Multidimensional femtosecond spectroscopies of molecular aggregates and semiconductor nanostructures: The nonlinear exciton equations

A unified description of nonlinear optical spectroscopies of molecular aggregates (starting with the Frenkel-Heitler-London Hamiltonian) and semiconductors (starting with the two-band model) is developed using the nonlinear exciton equations (NEE). The equations follow explicitly the complete set of one-, two-, and three-point dynamical exciton variables relevant for the third-order response. Effects of nuclear motions are incorporated through relaxation superoperators calculated perturbatively in exciton-phonon coupling. A Green's function expression for the third-order response is derived by solving the NEE using a new truncation scheme based on factorizing the three-point relaxation kernels. These results set the stage for designing multidimensional spectroscopies of excitons and analyzing them using coherence-transfer pathways. (C) 1998 American Institute of Physics. [S0021-9606(98)70545-8].