Isotropic second-order nonlinear optical susceptibilities

The second-order nonlinear optical susceptibility, in the electric dipole approximation, is only nonvanishing for materials that are noncentrosymmetric. Should the medium be isotropic, then only a chiral system, such as an optically active liquid, satisfies this symmetry requirement. We derive the quantum-mechanical form of the isotropic component of the sum- and difference-frequency susceptibility and discuss its unusual spectral properties. We show that any coherent second-order nonlinear optical process in a system of randomly oriented molecules requires the medium to be chiral, and the incident frequencies to be different and nonzero. Furthermore, a minimum of two nondegenerate excited molecular states are needed for the isotropic part of the susceptibility to be nonvanishing. The rotationally invariant susceptibility is zero in the static field limit and shows exceptionally sensitive resonance and dephasing effects that are particular to chiral centers.