Cooperative radiative decay in the nonlinear optical response of excitonic nanostructures

The nonlinear susceptibility ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ and the four-wave mixing signal from assemblies of molecules with nonoverlapping charge distributions and an arbitrary geometry are calculated using Green’s-function techniques. At low molecular density and under off-resonant excitation we recover the local-field approximation. The role of retarded interactions and cooperative spontaneous emission in the electrodynamics of confined excitons in molecular quantum wells is discussed.