bulk, implicitly labeling them as surface specific techniques. In 1982, T. F. Heinz and Y. R. Shen explicitly demonstrated for the first time that SHG could be used as a spectroscopic technique to probe molecular monolayers adsorbed to surfaces. Heinz and Shen adsorbed monolayers of laser dye rhodamine to a planar fused silica surface; the coated surface was then pumped by a nanosecond ultra-fast laser. SH light with characteristic spectra of the adsorbed molecule and its electronic transitions were measured as reflection from the surface and demonstrated a quadratic power dependence on the pump laser power. In SHG spectroscopy, one focuses on measuring twice the incident frequency 2ω given an incoming electric field in order to reveal information about a surface. Simply (for a more in-depth derivation see below), the induced second-harmonic dipole per unit volume, , can be written as where is known as the nonlinear susceptibility tensor and is a characteristic to the materials at the interface of study. The generated and corresponding have been shown to reveal information about the orientation of molecules at a surface/interface, the interfacial analytical chemistry of surfaces, and chemical reactions at interfaces. From planar surfaces Early experiments in the field demonstrated second-harmonic generation from metal surfaces. Eventually, SHG was used to probe the air-water interface, allowing for detailed information about molecular orientation and ordering at one of the most ubiquitous of surfaces. It can be shown that the specific elements of : where Ns is the adsorbate density, θ is the angle that the molecular axis z makes with the surface normal Z, and is the dominating element of the nonlinear polarizability of a molecule at an interface, allow one to determine θ, given laboratory coordinates . Using an interference SHG method to determine these elements of χ(2), the first molecular orientation measurement showed that the hydroxyl group of phenol pointed downwards into the water at the air-water interface (as expected due to the potential of hydroxyl groups to form hydrogen bonds). Additionally SHG at planar surfaces has revealed differences in pKa and rotational motions of molecules at interfaces. From non-planar surfaces Second-harmonic light can also be generated from surfaces that are ‘locally’ planar, but may have inversion symmetry (centrosymmetric) on a larger scale. Specifically, recent theory has demonstrated that SHG from small spherical particles (micro- and nanometer scale) is allowed by proper treatment of Rayleigh scattering. At the surface of a