# Attosecond Streaking Time Delays: Finite-Range Interpretation and Applications
## 3 Applications
### Relevance of the First Half-Cycle of Streaking Field
For example, \(t_{90\%}\) is defined as  
\[\left|\Delta t_{\mathrm{s}}(t^{\prime}-t_{i})\right|\leq 0.9\left|\Delta t_{ \mathrm{s}}(T_{\mathrm{s}}-t_{i})\right|\qquad\text{for}\quad t^{\prime}\geq t _{90\%} \tag{17}\]  
and \(t_{99\%}\) is analogous. The times \(t_{90\%}\) (stars) and \(t_{99\%}\) (circles) are marked on each of the curves in Figure 5a. As one can see from the comparison, in each case \(t_{90\%}<T/2\), which means that the accumulated time delays \(\Delta t_{\mathrm{s}}\) reaches \(90\%\) of the final value before the end of the first half cycle of the streaking field after transition of the photoelectron in the continuum. Furthermore, it is seen that the rate of convergence within the first half cycle of the streaking field improves as the XUV photon energy increases. The reason for this trend is that, as the kinetic energy of the photoelectron becomes higher, the faster it propagates away from the core. Therefore, by the time the sign of the field changes, due to the large decrease in the magnitude of the Coulomb potential, the remaining terms in the sum are sufficiently small such that they do not contribute significantly to the total value. We have found a similar trend (not shown) if the wavelength of the streaking field is increased. The conclusion that the accumulated streaking time delay achieves \(90\%\) of its final value within the first half cycle of the streaking pulse holds independent of the streaking pulse duration. This can be seen from the results in Figure 5b, in which the times \(t_{90\%}\) are presented for different pulse durations (symbols) as a function of the XUV frequency. For comparison, \(T/4=27.5\) a.u. (horizontal green lines) and \(T/2=55\) a.u. (horizontal blue dashed line) are also indicated. Again, for each case studied, we find that \(t_{90\%}<T/2\). Therefore, overall the results of our theoretical analysis support the assumption by [PERSON] et al. (2016) that the time delay is essentially obtained within the first half-cycle of the streaking field after the transition of the photoelectron in the continuum. Finally, we also consider the different contributions to the time delay (short-range, Coulomb-phase and logarithmic, see Equation (11)), separately. In Figure 5c, we compare the times at which each of these contributions reaches \(90\%\) of its final value with each other and with the time \(t_{90\%}\) for the total accumulated time delay. The results clearly show that it is the long-range logarithmic term (diamonds) that essentially determines the time after transition of the photoelectron in the continuum, at which the full time delay (stars) approaches its final value. On the other hand, the short-range (circles) and Coulomb (squares) terms converge much faster, clearly within much less than one quarter cycle of the streaking pulse (solid line). This is in agreement with the results discussed in Section 3.1 that the streaking pulse has a small effect on these two contributions to the streaking time delay. Furthermore, it supports another assumption in Ref. [26] that the information about the differences between short-range parts of different atomic potentials is incorporated in the streaking time delay accumulated within the first quarter cycle of the streaking field after emission of the photoelectron in the continuum.