Theory of Angular and Polarization Correlation in Tandem Two-Photon Processes: Application to Photoselection

Abstract

To facilitate the interpretation of photoselection and photochemical experiments that depend on light intensity, generalized intensity distribution and polarization correlation formulas are derived. These are expressed in terms of Euler angles and multipole transition moments taking into account (1) molecular multipole radiation up to any order, inclusive of their coherent interference, (2) angular distribution of radiation for a given polarization, (3) application to molecules of arbitrary point-group symmetry, (4) arbitrary orientation of the second photon (pertaining to the daughter molecule) with respect to the first photon (pertaining to the parent molecule). For application to oriented molecular systems, examples of the angular characteristics of multipole moments responsible for a fixed polarization, are given up to quadrupole, inclusive of interference effects. It is emphasized that, in contrast to electric dipole radiation where the polarization is unique, for multipole radiation, both polarization and propagation directions must be specified, and that the commonly known dipole or quadrupole intensity which come from space average must be used with caution. For random molecular systems, the space average of the product of intensities for the two tandem and physically distinct one-photon processes are shown to contain “cross” terms, which otherwise vanish, if the space average of intensity were taken independently for the first (parent) and the second photon (daughter molecule). The cross terms are shown to be the consequence of the definition of light intensity for an arbitrary choice of the molecular coordinate system (vs the choice of the principal coordinate system) and of using the same coordinate system for the parent and the daughter molecule. In the space average over the product of four rotation matrices (vs four direction cosines for dipole radiation), use was made of the Clebsch–Gordan series for the coupling among these rotational transformation matrices. The intensity (or probability) products of the two tandem and distinct one-photon processes were then obtained as functions of bipolar harmonics of the transition moments. The coupling of these bipolar harmonics, in turn, gives rise to the polarization correlation between the parent and the daughter molecule. Specific examples, up to electric and magnetic quadrupole, are given for viewing the daughter molecule in directions parallel as well as perpendicular to the incident (first) photon. Also given are the cases of the two photons being in different radiation modes and of different wavelengths.