Abstract
A framework is presented to calculate rotational line intensities in doubly-enhanced four-wave mixing (DEFMI)-spectroscopy for diatomic molecules following Hund's case a. The results are extended to include cases where one of the two intermediate states is slightly displaced from exact resonance. The model is shown to describe correctly the intensity patterns observed in DEFMI-spectra of CO. It is also successfully applied to evaluate the two-photon resonance-enhanced third harmonic generation (THG) line intensities in a case where a molecular transition is accidentally near-resonance at the three-photon level. Finally, it is shown that saturation greatly reduces the expected intensities if high laser powers are used.