Selection Rules for Three- and Four-Photon Raman Interactions

Abstract

The dipole moment induced by a radiation field may be expanded in terms of the electric field vector. The third‐ and fourth‐rank tensors in this expansion, $\beta$ and $\gamma$ , respectively, correspond to three‐ and four‐photon Raman effects. Diagrammatic perturbation theory is used to obtain explicit quantum‐mechanical expressions for the $\beta$ and $\gamma$ tensors. Selection rules for the symmetric $\gamma$ tensor and for the nonsymmetric $\beta$ and $\gamma$ tensors are then calculated for the important molecular point groups. The results are compared with those for the ordinary Raman effect, and conditions necessary for the observation of nonlinear effects are discussed.