Identifying the contributions of multiple-returning recollision orbits in strong-field above-threshold ionization

We calculate the photoelectron momentum distributions (PMDs) from strong-field above-threshold ionization of Ar in the co-linearly polarized two-color laser fields consisting a strong fundamental component and a much weaker second harmonic by solving the time-dependent Schrödinger equation. Utilizing the recently introduced phase-of-the-phase (PP) spectroscopy, we analyze the relative phase dependence of the PMDs of the recollision electrons and the jumps in the PP spectroscopy are observed. With the semi-classical model, we demonstrate that the phase jumps originate from the competition between the orbits where recollision occurs at different returnings. Thus, the relative contribution of the multiple-returning recollision orbits is unambiguously identified with the PP spectroscopy. Additionally, we show that the relative contribution of the multiple-returning recollision orbits depends on the laser wavelength and ellipticity. In elliptically polarized laser field, the yield of the high-energy photoelectrons favors the contribution of the second-returning recollision orbits. In 1600-nm laser field, the PP spectroscopy indicates that the relative contribution of multiple-returning recollision orbits is strongly sensitive to the electron energy.