We extend the powerful frequency-domain analysis of femtosecond two-photon absorption to the intermediate-field regime of considerable absorption yields, where additionally to the weak-field nonresonant two-photon transitions also four-photon transitions play a role. Consequently, we rationally find that the absorption is enhanced over the transform-limited pulse by any shaped pulse having a spectral phase that is antisymmetric around one-half of the transition frequency and a spectrum that is asymmetric around it (red or blue detuned according to the system). The enhancement increases as the field strength increases. The theoretical results for Na are verified experimentally.

• Received 8 June 2007

DOI:https://doi.org/10.1103/PhysRevA.77.021403