Nonlinear optical response in condensed phases: A microscopic theory using the multipolar Hamiltonian

A general scheme is presented for calculating the nonlinear optical response in condensed phases that provides a unified picture of excitons, polaritons, retardation, and local-field effects in crystals and in disordered systems. A fully microscopic starting point is taken by considering the evolution of the quantized radiation-matter system described by the multipolar (µ•D┴) Hamiltonian. For a molecular system with localized electronic states we derive equations of motion in which the instantaneous intermolecular interactions are explicitly recovered and the interaction with the Maxwell electric field is of the µ•E┴ type. It is shown that with total neglect of retardation, these equations lead to the usual expressions for nonlinear optical susceptibilities in terms of equilibrium correlation functions of the polarization field of the molecular system. A mean-field approximation for these equations of motion yields the commonly used local-field expression. Finally, a procedure is proposed for calculating the optical response that fully accounts for retardation, based on a hierarchy of equations of motion for polaritons.