Dipole-quadrupole polarization correlation in photo-selection

Abstract

The intensity and polarization correlation formulas for an electric dipole-electric quadrupole tandem two-photon process are explicitly developed using a general spherical-tensor formulation for multipole-radiation of any order. This is applicable to relative polarization studies in photoselection or photoluminescence studies. The molecules are oriented randomly with respect to the laboratory coordinates defined by the radiation field, and the intensity is written in terms of transition matrix elements taken over coordinates of the parent molecule (assumed to interact with one of the photons through the quadrupole mode) and the daughter molecule (assumed to interact with the other photon through the dipole mode). Some bipolar harmonics through the third order needed in the correlation are computed. As an alternative to the above spherical tensor formulation, we expressed the individual one-photon intensities for electric dipole and electric quadrupole transitions in terms of direction cosines between laboratory and molecular coordinates. Then, the two-photon intensities in terms of sixth power products of direction cosines are averaged over all molecular orientations in space. The two formulations yield identical results in terms of matrix elements over cartesian coordinates. This dipole-quadrupole correlation is evaluated for molecules of a few common point group symmetries.