To obtain the SHG amplitude and the absolute phase, we record SHG interference patterns generated by beating the SHG signals from two sources against one another (Fig. ): source 1 is Speelman and Geiger page 4 the electrode:electrolyte interface (producing the "signal") and source 2 is a 50 µm thin piece of zcut a-quartz wafer (producing the local oscillator, "LO") . The sample and the a-quartz wafer bracket a phase shifting unit consisting of a 1 mm thin fused silica plate mounted on a computerized rotating stage. Collecting the SHG intensity as a function of the rotational angle of the phase shifting unit produces signal + LO interference fringes that whose amplitudes and phases change as we vary the applied potential between -0.5 V and +0.9 V vs Ag/AgCl (Fig. ). At each applied potential, the SHG amplitude and phase are obtained through a custom fit function (please see Supplementary Information Note S2).