Effects of centrosymmetry on the nonresonant electronic third-order nonlinear optical susceptibility

The off-resonant electronic third-order optical susceptibility is derived in the dipole approximation using the method of averages. These results are studied in detail for the two-, three-, and N-level model to determine the origin of the susceptibility with symmetry considerations. If the matrix elements are independent, the third-order susceptibility is shown to be maximized in centrosymmetric structures in the two-level model while, for the general N-level system, weak coupling between the excited states is also required. To address the interdependence of the matrix elements, a two- and three-level system is perturbed to make the molecular potential asymmetric or more asymmetric, and the conditions on the matrix elements for maximizing the third-order susceptibility are derived. The dependence of the third-order susceptibility on the asymmetry of a harmonic oscillator and particle in a box are also discussed.