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Phase and time delays of atomic above-threshold ionization are usually experimentally explored by the reconstruction of attosecond harmonic beating by interference of two-photon transitions (RABBIT) technique. Theoretical studies of RABBIT rely on the perturbative treatment of the probe (NIR or visible) laser pulse with respect to the atomic electric field and the pump composed of a train of attosecond pulses made of several harmonics with frequencies multiple of the probe fundamental frequency. In this work we present a semiclassical non-perturbative description of the phase delays for the emission of electrons from hydrogen atoms based on the strong-field approximation as the relative phase between pump and probe pulses is varied, where more than two photons are involved. Ionization times are calculated within the saddle-point approximations and serve to individualize the different electron wave packets that produce the RABBIT interferometric scheme. We observe different behaviors of the phase delays at different intensities of the probe. For example, for moderate and intense probe fields, the harmonics and sidebands happen to be in phase ($ \gtrsim 4 \times 10^{11}$ W/cm$^2$). In turn, when the probe field is sufficiently weak, we recover the well-known rule of thumb for the phase delays developed within the perturbative RABBIT theory [see D. Guenot et al. Phys. Rev. A 85, 053424 (2012)]. We show that the intracycle interference of the different paths contributing to the final energy (sideband or high harmonic) is responsible for the different behaviors of the interference pattern. Comparisons with the numerical solution of the strong-field approximation and time-dependent Schr\"odinger equation confirm the reliability of our semiclassical non-perturbative theory., Comment: 42 pages, 12 figures, to be sent for peer reviewed publishing

Phase and time delays of atomic above-threshold ionization were recently experimentally explored in an $\omega -2\omega$ setting [Zipp et al, Optica 1, 361 (2014)]. The phases of wavepackets ejected from argon by a strong $2\omega$ pulse were probed as a function of the relative phase of a weaker $\omega$ probe pulse. Numerical simulations solving the time-dependent Schr\"{o}dinger equation (TDSE) displayed a sensitive dependence of the doubly differential momentum distribution on the relative phase between the $\omega$ and $2\omega$ fields. Moreover, a surprisingly strong variation of the extracted phase delays on the intensity of the probe pulse was found. We present a semiclassical strong-field description of the phase delays in the emission of electrons in an $\omega -2\omega$ setting and apply it to atomic hydrogen. Non-perturbative effects in both the $2\omega$ pump and the $\omega$ probe field are included. The semiclassical description allows tracing phase delays to path interferences between emission during different points in time of emission within the temporal unit cell of the two-color laser field. We find good agreement between the semiclassical saddle-point approximation, the full strong field approximation (SFA), and previous results applicable in the perturbative limit of probe fields. We show that the RABBIT-like perturbative description of phase delays breaks down for stronger fields and higher-energy electron emission. In this regime, characterization of the ionization signal requires an entire ensemble of phase delays {$\delta_i(E)$} with $i=1,2,\ldots$ the difference in photon numbers of the strong $2\omega$ field involved in the interfering paths. Comparison between SFA and TDSE calculations reveals the influence of the Coulomb field even in this strong-field scenario., Comment: 32 pages, 12 figures