Polarization Dependence of Three-Photon Phenomena for Randomly Oriented Molecules

Abstract

We examine the polarization dependence of phenomena involving the interaction of three photons and a molecule, in the regime where the interaction is complete before the molecule has time to rotate. We obtain an explicit general formula for the orientation average of the observed intensity, which will be applicable to a randomly oriented sample of molecules. The results apply to simultaneous three‐photon absorption, hyper‐Raman or double quantum scattering, or other simultaneous three‐photon effects in fluids. In viscous media the results apply to sequential three‐photon absorptions or to simultaneous two‐photon absorption followed by fluorescence, and to three‐step photochemical processes in solid matrices. An experimental procedure is given for determining all the available molecular parameters of such processes. Certain simplifications of the general procedure arise in special cases. In all cases the formulas obtained are of the form ${\mathrm{I=〈|\lambda }}_{\mathrm{A\mu B\nu C}}{T}_{\mathrm{ABC}}{|}^2{\mathrm{〉=P}}_i({\lambda }{\mu }{\nu }{\mathrm{)\hspace{0.17em}M}}_{\mathrm{ij}}{Q}_j({T})$ , where I is the intensity of the effect, $({\lambda }\mathrm{,\hspace{0.17em}}{\mu }\mathrm{,\hspace{0.17em}}{\nu })$ are the polarization vectors, T is the three‐photon tensor, the $P_i({\lambda }\mathrm{,\hspace{0.17em}}{\mu }\mathrm{,\hspace{0.17em}}{\nu })$ are a set of polarization parameters, the Q_j (T) are a set of molecular parameters, and M_ij is an averaging matrix. The P_i, M_ij, and Q_j are given explicitly for all cases considered. Thus the polarization dependence problem has been reduced to a linear algebra problem.