Theory of three-photon photoselection with application to the hexagonal point groups

The general problem of the polarization dependence of an orientationally averaged four-photon process in a rigid isotropic medium is examined. The theory is then reduced to the special case of three-photon photoselection (3PP) in which an excited state is first created by the simultaneous absorption of three identical photons and then the system is interrogated by a one-photon probe step (absorption or emission). When the probe signal is measured as a function of both excitation and probing polarizations, five unique transition tensor invariants can be determined. These five invariants provide a characteristic signature of the symmetry of the initial three-photon absorption (3PA). A symmetry analysis is illustrated within the hexagonal point groups where it is demonstrated how the measurement of a single photoselection polarization ratio formally allows, with one exception, a unique symmetry assignment to be made for any three-photon allowed transition. This measurement makes use of circularly polarized excitation with variably polarized probing. The polarized probe step in a 3PP experiment provides information concerning the three-photon transition beyond that available from a simple polarized 3PA study.