One-electron second-order optical activity of a helix

The second-order nonlinear-optical response of a chiral molecule is calculated. We model the optical response classically using a single electron bound to a helical path. The helical motion of the electron causes optical activity in the second-order response. The hyperpolarizability tensor of a single helix and the susceptibility tensor for a thin film of helices are given. We examine the process of second-harmonic generation from a chiral surface using the calculated susceptibility tensor. The efficiency of the harmonic generation is different for left- and right-hand circularly polarized fundamental light, which is ascribed to be a form of nonlinear optical activity. The roles of pitch and radius of the helix are readily seen in the microscopic and macroscopic second-order optical responses and in the surface second-harmonic generation, which may provide some insight for synthesizing new chiral compounds. Our results also allow us to draw conclusions about the relative strength and importance to second-order optical activity of electric- and magnetic-dipole transitions. For instance, we confirm that optical activity can occur in surface second-harmonic generation from electric-only response, but we find that magnetic response can make a similar contribution and thus should not be ignored.