A New Imaginary Term in the Second-Order Nonlinear Susceptibility from Charged Interfaces

Nonresonant second harmonic generation (SHG) phase and amplitude measurements obtained from the silica-water interface at varying pH values and an ionic strength of 0.5 M point to the existence of a nonlinear susceptibility term, which we call χ_X⁽³⁾, that is associated with a 90° phase shift. Including this contribution in a model for the total effective second-order nonlinear susceptibility produces reasonable point estimates for interfacial potentials and second-order nonlinear susceptibilities when χ_X⁽³⁾ ≈ 1.5χ_water⁽³⁾. A model without this term and containing only traditional χ⁽²⁾ and χ⁽³⁾ terms cannot recapitulate the experimental data. The new model also provides a demonstrated utility for distinguishing apparent differences in the second-order nonlinear susceptibility when the electrolyte is NaCl versus MgSO₄, pointing to the possibility of using heterodyne-detected SHG to investigate ion specificity in interfacial processes.