Second-order nonlinear optical signatures of surface chirality

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Abstract
Second-harmonic generation can be used to probe chiral properties of surfaces and thin films with in-plane isotropy. We present a general formalism to analyse such chiral effects and apply it to review known effects and to introduce new effects. The formalism is based on expanding the fundamental and second-harmonic fields in terms of their p- and s-polarized components. Each second-harmonic signal can then be described in terms of only three nonlinear coefficients, which are associated with the quadratic combinations of the fundamental-field components. The coefficients can be classified as achiral (allowed for all isotropic surfaces) or chiral (allowed only for chiral surfaces) independent of the details of the nonlinear light-matter interaction. The basic signatures of chirality are intensity-difference effects in which the efficiencies of second-harmonic generation are different for left- and right-hand circularly-polarized light or two orthogonal linear polarizations, for example. These effects depend on proper phase relations between the achiral and chiral coefficients. Measurements in which the state of polarization of the fundamental beam is continuously varied by a rotating quarter-wave plate are shown to be sensitive to chirality independent of any particular phase relation between the coefficients. Such measurements can also be used to determine uniquely the relative complex values of the coefficients and thus to characterize completely the nonlinear chiral response. The ability of the techniques to distinguish absolutely between the enantiomers of a chiral sample is possible only if interference between the electric-dipole and higher-multipole parts of the coefficients dominates the chiral response.