Figure 2. Experimental and theoretical background of chiral SFG.

(a) An SFG experiment for studying interfaces is set up by overlapping a visible beam and an infrared beam at an interface and detecting SFG signals in the reflection geometry. The visible and infrared beams are often linearly polarized in s- or p-polarization, and the s- and p-components of the SFG signal can be isolated and measured. The setting of polarization can vary, allowing for measurements of individual or a subset of the 27 second-order susceptibility (χ⁽²⁾) elements (equations 1 and 2). (b) An achiral interface has C_∞v symmetry whereas a chiral interface has C_∞ symmetry. Group theory dictates that seven (blue) out of the 27 elements are non-zero for both achiral and chiral surfaces, but an additional six orthogonal ${\chi }_{IJK (I\ne J\ne K)}^{\left(2\right)}$ elements (red) are non-zero only for a chiral interface. Under the condition of electronic non-resonance, the psp polarization setting shown in (a) can be used to measure the orthogonal ${\chi }_{zyx}^{\left(2\right)}$ element in chiral SFG experiments. Adapted with permission from ref 20. Copyright 2014 American Chemical Society.