# Attosecond Streaking Time Delays: Finite-Range Interpretation and Applications
## 1 Introduction  
To resolve dynamics in matter on ultrashort time scales, a variety of pulse technologies, e.g., ultrashort electron pulses, femtosecond (1 fs = 10\({}^{-15}\) s) and attosecond (1 as = 10\({}^{-18}\) s) laser pulses, and X-ray free electron laser pulses have been developed. Among these, attosecond pulses are, in general, not yet intense enough to be used in pump-probe measurements. To gain resolution on the attosecond time scale, a number of methods have been explored in which a combination of an attosecond extreme ultraviolet (XUV) pulse and a second femtosecond (near-)infrared (IR) laser pulse is applied (for recent overviews, see e.g., [1; 2; 3]). One of these techniques is the attosecond streak camera method [4], in which an attosecond pulse photoionizes a target (via the absorption of a single photon) and a few-cycle infrared pulse is used to modulate the final momentum of the photoelectron. By varying the relative delay between the two pulses, an oscillating streaking pattern for the final photoelectron momentum \(\mathbf{k}_{f}\) is observed, which can be represented by:  
\[\mathbf{k}_{f}^{(n,l)}(t_{i})=\mathbf{k}_{0}-\mathbf{A}_{s}(t_{i}+\Delta t_{s} ^{(n,l)}), \tag{1}\]  
where \(\mathbf{k}_{0}\) is the field-free momentum of the electron, initially bound in the \(|n,l\rangle\) state of an atom, upon release into the streaking field, represented by the vector potential \(\mathbf{A}(t)\), at time \(t_{i}\). The offset \(\Delta t_{s}^{(n,l)}\) with respect to the release time of the photoelectron in the argument of the vector potential is typicallyreferred to as the streaking time delay. Hence, the time delay is visualized as the offset in the streaking trace of the momentum of the photoelectron propagating in the Coulomb potential as compared to that of a free photoelectron (c.f., Figure 1). We note that, in an attosecond streaking experiment (e.g., [5]), the temporal information is usually gained via the comparison of streaking traces from photoelectrons exposed to the same streaking field, but which populated different orbitals initially. This corresponds to the difference of streaking time delays from the two states involved (c.f., Figure 1). However, in theoretical analysis, the focus of studies is primarily the streaking time delay \(\Delta t_{s}^{(n,l)}\), as defined in Equation (1). Since in the remainder of the article the initial state is typically implied, we simply refer to this quantity as \(\Delta t_{s}\) below. Various theoretical work has established that the streaking time delay obtained in numerical simulations can be written as a sum:  
\[\Delta t_{s}=\Delta t_{WS}+\Delta t_{CLC}, \tag{2}\]  
where \(\Delta t_{WS}\) is the Wigner-Smith time delay [6; 7] and \(\Delta t_{CLC}\) is a term that accounts for the coupling between the streaking field and long-range Coulomb potential. Justification of this approach as well as theoretical analysis of additional effects, such as multielectron contributions or the role of the attochirp, have been discussed in review articles recently (e.g., [8; 9; 10]). Here, we focus on a review of recent analysis of the streaking time delay via the investigation of the electron dynamics in the streaking field after transition of the photoelectron into the continuum upon absorption of an XUV photon. Classical estimates and predictions of model formulas related to this analysis have been found to be in good agreement with results of ab initio numerical simulations. This established a basis to use the approach to gain insights into the interpretation and analysis of various aspects of the streaking time delay in photoionization. Specifically, it leads to the interpretation that the delay in photoionization is only accumulated until the streaking pulse ceases. Hence, the streaking measurement probes the (long range) potential of the parent ion over a _finite range_ only.