Kramers–Kronig relation in attosecond transient absorption spectroscopy
The Kramers–Kronig relation (KKR) has a wide range of applications in extreme ultraviolet (XUV) and x-ray spectroscopy. However, the validity of KKR for many of these applications has not been systematically studied, while it is known to require careful attention in nonlinear and pump–probe experiments in optical domain spectroscopy. Here, we study the validity of KKR in XUV attosecond transient absorption spectroscopy pump–probe measurements both experimentally and theoretically using argon Fano resonances as a case study. Experiments are enabled by a phase-resolved method dubbed Complex Attosecond Transient-absorption Spectroscopy (CATS). Although the estimations based on the rotating-wave approximation suggest that KKR violation could be expected in the studied case, our results validate KKR and provide a solid basis for its application in a broad range of attosecond spectroscopy experiments.