Decomposition of the transition phase in multi-sideband RABBITT schemes

Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBITT) is a technique that can be used to determine the phases of atomic transition elements in photoionization processes. In the traditional RABBITT scheme, the so-called "asymptotic approximation" considers the measured phase as a sum of the Wigner phase linked to a single-photon ionization process and the continuum-continuum (cc) phase associated with further single-photon transitions in the continuum. In this paper, we explore the possibility of extending the asymptotic approximation to multi-sideband RABBITT schemes. The predictions from this approximation are then compared with results obtained by an {\it ab initio} calculation based on solving the time-dependent Schrödinger equation for atomic hydrogen.