## 2 Amplification Properties of Excimers for Long and Intense Short Pulses
### Contrast Issues for Short-Pulse Amplification in Excimers
The former considerations suggest that even in _KrF_--as the best choice among short-pulse excimer amplifiers where \(\beta\approx 1\) --one must face a certain decrease of the gain coefficient for short, intense pulses. This is caused not only by the saturation of the gain in the presence of nonsaturable absorption, but also by the limited access to the population on the B state by the short pulse (for different reasons in the small-signal and saturated regimes, as explained before). A similar correction of the local extraction efficiency (\(\eta\)) curves with the same value of \(K\) is necessary to get the overall local efficiency (\(\eta^{*}\)), as defined by Equation (8). The dependence of \(c^{*}\) and \(\eta^{*}\) on the normalized energy density are shown in Figure 6 for two values of \(g_{0}^{*}/\alpha\); namely for 10 and 15. Actually, the \(\eta(\varepsilon)\) and \(c(\varepsilon)\) quantities, defined by Equations (5) and (6), respectively, are obtained by solving numerically the Equations (1) and (2) coupled differential equations for different initial gain coefficients; for different \(n_{2}(t=0)\) values (for more details, see Section 1.4). It is seen that both curves are dependent on \(g_{0}^{*}/\alpha\); better contrasts and extraction efficiencies can be realized in case of larger \(g_{0}^{*}/\alpha\) values. Since the initial gas mixture and the pumping conditions influence both \(g_{0}^{*}\) and \(\alpha\), both must be optimized for the best ratio. Absorption is mainly caused by the fluorine content of the gas mixture; therefore, the unpumped volume must be minimized, moreover,by optimized pumping, the highest possible gain coefficient must be produced with the lowest possible fluor partial pressure. As seen in Figure 6, the overall contrast coefficient (\(c^{*}\)), depending slightly on the \(g_{0}^{*}/\alpha\) ratio, is  
\[c^{*}(X)=0.46\text{ and } \tag{17}\]  
\[c^{*}(Y)=0.28 \tag{18}\]  
at \(X\) and \(Y\) values of the normalized energy density. Since the optimum energy density, defined by the arrows \(X\) and \(Y\) for pre- and power amplifiers, is generally adjusted for the output-end of the amplifier, in both cases, the \"integrated\" value of \(c^{*}\) is somewhat larger for amplifiers of finite \(g_{0}L\) product (where the \"input-end\" of the amplifier tends to increase the integrated value). For this reason, in our following considerations,  
\[c^{*}_{pre}=0.5\text{ and } \tag{19}\]  
\[c^{*}_{power}=0.3 \tag{20}\]  
values are used for the evaluation of the performance of _KrF_ preamplifiers and power amplifiers, respectively. Then, a similar consideration can also be done for the other two excimers; for _XeCl_ and _XeF_. In both cases, measuring \(K\) and calculating the energy density dependence of \(\eta^{*}\) and \(c^{*}\) of the active media, thus \"separating\" the effect of the B and X states to the gain, makes it possible to define whether transient ground-state absorption (with a given \(\sigma_{a}\) absorption cross-section) occurs at all, and whether its contribution dominates over the eventual initial (nonsaturable) absorption of the active medium. In our calculations performed both for _XeCl_ and _XeF_, the initial nonsaturable absorption of the medium (\(\alpha\)) could be neglected for two reasons: at the longer wavelength of these excimers, this kind of absorption was found to be much smaller than in the _KrF_ case (\(g_{0}/\alpha\gg 15\)), moreover, its effect occurs in a relatively high energy density range, which is hardly accessible due to the \"early-emerging\" saturation of short-pulse amplification, where the effect of the transient ground-state absorption dominates (deteriorates) both the overall efficiency and contrast coefficient. Figure 6: Overall gain contrast coefficient \(c^{*}\) and overall extraction efficiency (\(\eta^{*}\) ) as a function of the normalized energy density (\(\epsilon^{*}\) ) in a _KrF_ amplifier. The solid and dashed curves belong to \(g_{0}^{*}/\alpha=10\) and \(15\), respectively.