Multiphoton rotational line strength in diatomic molecules and for states with Hund’s case-(a) or case-(b) coupling

The n-photon rotational line strength is studied for diatomic molecules and for transitions between two states which both belong to Hund's case-(b) coupling, as well as for transitions between a state with Hund's case-(a) coupling and a state with Hund's case-(b) coupling. We suppose that all the absorbed photons have the same energy and the same polarization state which can be linear or circular. Explicit forms for the rotational line factors of any spin multiplicity are presented and selection rules are obtained from angular momentum conservation arguments. The number and labeling of the n-photon rotational branches have also been considered.