extraction. Since the density of accessible molecules in the B state is coupled to the logarithm of the small-signal gain, the gain coefficients for short (\(g_{0}\)) and long pulses (\(g_{0}^{*}\)) are expected to be different. This, however, leads to more pronounced amplification of the long temporal noise than that of the short signal pulse. This phenomenon was already studied in [51], where, for the estimation of the ratio (\(K\)) of the small-signal gain coefficients for short and long pulses (\(K=\frac{g_{0}}{g_{0}^{*}}\)), a simple equation was used, based on the measurement of the short pulse gain (\(G_{short}\)) and the ASE energy (\(E_{\rm ASE}\)). Unfortunately, this method resulted in an inaccurate and unexpectedly high value for \(K\), i.e., \(K=0.9\)\(\pm\) 0.3. The reported high value of \(K\) (nearly 1) predicts a similar gain for both the short signal pulse and for the ASE, which, however, is in contrast to our experimental observations.