Numerical Liouville approach. Third-order nonlinear optical susceptibilities in THG, EFISH and DFWM

A new nonperturbative method is developed for calculation of the third-order nonlinear optical susceptibilities χg3(ω) in third-harmonic generation, electric-field-induced second-harmonic generation and degenerate four-wave mixing for N-state quantum systems interacting with intense electric fields. The present method is based on numerically exact solutions of the Liouville equation, so that it can provide nonlinear optical spectra valid for arbitrary laser intensities, frequencies and relaxation. We apply this approach to the nonlinear optical spectra for t-octatetraene. Comparisons between the present nonperturbative and the conventional perturbative results are also carried out.