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We extend the powerful frequency-domain analysis of femtosecond two-photonabsorption to the intermediate-field regime, which involves both two- andfour-photon transitions. Consequently, we find a broad family of shaped pulsesthat enhance the absorption over the transform-limited pulse. It includes anyspectral phase that is anti-symmetric around half the transition frequency. Thespectrum is asymmetric around it. The theoretical framework and results for Naare verified experimentally. This work opens the door for rational femtosecondcoherent control in a regime of considerable absorption yields.

Enhancement of Intermediate-Field Two-Photon Absorption by Rationally-Shaped Femtosecond Pulses