Nonlinear Optical Properties of Liquids

Nonlinear optical polarization quadratic in the optical electric fields is shown to occur in optically active liquids and to lead to sum- and difference-frequency generation; second-harmonic generation is forbidden. The nonlinearity is described by components of the second-order polarizability tensor ${\chi }_{\mathrm{ijk}}$ antisymmetric in $j$ and $k$; the form of the antisymmetric part of ${\chi }_{\mathrm{ijk}}$ is given for all the crystal classes and textures and for isotropic media. The magnitude of nonlinear polarizability of liquids is estimated from second-order perturbation theory and calculated to be readily detectable in many optically active liquids. The mechanism of the nonlinearity is illustrated by a simple single-electron molecular model.