Efficient orientational averaging of nonlinear optical signals in multi-chromophore systems

The simulation of nonlinear optical signals measured in isotropic media requires averaging over the orientations of the chromophores. Herein, we discuss the evaluation of orientationally averaged four-wave-mixing, six-wave-mixing, etc., signals in terms of contracted transition dipole moment operators, which were introduced earlier for the orientational averaging of linear absorption signals. We demonstrate that the contracted transition dipole moment operators substantially facilitate the orientational averaging of nonlinear signals in multi-chromophore systems. We consider both the perturbative evaluation of signals (through nonlinear response functions) as well as the nonperturbative evaluation (through the numerical calculation of the nonlinear polarization of driven systems).