Second harmonic generation null angle polarization analysis for determining interfacial potential at charged interfaces

Methods of quantifying the electrostatics of charged interfaces are important in a range of research areas. The surface-selective nonlinear optical technique second harmonic generation (SHG) is a sensitive probe of interfacial electrostatics. Recent work has shown that detection of the SHG phase in addition to its amplitude enables direct quantification of the interfacial potential. However, the experimental challenge of directly detecting the phase interferometrically with sufficient precision and stability has led to the proposal and development of alternative techniques to recover the same information, notably through wavelength scanning or angle scanning, each of which has their own associated experimental challenges. Here, we propose a new polarization-based approach to recover the required phase information, building upon the previously established nonlinear optical null ellipsometry (NONE) technique. Although NONE directly returns only relative phase information between different tensor elements of the second-order susceptibility, it is shown that a symmetry relation that connects the tensor elements of the potential-dependent third-order susceptibility can be used to generate the absolute phase reference required to calculate the interfacial potential. The sensitivity of the technique to potential at varying surface charge densities and ionic strengths is explored by means of simulated data of the silica:water interface. The error associated with the use of the linearized Poisson-Boltzmann approximation is discussed and compared to the error associated with the precision of the measured NONE null angles. Overall, the results suggest that NONE is a promising approach for performing phase-resolved SHG based quantification of interfacial potentials that experimentally requires only the addition of standard polarization optics to the basic single-wavelength, fixed-angle SHG apparatus.