Dynamic characteristics of coherent and population grating processes in resonant degenerate four-wave mixing

With an aim of understanding dynamic characteristics of the degenerate four-wave mixing process for molecules with resonant optical hyperpolarizability, we have theoretically and experimentally investigated the compound N,N′-bis(2,5-di-tert-butylphenyl)-3,4,9,10-perylenedicarboximide in chloroform solution using subpicosecond forward degenerate four-wave mixing. It follows from the theoretical and experimental results that a resonant degenerate four-wave mixing actually involves two dynamic processes, i.e., a coherent nonlinear response involving four-photon parametric mixing and an incoherent nonlinear response due to diffraction from the population grating. The contribution of each process to the resonant degenerate four-wave mixing signal and the dynamic characteristics of each process are discussed. In this paper, we present both a theoretical derivation and a numerical simulation for resonant degenerate four-wave mixing. An equivalent third-order optical susceptibility χ_g⁽³⁾ describing the contribution from the population grating process is introduced. Temporal behavior of the degenerate four-wave mixing signal is studied at different incident power intensities, and the dependence of signal strength on the intensity is investigated. Numerical simulation using the theoretical model presented here is used satisfactorily to explain the experimental results.