Time-Dependent Theory of Electron Emission Perpendicular to Laser Polarization for Reconstruction of Attosecond Harmonic Beating by Interference of Multiphoton Transitions

We present a time-dependent nonperturbative theory of the reconstruction of attosecond beating by interference of multiphoton transitions (RABBIT) for photoelectron emission from hydrogen atoms in the direction perpendicular to the laser polarization axis. Extending our recent semiclassical strong-field approximation (SFA) model developed for parallel emission [López et al., Phys. Rev. A 110, 013104 (2024)], we derive analytical expressions for the transition amplitudes and demonstrate that the photoelectron probability distribution can be factorized into interhalf- and intrahalfcycle interference contributions, the latter modulating the intercycle pattern responsible for sideband formation. We identify the intrahalfcycle interference between trajectories born within the same half cycle as the mechanism governing attosecond phase delays in the perpendicular geometry. Our results reveal the suppression of even-order sidebands due to destructive interhalfcycle interference, leading to a characteristic spacing between adjacent peaks that doubles the standard spacing observed along the polarization axis. Comparisons with numerical calculations of the SFA and the ab initio solution of the time-dependent Schrödinger equation confirm the accuracy of the semiclassical description. This work provides a unified framework for understanding quantum interferences in attosecond chronoscopy, bridging the cases of parallel and perpendicular electron emission in RABBIT-like protocols.