Second-harmonic generation from chiral surfaces

We present a theory of second-harmonic generation from chiral surfaces including contributions of electric and magnetic dipole transitions to the surface nonlinearity. The nonlinear polarization and magnetization of the surface as well as the second-harmonic fields that are radiated in the reflected and transmitted directions are expressed in terms of the six possible bilinear combinations of the components of the electric field of the fundamental beam. For the case in which the polarization of the fundamental beam is controlled by means of a quarter-wave plate between p-polarized linear and left- and right-hand circular, the second-harmonic fields can be expanded in terms of only three different functions of the rotation angle of the wave plate. The process exhibits nonlinear optical activity, i.e., it responds differently to the two circular polarizations of the fundamental beam if the phases of certain expansion coefficients are different. The theory is used to explain the results of a recent experiment and excellent agreement is found. The results suggest that in the experiment the largest components of the susceptibility tensors that include magnetic contributions were of the order of ∼10% of those of the electric dipole-allowed susceptibility tensor.