Figure 3.

Microscopic view of the hyperpolarizability $\beta$ of a carbon monoxide molecule (a) and macroscopic view of the non-linear second-order susceptibility ${\chi }^{\left(2\right)}$ of a carbon monoxide layer adsorbed on a platinum substrate (b). $\beta$ and ${\chi }^{\left(2\right)}$ are third-rank tensors with 27 components that can be probed by SFG spectroscopy as a function of the SFG, Visible and IR laser beams polarization: p or s as defined in Figure 2. These non-linear physical values are related through a coordinate transformation T from the molecular frame to the laboratory (interface).