Polaritons and retarded interactions in nonlinear optical susceptibilities

The role of retarded intermolecular interactions (polariton effects) in the nonlinear optical susceptibilities of condensed phases is studied. A systematic method for calculating these susceptibilities is developed, based on the derivation of reduced equations of motion which couple the electronic variables to the Maxwell (internal) electric field E. The susceptibilities are obtained by iteratively solving these equations in powers of E. Thus, the common introduction of intermediate susceptibilities with respect to either the external or the local electric field is avoided. Our method allows for the incorporation of polariton dynamics into the equations of motion. A clear distinction between microscopic and macroscopic polariton effects is made. Explicit forms for the linear (χ(1)) and second order (χ(2)) susceptibilities in molecular crystals are derived, which microscopically account for polariton–phonon scattering. Our theory provides an explanation for a recent series of linear and nonlinear optical experiments in naphtalene crystals which were found to contradict existing theories of nonlinear susceptibilities.