Complex-gate all-optical frequency-resolved optical gating for ultrabroadband isolated attosecond pulse characterization

We experimentally demonstrate all-optical frequency-resolved optical gating (AO-FROG) for the characterization of ultrabroadband isolated attosecond pulses (IAPs) generated by a mid-infrared sub-cycle laser field. By extending the AO-FROG framework beyond the conventional phase-only modulation approximation, we develop a strong-field approximation (SFA)-based theoretical framework and show that the weak perturbing field induces both phase and amplitude modulations during high-order harmonic generation. A complex-valued gate function is therefore required for accurate pulse reconstruction. Using a 2.26-$μ$m sub-cycle driving laser, we characterize IAPs spanning 100-180 eV in argon. The measured AO-FROG traces exhibit delay-dependent spectral modulations arising from perturbation-induced modifications of the electron trajectories and ionization probability. SFA simulations reproduce the experimental observations and confirm the importance of including ionization-induced amplitude modulation. The reconstructed temporal and spectral properties reveal an IAP duration of approximately 300 as and its spectral phase, providing access to the attosecond chirp of the generated pulses. Our results establish AO-FROG as a promising approach for temporal characterization of ultrabroadband attosecond sources driven by long-wavelength infrared fields.