Surface second-harmonic generation from chiral materials

We present a theory of second-harmonic generation from thin films of chiral materials. The formalism makes distinct the contributions of electric- and magnetic-dipole transitions to the radiative process. Three susceptibility tensors form a minimal description of the optical nonlinearity, two for the nonlinear surface polarization and one for the nonlinear surface magnetization. The influence of optical interfaces is made explicit by using Fresnel coefficients to describe the reflection and transmission of the fundamental and second-harmonic radiation. Hence, the characterization and metrology of chiral materials by surface second-harmonic generation are given a firm theoretical foundation. In agreement with recent experimental observations, second-harmonic signals from chiral surfaces are predicted to depend sensitively upon whether the fundamental light is right- or left-hand circularly polarized. We show that this second-harmonic-generation circular-dichroism effect is a key signature of chirality and originates fundamentally from contributions of magnetic-dipole transitions to the nonlinear polarization and magnetization of the surface.