EXCITONS IN CONFINED GEOMETRIES - SIZE SCALING OF NONLINEAR SUSCEPTIBILITIES

The third-order nonlinear optical response of one-dimensional molecular aggregates of arbitrary size is calculated using equations of motion for single-exciton and two-exciton variables. These equations map the system onto the dynamics of N(N + 1)/2 coupled nonlinear oscillators, where N is the number of molecules in the aggregate. The scaling of the generalized third-order hyperpolarizability gamma(3) with N is analyzed in detail. The complete wave vector and frequency dependence of gamma(3) is maintained and cooperative radiative decay (superradiance) is incorporated. Comparison is made with the density-matrix approach which provides a fully time-ordered expression.