Determining nonlinear optical coefficients of metals by multiple angle of incidence heterodyne-detected sum-frequency generation spectroscopy.

We illustrate a technique by which heterodyne-detected sum-frequency generation spectroscopy is performed at multiple angles of incidence in order to decompose components of the second-order susceptibility tensor when all beams are polarized parallel to the plane of incidence. As an illustration, we study the non-vibrationally resonant gold response. We benchmark our results by comparing with measurements obtained in a polarization scheme that isolates a single element of the susceptibility tensor. Our technique is particularly valuable in the case of metal substrates, where the surface selection rule often prevents spectra from being acquired in multiple beam polarizations.