Irreducible tensors and selection rules for three-frequency absorption

Abstract

In this paper rate equations and selection rules are derived for the most general case of three‐photon absorption, where the photons all have different frequencies and directions of propagation. The rate equations are re‐expressed in terms of irreducible tensor products, and the relationship between these and the more familiar isotropic molecular parameters is given in full for the first time. The selection rules are examined in detail and a classification scheme for the allowed transitions is given together with a method of experimentally distinguishing between the classes. It is shown that once assignment of a transition to one of the 11 possible classes has been carried out, the symmetry of the excited state can in many cases be unambiguously identified. The connection with the classification schemes previously developed for single and double‐beam three‐photon absorption is also discussed, and finally, a special experimental arrangement is proposed which should give rise to a spectrum in which the only transitions to occur are those forbidden by both single and double‐beam excitation.