Comparison of continuum-continuum and Coulomb-laser-coupling delays from visible to midinfrared wavelengths

Attosecond photoionization delays yield time-resolved information about the dynamics of electrons within atoms and molecules. Over the past decade, two pump-probe techniques have become the primary experimental methods for extracting such delays. Both methods use an attosecond XUV pump pulse to initiate the photoionization process, while an infrared laser field is used to modify the photoelectron's final momentum and provide timing information. The initial photoionization step is described by the Wigner delay, which is specific to the ionization target. However, both experimental techniques must account for an additional contribution to the measured delay due to the presence of the infrared field. Such contributions are called the Continuum-Continuum (CC) and Coulomb-Laser-Coupling (CLC) delay for the Reconstruction of Attosecond Beating By Two-photon Transitions and streaking methods, respectively. Here, we compare the various proposed formulas for CLC and CC delays using analytical and numerical methods across a range of wavelengths spanning visible to midinfrared. We show that one of the CC definitions is nearly equal to the CLC delay over a range of photoelectron energies and wavelengths. We furthermore obtain alternate expressions for the CC delays. These expressions are simpler to use and show close correspondence to the CLC delays. Based on this correspondence, we suggest a correction to the CLC delay for low-energy electrons, where the currently used approximation breaks down. Our work provides guidance for when it is valid to treat CC and CLC delays as being equivalent.